Cc3 Ch. 5 Closure By Mr. Cheung

1) To rent a jet ski at Sam's costs $25 plus $3 per hour. At Claire's, it costs $5 plus $8 per hour. At how many hours will the rental cost at both shops be equal?

The rental cost at Sam's is $25 plus $3 per hour, while at Claire's it is $5 plus $8 per hour. To find the number of hours at which the rental cost at both shops will be equal, we need to set up an equation. Let x be the number of hours. The equation will be: 25 + 3x = 5 + 8x. By solving this equation, we find that x = 4. Therefore, at 4 hours, the rental cost at both shops will be equal.

Explanation

The rental cost at Sam's is $25 plus $3 per hour, while at Claire's it is $5 plus $8 per hour. To find the number of hours at which the rental cost at both shops will be equal, we need to set up an equation. Let x be the number of hours. The equation will be: 25 + 3x = 5 + 8x. By solving this equation, we find that x = 4. Therefore, at 4 hours, the rental cost at both shops will be equal.

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2)

Write the rule that can be best used to represent the table above (in y = mx+b form).

The given correct answer is y = 2x - 1. This equation represents a linear relationship between the variables x and y, where the coefficient of x is 2 and the constant term is -1. This means that for every increase of 1 in x, y will increase by 2. The equation is in the standard form of a linear equation, y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the slope is 2 and the y-intercept is -1.

Explanation

The given correct answer is y = 2x - 1. This equation represents a linear relationship between the variables x and y, where the coefficient of x is 2 and the constant term is -1. This means that for every increase of 1 in x, y will increase by 2. The equation is in the standard form of a linear equation, y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the slope is 2 and the y-intercept is -1.

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3) Use the Equal Values Method to solve for the following systems of equations. y = 3x − 1 y = 3x + 2

No solution

Infinite solutions

(1, 2)

(2, 1)

The given system of equations is y = 3x - 1 and y = 3x + 2. By comparing the coefficients of x in both equations, we can see that they are the same (3). However, the constant terms (-1 and 2) are different. This means that the lines represented by these equations have the same slope but different y-intercepts. Therefore, the lines are parallel and will never intersect, resulting in no solution.

Explanation

The given system of equations is y = 3x - 1 and y = 3x + 2. By comparing the coefficients of x in both equations, we can see that they are the same (3). However, the constant terms (-1 and 2) are different. This means that the lines represented by these equations have the same slope but different y-intercepts. Therefore, the lines are parallel and will never intersect, resulting in no solution.

4)

Which colored line best represents the graph of the equation y = 4x + 3?

Red

Blue

Green

Purple

The correct answer is Red because the equation y = 4x + 3 represents a linear function with a positive slope of 4. The red line is the only one that has a positive slope and is consistent with the equation given.

Explanation

The correct answer is Red because the equation y = 4x + 3 represents a linear function with a positive slope of 4. The red line is the only one that has a positive slope and is consistent with the equation given.

5) Solve for x. 3(2x − 1) + 7 = −44

X = -8

X = -6

X = -10

X = 6

By distributing the 3 to both terms inside the parentheses, the equation becomes 6x - 3 + 7 = -44. Simplifying further, we get 6x + 4 = -44. Subtracting 4 from both sides gives 6x = -48. Finally, dividing both sides by 6, we find that x = -8.

Explanation

By distributing the 3 to both terms inside the parentheses, the equation becomes 6x - 3 + 7 = -44. Simplifying further, we get 6x + 4 = -44. Subtracting 4 from both sides gives 6x = -48. Finally, dividing both sides by 6, we find that x = -8.

6) Solve for x. 6(2x − 5) = −(x + 4)

X = 2

X = 1

X = -1

X = -4

By distributing the 6 to both terms inside the parentheses, we get 12x - 30. By distributing the negative sign to both terms inside the other parentheses, we get -x - 4. Combining like terms, we have 12x - 30 = -x - 4. By moving all the x terms to one side of the equation and the constant terms to the other side, we get 13x = 26. Dividing both sides by 13, we find that x = 2.

Explanation

By distributing the 6 to both terms inside the parentheses, we get 12x - 30. By distributing the negative sign to both terms inside the other parentheses, we get -x - 4. Combining like terms, we have 12x - 30 = -x - 4. By moving all the x terms to one side of the equation and the constant terms to the other side, we get 13x = 26. Dividing both sides by 13, we find that x = 2.

7) Use the Equal Values Method to solve for the following systems of equations. y = 7x − 5 y = −2x + 13

X = 2 and y = 9

X = 9 and y = 2

X = 5 and y = 3

X = 3 and y = 5

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Explanation

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8) Solve for x. That is, get the x variable by itself on one side of the equation. 3(x + 2) = y − 6

To solve for x in the equation 3(x + 2) = y - 6, we need to isolate the x variable. We can start by distributing the 3 to both the x and 2 inside the parentheses, which gives us 3x + 6. The equation now becomes 3x + 6 = y - 6. To isolate the x variable, we can subtract 6 from both sides of the equation, resulting in 3x = y - 12. Finally, to solve for x, we divide both sides of the equation by 3, giving us the solution x = (y - 12)/3.

Explanation

To solve for x in the equation 3(x + 2) = y - 6, we need to isolate the x variable. We can start by distributing the 3 to both the x and 2 inside the parentheses, which gives us 3x + 6. The equation now becomes 3x + 6 = y - 6. To isolate the x variable, we can subtract 6 from both sides of the equation, resulting in 3x = y - 12. Finally, to solve for x, we divide both sides of the equation by 3, giving us the solution x = (y - 12)/3.

9) To rent a jet ski at Sam's costs $25 plus $3 per hour. At Claire's, it costs $5 plus $8 per hour. Let x = the number of hours rented, and y = the total cost for the rentals. Which two equations could be used to represent the cost the rent the jet skis at Sam's and Claire's? (Select all that apply)

Y = 3x + 25

Y = 8x + 5

Y = 25x + 3

Y = 5x + 8

The equation y = 3x + 25 represents the cost to rent a jet ski at Sam's, where $25 is the initial cost and $3 per hour is added. The equation y = 8x + 5 represents the cost to rent a jet ski at Claire's, where $5 is the initial cost and $8 per hour is added.

Explanation

The equation y = 3x + 25 represents the cost to rent a jet ski at Sam's, where $25 is the initial cost and $3 per hour is added. The equation y = 8x + 5 represents the cost to rent a jet ski at Claire's, where $5 is the initial cost and $8 per hour is added.

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10) Solve for y. That is, get the y variable by itself on one side of the equation. 2x + 5y = 10

Y = -2x + 2

Y = -5x + 5

To solve for y, we need to isolate the y variable on one side of the equation. In this case, we can start by subtracting 2x from both sides of the equation. This gives us 5y = -2x + 10. Next, we divide both sides of the equation by 5 to solve for y. This gives us y = (-2/5)x + 2. Therefore, the correct answer is y = -2/5x + 2.

Explanation

To solve for y, we need to isolate the y variable on one side of the equation. In this case, we can start by subtracting 2x from both sides of the equation. This gives us 5y = -2x + 10. Next, we divide both sides of the equation by 5 to solve for y. This gives us y = (-2/5)x + 2. Therefore, the correct answer is y = -2/5x + 2.