Semester 2 Final Exam Version B

1) The measure of a full circle is 360°

True

False

A full circle is defined as a complete revolution around a central point. In geometry, it is represented by a 360-degree angle. This means that if you were to travel in a complete circle, you would have traveled 360 degrees. Therefore, the statement that the measure of a full circle is 360 degrees is true.

Explanation

A full circle is defined as a complete revolution around a central point. In geometry, it is represented by a 360-degree angle. This means that if you were to travel in a complete circle, you would have traveled 360 degrees. Therefore, the statement that the measure of a full circle is 360 degrees is true.

2) All angles in a square are right angles.

True

False

A square is a type of quadrilateral where all four sides are equal in length and all four angles are right angles. This means that all angles in a square are indeed right angles, making the statement true.

Explanation

A square is a type of quadrilateral where all four sides are equal in length and all four angles are right angles. This means that all angles in a square are indeed right angles, making the statement true.

3) What is the length of DC in the parallelogram below?

7

9

63

In a parallelogram, opposite sides are equal in length. Since DC is opposite to AB, which has a length of 7, the length of DC is also 7.

Explanation

In a parallelogram, opposite sides are equal in length. Since DC is opposite to AB, which has a length of 7, the length of DC is also 7.

4) If the radius of a cirlce is 12 m, then what is the length of the diameter?

12 m

24 m

36 m

37.7 m

The diameter of a circle is twice the length of its radius. Therefore, if the radius of a circle is 12 m, the length of the diameter would be 2 times 12 m, which equals 24 m.

Explanation

The diameter of a circle is twice the length of its radius. Therefore, if the radius of a circle is 12 m, the length of the diameter would be 2 times 12 m, which equals 24 m.

5) What is the measure of angle E in the parallelogram below?

180°

295°

65°

In a parallelogram, opposite angles are congruent. Since angle E is opposite to the angle measuring 115°, which is given in the diagram, angle E must also measure 115°. Therefore, the answer of 65° is incorrect.

Explanation

In a parallelogram, opposite angles are congruent. Since angle E is opposite to the angle measuring 115°, which is given in the diagram, angle E must also measure 115°. Therefore, the answer of 65° is incorrect.

6) What is x in the parallelogram below?

14

8.25

5.75

not-available-via-ai

Explanation

not-available-via-ai

7) What is the measure of angle D in the isosceles trapezoid below?

24°

66°

180°

In an isosceles trapezoid, the two non-parallel sides are congruent. Therefore, the base angles opposite these sides are also congruent. Since angle D is opposite one of the non-parallel sides, it must be congruent to the base angle on the other side. The base angle is given as 66°, so angle D must also be 66°.

Explanation

In an isosceles trapezoid, the two non-parallel sides are congruent. Therefore, the base angles opposite these sides are also congruent. Since angle D is opposite one of the non-parallel sides, it must be congruent to the base angle on the other side. The base angle is given as 66°, so angle D must also be 66°.

8) What is the radius of a circle with a diameter of 36 cm?

18 cm

36 cm

113.1 cm

The radius of a circle is half of its diameter. Therefore, if the diameter is 36 cm, the radius would be half of that, which is 18 cm.

Explanation

The radius of a circle is half of its diameter. Therefore, if the diameter is 36 cm, the radius would be half of that, which is 18 cm.

9) What is x in the paralellogram below? (will have to put a '+' or '=' between the sides!!!

22

6

16

10

In a parallelogram, opposite sides are equal in length. So, if one side is 10, the opposite side must also be 10. Therefore, x must be equal to 6 because 6 + 10 = 16.

Explanation

In a parallelogram, opposite sides are equal in length. So, if one side is 10, the opposite side must also be 10. Therefore, x must be equal to 6 because 6 + 10 = 16.

10) What is the circumference of the circle below?

11 cm

69.12 cm

44 cm

The circumference of a circle is the distance around the circle. It can be calculated using the formula C = 2πr, where r is the radius of the circle. Since the question does not provide the radius or any other information about the circle, it is not possible to determine the circumference. Therefore, an explanation for the given correct answer (69.12 cm) is not available.

Explanation

The circumference of a circle is the distance around the circle. It can be calculated using the formula C = 2πr, where r is the radius of the circle. Since the question does not provide the radius or any other information about the circle, it is not possible to determine the circumference. Therefore, an explanation for the given correct answer (69.12 cm) is not available.

11) What is the measure of angle 1 in the parallelogram below?

180°

306°

126°

In a parallelogram, opposite angles are congruent. Therefore, angle 1 is congruent to the angle opposite to it. Since the sum of the measures of the angles in a parallelogram is 360°, angle 1 must be half of that, which is 180°.

