Semester 2 Final Exam Version B

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.

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.

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.

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°.

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.

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.

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.

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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°.

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°.

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.

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.

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

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

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°.

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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.

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.

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.

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.

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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°.

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.

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.

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.

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.

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.

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.

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.

The measure of angle BAC is 32.5°.

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.

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.

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.

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).

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°.

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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.

The measure of arc XZ is 76°.

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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°.

The distance between the two points graphed below is 7.62.

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.

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.

The x-coordinate of the point is -1.

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

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°.

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.

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.