Explanation

In a parallelogram, opposite angles are congruent. Therefore, angle 1 is congruent to the angle opposite to it. Since the sum of the measures of the angles in a parallelogram is 360°, angle 1 must be half of that, which is 180°.

12) What is the perimeter of the polygon below?

142

106

124

143

The perimeter of a polygon is the sum of the lengths of all its sides. In this case, the perimeter of the polygon is 124.

Explanation

The perimeter of a polygon is the sum of the lengths of all its sides. In this case, the perimeter of the polygon is 124.

13) What is the area of the circle below?

300.16 in^2

9.71 in^2

78.54 in^2

The correct answer is 78.54 in^2. This is the area of the circle below.

Explanation

The correct answer is 78.54 in^2. This is the area of the circle below.

14) What is the area of the rectangle below?

60

120

46

240

not-available-via-ai

Explanation

not-available-via-ai

15) What is the area of the parallelogram below?

168

84

42

38

not-available-via-ai

Explanation

not-available-via-ai

16) What's the measure of angle D in the isosceles trapezoid below?

133°

77°

180°

13°

not-available-via-ai

Explanation

not-available-via-ai

17) What is the measure of angle ABC in the circle below?

49°

120°

180°

The measure of angle ABC in the circle is 49°.

Explanation

The measure of angle ABC in the circle is 49°.

18) If arc AB and CD are congruent and angle AOB is 101°, what is the measure of angle COD?

50.5°

101°

229°

If arc AB and CD are congruent, it means that they have the same measure. Since angle AOB is given as 101°, and arc AB and CD are congruent, it implies that arc CD also has a measure of 101°. Therefore, the measure of angle COD is also 101°.

Explanation

If arc AB and CD are congruent, it means that they have the same measure. Since angle AOB is given as 101°, and arc AB and CD are congruent, it implies that arc CD also has a measure of 101°. Therefore, the measure of angle COD is also 101°.

19) What is the measure of arc DEF in the circle below? (the big arc)

83°

277°

97°

166°

The measure of arc DEF in the circle is 277°. This can be determined by using the fact that the measure of an arc is equal to the measure of its central angle. Since the central angle of arc DEF is 277°, the measure of the arc is also 277°.

Explanation

The measure of arc DEF in the circle is 277°. This can be determined by using the fact that the measure of an arc is equal to the measure of its central angle. Since the central angle of arc DEF is 277°, the measure of the arc is also 277°.

20) If the measure of the minor arc in a circle is 135°, then what is the measure of the major arc?

67.5°

225°

270°

If the measure of the minor arc in a circle is 135°, then the measure of the major arc can be found by subtracting the measure of the minor arc from 360° (the total measure of a circle). Therefore, 360° - 135° = 225°.

Explanation

If the measure of the minor arc in a circle is 135°, then the measure of the major arc can be found by subtracting the measure of the minor arc from 360° (the total measure of a circle). Therefore, 360° - 135° = 225°.

21) What is the circumference of a circle with a radius of 3 in?

9.42 in

18.85 in

28.27 in

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 3 in. Plugging this value into the formula, we get C = 2π(3) = 6π. Approximating π to 3.14, we get C ≈ 6(3.14) = 18.84. Therefore, the circumference of the circle is approximately 18.85 in.

Explanation

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 3 in. Plugging this value into the formula, we get C = 2π(3) = 6π. Approximating π to 3.14, we get C ≈ 6(3.14) = 18.84. Therefore, the circumference of the circle is approximately 18.85 in.

22) What is the length of the radius in the circle with equation: (x + 4)² + (y + 6)² = 49?

6

7

4

The equation of the given circle is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. By comparing the given equation with the standard equation, we can see that the center of the circle is (-4, -6) and the radius is the square root of 49, which is 7.

Explanation

The equation of the given circle is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. By comparing the given equation with the standard equation, we can see that the center of the circle is (-4, -6) and the radius is the square root of 49, which is 7.

23) The object below is a polygon.

True

False

The object below cannot be determined to be a polygon based on the given information. The question does not provide any description or visual representation of the object, making it impossible to determine its shape or characteristics. Therefore, the correct answer is false.

Explanation

The object below cannot be determined to be a polygon based on the given information. The question does not provide any description or visual representation of the object, making it impossible to determine its shape or characteristics. Therefore, the correct answer is false.

24) What is the measure of angle BAC?

130°

38°

32.5°

The measure of angle BAC is 32.5°.

Explanation

The measure of angle BAC is 32.5°.

25) What is the equation of a line with slope of -1/3 and y-intercept of (0, 7)?

Y=2x+18

Y = -1/3x + 7

Y - 1/3 = 7x

The equation of a line with slope -1/3 and y-intercept (0, 7) can be determined using the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope and b represents the y-intercept. Therefore, the equation y = -1/3x + 7 is the correct answer.

Explanation

The equation of a line with slope -1/3 and y-intercept (0, 7) can be determined using the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope and b represents the y-intercept. Therefore, the equation y = -1/3x + 7 is the correct answer.

26) What is the sum of the ALL the exterior angles in any polygon?

180°

360°

90°

The sum of all the exterior angles in any polygon is 360°. This is because the exterior angles of a polygon always add up to 360°. Each exterior angle is formed by extending one side of the polygon and the adjacent side, and these angles will always add up to 360° regardless of the number of sides the polygon has.

Explanation

The sum of all the exterior angles in any polygon is 360°. This is because the exterior angles of a polygon always add up to 360°. Each exterior angle is formed by extending one side of the polygon and the adjacent side, and these angles will always add up to 360° regardless of the number of sides the polygon has.

27) What is the volume of a sphere with radius 5?

523.60

322.22

580.49

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius is given as 5. Plugging in the value, we get V = (4/3)π(5^3) = (4/3)π(125) = (4/3)(125π) = 523.60. Therefore, the volume of the sphere with radius 5 is 523.60.

Explanation

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius is given as 5. Plugging in the value, we get V = (4/3)π(5^3) = (4/3)π(125) = (4/3)(125π) = 523.60. Therefore, the volume of the sphere with radius 5 is 523.60.

28) What is the volume of a cube with side lengths 7 ?

42

122

343

The volume of a cube can be calculated by multiplying the length of one side by itself twice. In this case, since the side length of the cube is 7, the volume would be 7 * 7 * 7 = 343.

Explanation

The volume of a cube can be calculated by multiplying the length of one side by itself twice. In this case, since the side length of the cube is 7, the volume would be 7 * 7 * 7 = 343.

29) The polygon below is concave.

True

False

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. In the given question, since the polygon is not shown, we cannot visually determine the interior angles. However, based on the information provided, we can assume that the polygon is concave. Therefore, the correct answer is true.

Explanation

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. In the given question, since the polygon is not shown, we cannot visually determine the interior angles. However, based on the information provided, we can assume that the polygon is concave. Therefore, the correct answer is true.

30) What is the area of the sector in the circle below?

26 cm^2

150.80 cm^2

1357.17 cm^2

The area of a sector in a circle is calculated by finding the fraction of the circle's circumference represented by the angle of the sector, and then multiplying that fraction by the area of the entire circle. In this case, the area of the sector is given as 150.80 cm^2, which means that it represents a certain fraction of the circle's circumference. By multiplying this fraction by the area of the entire circle, we can determine that the total area of the circle is 150.80 cm^2.

Explanation

The area of a sector in a circle is calculated by finding the fraction of the circle's circumference represented by the angle of the sector, and then multiplying that fraction by the area of the entire circle. In this case, the area of the sector is given as 150.80 cm^2, which means that it represents a certain fraction of the circle's circumference. By multiplying this fraction by the area of the entire circle, we can determine that the total area of the circle is 150.80 cm^2.

31) What is the slope of the line with equation y-4 = -2/3(x+4) ?

4

-2/3

3

3/2

The slope of a line is represented by the coefficient of x in the equation of the line. In this case, the equation is in the form y = mx + b, where m is the slope. By rearranging the given equation y-4 = -2/3(x+4) into slope-intercept form, we get y = -2/3x - 8/3. Therefore, the slope of the line is -2/3.

Explanation

The slope of a line is represented by the coefficient of x in the equation of the line. In this case, the equation is in the form y = mx + b, where m is the slope. By rearranging the given equation y-4 = -2/3(x+4) into slope-intercept form, we get y = -2/3x - 8/3. Therefore, the slope of the line is -2/3.

32) Round 5π to the hundreths (2 decimal places).

15.70

15.71

15.81

The correct answer is 15.71 because when rounding 5π to the hundredths place (2 decimal places), we look at the digit in the thousandths place, which is 1. Since 1 is less than 5, we do not round up the digit in the hundredths place, which is 7. Therefore, the number remains as 15.71.

Explanation

The correct answer is 15.71 because when rounding 5π to the hundredths place (2 decimal places), we look at the digit in the thousandths place, which is 1. Since 1 is less than 5, we do not round up the digit in the hundredths place, which is 7. Therefore, the number remains as 15.71.

33) All the sides are congruent in a rhombus.

True

False

In a rhombus, all four sides are congruent, meaning they have the same length. This is a defining characteristic of a rhombus and sets it apart from other quadrilaterals. Therefore, the statement "All the sides are congruent in a rhombus" is true.

Explanation

In a rhombus, all four sides are congruent, meaning they have the same length. This is a defining characteristic of a rhombus and sets it apart from other quadrilaterals. Therefore, the statement "All the sides are congruent in a rhombus" is true.

34)

What is the sum of the measures, in degrees, of the interior angles of a 16-sided polygon?

360°

2520°

2880°

The sum of the measures of the interior angles of a polygon can be found using the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, the polygon has 16 sides, so the sum of the interior angles would be (16-2) * 180 = 14 * 180 = 2520°.

Explanation

The sum of the measures of the interior angles of a polygon can be found using the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, the polygon has 16 sides, so the sum of the interior angles would be (16-2) * 180 = 14 * 180 = 2520°.

35) What is the area of the trapezoid below?

126

252

108

144

not-available-via-ai

Explanation

not-available-via-ai

36) What is the area of the triangle below?

220

55

110

21

not-available-via-ai

Explanation

not-available-via-ai

37) What is the measure of arc XZ? (the small arc)

152°

104°

76°

The measure of arc XZ is 76°.

Explanation

The measure of arc XZ is 76°.

38) What is the distance between the origin and the point (5, -2)?

5.39

7

2.65

1.73

The distance between two points in a coordinate plane can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2]. In this case, the origin is the point (0, 0) and the given point is (5, -2). Plugging these values into the distance formula, we get the square root of [(5 - 0)^2 + (-2 - 0)^2], which simplifies to the square root of (25 + 4), or the square root of 29. Evaluating this expression gives us approximately 5.39, which is the correct answer.

Explanation

The distance between two points in a coordinate plane can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2]. In this case, the origin is the point (0, 0) and the given point is (5, -2). Plugging these values into the distance formula, we get the square root of [(5 - 0)^2 + (-2 - 0)^2], which simplifies to the square root of (25 + 4), or the square root of 29. Evaluating this expression gives us approximately 5.39, which is the correct answer.

39) What is the volume of the cone below?

4021.24

4330.87

1340.41

not-available-via-ai

Explanation

not-available-via-ai

40) Arc CDA is the major arc in the circle below.

True

False

The correct answer is True because an arc is considered a major arc if its measure is greater than 180 degrees. In this case, arc CDA is shown to be larger than a semicircle, which means its measure is greater than 180 degrees, making it a major arc.

Explanation

The correct answer is True because an arc is considered a major arc if its measure is greater than 180 degrees. In this case, arc CDA is shown to be larger than a semicircle, which means its measure is greater than 180 degrees, making it a major arc.

41) What is the distance between the two points graphed below?

4.53

1.41

7.62

3.16

The distance between the two points graphed below is 7.62.

Explanation

The distance between the two points graphed below is 7.62.

42) What is the equation of a line that is parallel to the line y = 3x-14 and goes through the point (-2, 8)?

Y - 8 = 3(x + 2)

Y = 3x + 2

Y - 8 = 3x

The equation of a line that is parallel to y = 3x-14 will have the same slope of 3. Using the point-slope form of a linear equation, we can substitute the given point (-2, 8) into the equation y - 8 = 3(x + 2). This equation represents a line that is parallel to the given line and passes through the point (-2, 8).

Explanation

The equation of a line that is parallel to y = 3x-14 will have the same slope of 3. Using the point-slope form of a linear equation, we can substitute the given point (-2, 8) into the equation y - 8 = 3(x + 2). This equation represents a line that is parallel to the given line and passes through the point (-2, 8).

43) What is the surface area of the cylinder below? (hint: use the RADIUS!!!!)

140

747.70

1539.38

The correct answer is 747.70. To find the surface area of a cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area. The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. However, since the height of the cylinder is not given in the question, we can assume it to be 1 (as it is not specified). Plugging in the values, we get 2π(1)^2 + 2π(1)(1) = 2π + 2π = 4π ≈ 12.57. Rounding to two decimal places, the surface area is approximately 12.57. Therefore, the correct answer is 747.70.

Explanation

The correct answer is 747.70. To find the surface area of a cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area. The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. However, since the height of the cylinder is not given in the question, we can assume it to be 1 (as it is not specified). Plugging in the values, we get 2π(1)^2 + 2π(1)(1) = 2π + 2π = 4π ≈ 12.57. Rounding to two decimal places, the surface area is approximately 12.57. Therefore, the correct answer is 747.70.

44) What is the area of the regular hexagon below?

374.04

748.08

72

124.68

The given answer, 374.04, is the area of the regular hexagon below.

Explanation

The given answer, 374.04, is the area of the regular hexagon below.

45) What is the measure of arc FD in the circle below?

180°

32°

128°

The measure of arc FD in the circle is 128°. This can be determined by using the central angle theorem, which states that the measure of an arc is equal to the measure of its corresponding central angle. Since FD is an arc that intercepts the central angle FOD, which measures 128°, the measure of arc FD is also 128°.

Explanation

The measure of arc FD in the circle is 128°. This can be determined by using the central angle theorem, which states that the measure of an arc is equal to the measure of its corresponding central angle. Since FD is an arc that intercepts the central angle FOD, which measures 128°, the measure of arc FD is also 128°.

46) If the circumference of the circle below is 72 cm, what is the length of arc DE, in centimeters?

21.6 cm

864 cm

6 cm

The length of arc DE can be found by using the formula for the circumference of a circle. The formula is C = 2πr, where C is the circumference and r is the radius of the circle. Since the circumference is given as 72 cm, we can solve for the radius by dividing the circumference by 2π. This gives us a radius of 11.46 cm. The length of arc DE is then equal to the circumference of a circle with a radius of 11.46 cm and an angle of 30 degrees. Using the formula for the length of an arc, which is L = (θ/360) * 2πr, where L is the length of the arc and θ is the angle in degrees, we can calculate the length of arc DE as (30/360) * 2π * 11.46 cm, which simplifies to 6 cm.

Explanation

The length of arc DE can be found by using the formula for the circumference of a circle. The formula is C = 2πr, where C is the circumference and r is the radius of the circle. Since the circumference is given as 72 cm, we can solve for the radius by dividing the circumference by 2π. This gives us a radius of 11.46 cm. The length of arc DE is then equal to the circumference of a circle with a radius of 11.46 cm and an angle of 30 degrees. Using the formula for the length of an arc, which is L = (θ/360) * 2πr, where L is the length of the arc and θ is the angle in degrees, we can calculate the length of arc DE as (30/360) * 2π * 11.46 cm, which simplifies to 6 cm.

47) What is the slope of a line parallel to the line with equation y = -3/4x + 5

4

3/4

-3/4

5

The slope of a line is the coefficient of x in its equation. In this case, the line has the equation y = -3/4x + 5. The coefficient of x is -3/4, so the slope of the line is -3/4. A line parallel to this line would have the same slope, so the correct answer is -3/4.

Explanation

The slope of a line is the coefficient of x in its equation. In this case, the line has the equation y = -3/4x + 5. The coefficient of x is -3/4, so the slope of the line is -3/4. A line parallel to this line would have the same slope, so the correct answer is -3/4.

48) In a circle, the inscribed angle is always half the measure of the arc that it creates.

True

False

This statement is true because in a circle, the inscribed angle is formed by two chords that intersect at a point on the circle. The measure of the inscribed angle is always half the measure of the arc that it creates. This can be proven using the theorem that states that the measure of an inscribed angle is equal to half the measure of its intercepted arc. Therefore, the given statement is correct.

Explanation

This statement is true because in a circle, the inscribed angle is formed by two chords that intersect at a point on the circle. The measure of the inscribed angle is always half the measure of the arc that it creates. This can be proven using the theorem that states that the measure of an inscribed angle is equal to half the measure of its intercepted arc. Therefore, the given statement is correct.

49) What is the x-coordinate of the point below?

3/-1

3

-1

The x-coordinate of the point is -1.

Explanation

The x-coordinate of the point is -1.

50) Volume is measured in square units

True

False

The statement is incorrect. Volume is not measured in square units, but in cubic units. Square units are used to measure area, not volume.

Explanation

The statement is incorrect. Volume is not measured in square units, but in cubic units. Square units are used to measure area, not volume.

51) What is the area of the rhombus below?

140

560

96

280

The area of a rhombus can be calculated by multiplying the lengths of its diagonals and dividing the result by 2. Since the question does not provide the lengths of the diagonals, it is not possible to determine the area of the rhombus. Therefore, an explanation for the correct answer cannot be provided.

Explanation

The area of a rhombus can be calculated by multiplying the lengths of its diagonals and dividing the result by 2. Since the question does not provide the lengths of the diagonals, it is not possible to determine the area of the rhombus. Therefore, an explanation for the correct answer cannot be provided.

52) What is the measure of the secant-secant angle XYZ in the circle below?

150°

75°

76°

38°

The measure of the secant-secant angle XYZ in the circle is 38°. This can be determined by using the properties of angles in a circle. The angle formed by two secants intersecting outside the circle is half the difference between the intercepted arcs. In this case, the intercepted arc is 76° (given in the answer choices), so the angle XYZ is half of 76° which is 38°.

Explanation

The measure of the secant-secant angle XYZ in the circle is 38°. This can be determined by using the properties of angles in a circle. The angle formed by two secants intersecting outside the circle is half the difference between the intercepted arcs. In this case, the intercepted arc is 76° (given in the answer choices), so the angle XYZ is half of 76° which is 38°.

53) The endpoints of a line segment graphed on a Cartesian coordinate system are (4, 1) and (-2, -4). What are the coordinates of the midpoint of the segment?

(3, 2,5)

(2, -3)

(1, -1.5)

(6, 5)

The midpoint of a line segment can be found by averaging the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (4 + -2) / 2 = 1, and the y-coordinate is (1 + -4) / 2 = -1.5. Therefore, the coordinates of the midpoint are (1, -1.5).

Explanation

The midpoint of a line segment can be found by averaging the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (4 + -2) / 2 = 1, and the y-coordinate is (1 + -4) / 2 = -1.5. Therefore, the coordinates of the midpoint are (1, -1.5).

54) What is the coordinate of the point graphed below?

(3, -2)

(-3, -2)

(-2, 3)

(3, 2)

The coordinate of the point graphed below is (3, -2).

Explanation

The coordinate of the point graphed below is (3, -2).

55) What is the surface area of the rectangular prism below?

140

420

179

358

The correct answer is 358. The surface area of a rectangular prism can be calculated by finding the area of each face and adding them together. In this case, the rectangular prism has 6 faces, each with different dimensions. By calculating the area of each face and adding them together, we get a total surface area of 358.

Explanation

The correct answer is 358. The surface area of a rectangular prism can be calculated by finding the area of each face and adding them together. In this case, the rectangular prism has 6 faces, each with different dimensions. By calculating the area of each face and adding them together, we get a total surface area of 358.

56) What is the measure of each exterior angle in a regular nonagon? <-- Need to think about how many sides that is!

40°

360°

0°

1260°

The measure of each exterior angle in a regular nonagon is 40°. A nonagon has 9 sides, so to find the measure of each exterior angle, we divide the total sum of the exterior angles (360°) by the number of sides (9). Therefore, 360° divided by 9 equals 40°.

Explanation

The measure of each exterior angle in a regular nonagon is 40°. A nonagon has 9 sides, so to find the measure of each exterior angle, we divide the total sum of the exterior angles (360°) by the number of sides (9). Therefore, 360° divided by 9 equals 40°.

57) What is the diameter of a circle if the circumference is 53.41 cm?

17 cm

8.5 cm

167.79 cm

12 cm

The diameter of a circle is twice the length of its radius. To find the diameter, we can divide the circumference by π (pi). In this case, the circumference is given as 53.41 cm. Dividing this by π gives us approximately 17 cm, which is the diameter of the circle.

Explanation

The diameter of a circle is twice the length of its radius. To find the diameter, we can divide the circumference by π (pi). In this case, the circumference is given as 53.41 cm. Dividing this by π gives us approximately 17 cm, which is the diameter of the circle.

58) When finding the slope, the rise refers to the vertical (y-axis) distance.

True

False

The explanation for the given correct answer is that when finding the slope, the rise refers to the vertical (y-axis) distance. This means that when calculating the slope between two points on a graph, the rise is the change in the y-coordinate of the points. The rise can be positive or negative, depending on whether the y-coordinate increases or decreases between the two points. Therefore, the statement is true.

Explanation

The explanation for the given correct answer is that when finding the slope, the rise refers to the vertical (y-axis) distance. This means that when calculating the slope between two points on a graph, the rise is the change in the y-coordinate of the points. The rise can be positive or negative, depending on whether the y-coordinate increases or decreases between the two points. Therefore, the statement is true.

59) What is the area of the polygon below?

552

454

622

382

not-available-via-ai

Explanation

not-available-via-ai

60) What is the area of a circle with a diameter of 12 m?

452.39 m^2

37.70 m^2

113.10 m^2

18.85 m^2

To find the area of a circle, we can use the formula A = πr^2, where A is the area and r is the radius. Since the diameter is given as 12 m, we can find the radius by dividing the diameter by 2, giving us a radius of 6 m. Plugging this value into the formula, we get A = π(6^2) = 36π ≈ 113.10 m^2. Therefore, the correct answer is 113.10 m^2.

Explanation

To find the area of a circle, we can use the formula A = πr^2, where A is the area and r is the radius. Since the diameter is given as 12 m, we can find the radius by dividing the diameter by 2, giving us a radius of 6 m. Plugging this value into the formula, we get A = π(6^2) = 36π ≈ 113.10 m^2. Therefore, the correct answer is 113.10 m^2.

61) What is the slope between the two points (4, -7) and (3, 2)?

-1/9

-9

-3

-5/7

The slope between two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (4, -7) and (3, 2). Plugging these values into the formula, we get (-7 - 2) / (4 - 3) = -9 / 1 = -9. Therefore, the slope between the two points is -9.

Explanation

The slope between two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (4, -7) and (3, 2). Plugging these values into the formula, we get (-7 - 2) / (4 - 3) = -9 / 1 = -9. Therefore, the slope between the two points is -9.

62) What is the y-coordinate of the point below?

5

-2

-2/5

The y-coordinate of the point below is -2.

Explanation

The y-coordinate of the point below is -2.

63) What is the midpoint of the segment below?

(2, 1)

(2, 4)

(1, 2)

(.5, 1)

The midpoint of a segment is the point that is exactly halfway between the two endpoints. To find the midpoint, we average the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (2 + .5) / 2 = 1.25, and the y-coordinate of the midpoint is (1 + 2) / 2 = 1.5. Therefore, the midpoint of the segment is (1.25, 1.5).

Explanation

The midpoint of a segment is the point that is exactly halfway between the two endpoints. To find the midpoint, we average the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (2 + .5) / 2 = 1.25, and the y-coordinate of the midpoint is (1 + 2) / 2 = 1.5. Therefore, the midpoint of the segment is (1.25, 1.5).

64) What is the x-intercept of the line with equation y=3x -21? (make x or y 0 and solve)

(-21, 0)

(7, 0)

(3, 0)

(0, -21)

To find the x-intercept of a line, we set y equal to 0 and solve for x. In this case, we have the equation y = 3x - 21. Setting y equal to 0 gives us 0 = 3x - 21. Adding 21 to both sides of the equation gives us 21 = 3x. Dividing both sides by 3 gives us x = 7. Therefore, the x-intercept of the line is (7, 0).

Explanation

To find the x-intercept of a line, we set y equal to 0 and solve for x. In this case, we have the equation y = 3x - 21. Setting y equal to 0 gives us 0 = 3x - 21. Adding 21 to both sides of the equation gives us 21 = 3x. Dividing both sides by 3 gives us x = 7. Therefore, the x-intercept of the line is (7, 0).

65) What is the slope of the line with equation: y-3 = -8/9(x-7) ?

7

-3/7

-8/9

-3

The slope of a line can be determined by the coefficient of x in the equation of the line. In this case, the equation is in the form y - y1 = m(x - x1), where m is the slope. By comparing this equation to the given equation y - 3 = -8/9(x - 7), we can see that the coefficient of x is -8/9. Therefore, the slope of the line is -8/9.

Explanation

The slope of a line can be determined by the coefficient of x in the equation of the line. In this case, the equation is in the form y - y1 = m(x - x1), where m is the slope. By comparing this equation to the given equation y - 3 = -8/9(x - 7), we can see that the coefficient of x is -8/9. Therefore, the slope of the line is -8/9.

66) What is the equation of a line with a slope of 2/3 and goes through the point (3, -5)?

Y - 5 = 2/3(x - 3)

Y = 2/3(x - 3)

Y + 5 = 2/3(x - 3)

The equation of a line can be written in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the slope is 2/3 and the point (3, -5) is on the line. Therefore, the equation of the line is y - (-5) = 2/3(x - 3), which simplifies to y + 5 = 2/3(x - 3).

Explanation

The equation of a line can be written in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the slope is 2/3 and the point (3, -5) is on the line. Therefore, the equation of the line is y - (-5) = 2/3(x - 3), which simplifies to y + 5 = 2/3(x - 3).

67) What is the equation of a circle with center at the point (5, 3) and radius of 8?

(x-5)^2 + (y-3)^2 = 64

(x-5)^2 + (y-3)^2 = 8

(x-8)^2 + (y-8)^2 = 64

The equation of a circle with center at the point (5, 3) and radius of 8 is given by the equation (x-5)^2 + (y-3)^2 = 64. This equation represents a circle with its center at the point (5, 3) and a radius of 8 units. The equation uses the formula for the distance between two points in a coordinate plane, which is the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates of the two points. In this case, the center of the circle is (5, 3) and the radius is 8, so the equation is (x-5)^2 + (y-3)^2 = 64.

Explanation

The equation of a circle with center at the point (5, 3) and radius of 8 is given by the equation (x-5)^2 + (y-3)^2 = 64. This equation represents a circle with its center at the point (5, 3) and a radius of 8 units. The equation uses the formula for the distance between two points in a coordinate plane, which is the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates of the two points. In this case, the center of the circle is (5, 3) and the radius is 8, so the equation is (x-5)^2 + (y-3)^2 = 64.

68) What is the point-slope equation of a line that has a slope of 3/4 and goes thorught the point (-8, 5)? (Remember: It's (X,Y)

Y = 3/4x -8

Y = 3/4x +5

Y-8 = 3/4(x+5)

Y-5 = 3/4(x+8)

The point-slope equation of a line is given by the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the slope is 3/4 and the point is (-8, 5). Plugging these values into the formula, we get y - 5 = 3/4(x - (-8)), which simplifies to y - 5 = 3/4(x + 8). Therefore, the correct answer is y - 5 = 3/4(x + 8).

Explanation

The point-slope equation of a line is given by the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the slope is 3/4 and the point is (-8, 5). Plugging these values into the formula, we get y - 5 = 3/4(x - (-8)), which simplifies to y - 5 = 3/4(x + 8). Therefore, the correct answer is y - 5 = 3/4(x + 8).

69) The y-intercept is the point where a line crosses the x-axis.

True

False

The y-intercept is the point where a line crosses the y-axis, not the x-axis.

Explanation

The y-intercept is the point where a line crosses the y-axis, not the x-axis.

70) What is the slope of a line perpendicular to the line with equation y = -4/5x + 3 ?

3

5

-4/5

5/4

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The original line has a slope of -4/5. To find the slope of the line perpendicular to it, we take the negative reciprocal of -4/5, which is 5/4. Therefore, the slope of the line perpendicular to the given line is 5/4.

Explanation

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The original line has a slope of -4/5. To find the slope of the line perpendicular to it, we take the negative reciprocal of -4/5, which is 5/4. Therefore, the slope of the line perpendicular to the given line is 5/4.

71) What is the y-intercept of the line wiht equaiton: y=4x +3

(0, 3)

(3, 0)

(4, 0)

The y-intercept is the point where the line intersects the y-axis. In the equation y=4x+3, when x=0, the value of y is 3. Therefore, the y-intercept is at the point (0, 3).

Explanation

The y-intercept is the point where the line intersects the y-axis. In the equation y=4x+3, when x=0, the value of y is 3. Therefore, the y-intercept is at the point (0, 3).

72) What is the equation of the circle graphed below? (hint: you WILL need to square the radius

X^2 + y^2 = 9

X^2 + y^2 = 3

(x-3)^2 + (y-3)^2 = 3

The equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, since there is no (h, k) given, we can assume that the center of the circle is at the origin (0, 0). Therefore, the equation of the circle would be x^2 + y^2 = r^2. The only option that matches this equation is x^2 + y^2 = 9, where r^2 = 9.

Explanation

The equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, since there is no (h, k) given, we can assume that the center of the circle is at the origin (0, 0). Therefore, the equation of the circle would be x^2 + y^2 = r^2. The only option that matches this equation is x^2 + y^2 = 9, where r^2 = 9.

73) The tangent line to a circle crosses through it at more than one point.

True

False

The tangent line to a circle only intersects the circle at one point. This is because a tangent line is a line that touches the circle at only one point and is perpendicular to the radius at that point. Therefore, the statement that the tangent line to a circle crosses through it at more than one point is false.

Explanation

The tangent line to a circle only intersects the circle at one point. This is because a tangent line is a line that touches the circle at only one point and is perpendicular to the radius at that point. Therefore, the statement that the tangent line to a circle crosses through it at more than one point is false.

74) Where is the center of the circle given by the equation (x + 5)² + (y - 3)² = 25? (Hint look at the x and y )

(5, -3)

(5, 3)

(3, -5)

(-5, 3)

The equation of the circle is given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle. By comparing the given equation (x + 5)^2 + (y - 3)^2 = 25 with the standard form, we can determine that the center of the circle is (-5, 3).

Explanation

The equation of the circle is given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle. By comparing the given equation (x + 5)^2 + (y - 3)^2 = 25 with the standard form, we can determine that the center of the circle is (-5, 3).

75) What is the equation of the circle graphed below? (hint: you WILL need to square the radius)

(x-3)^2 + (y+1)^2 = 2

(x+3)^2 + (y-1)^2 = 4

(x-3)^2 + (y+1)^2 = 4

The equation of a circle is given by (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius. In the given answer, the equation is (x-3)^2 + (y+1)^2 = 4, which matches the form of the equation for a circle. Therefore, the equation represents a circle with center at (3,-1) and radius 2.

Explanation

The equation of a circle is given by (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius. In the given answer, the equation is (x-3)^2 + (y+1)^2 = 4, which matches the form of the equation for a circle. Therefore, the equation represents a circle with center at (3,-1) and radius 2.