Question

B. The top of the chair lift occurs at y=20. Explain how Gavin can find the coordinates of the chair when it reaches the top of the chair lift. The y-coordinate will be 20, so let the coordinates of the point be ( , 20). Then 20=12x+52. Solving for x shows that x= . The coordinates of the chair at the top of the chair lift are ( , ).

Answer 1

To determine the x-coordinate of the chair at the top of the chair lift, solve the given equation 20 = 12x + 52 by isolating x, resulting in the coordinates approximately (-2.67, 20).

Step-by-step explanation:

To find the coordinates of the chair when it reaches the top of the chair lift, where the y-coordinate is known to be 20, we need to solve the equation given for x. The equation provided is 20 = 12x + 52. By solving for x, we can determine the x-coordinate of the chair at the top.

The steps to solve for x are as follows:

Subtract 52 from both sides of the equation, resulting in -32 = 12x.

Divide both sides by 12, giving x = -32 / 12.

Reduce the fraction to get x = -8/3 or approximately -2.67.

Therefore, the coordinates of the chair at the top of the chair lift are approximately (-2.67, 20).

Answer 2

The coordinates of the chair at the top of the chair lift are (-8/3, 20). This is determined by solving the equation (20 = 12x + 52), which yields (x = -8/3). Therefore, the final coordinates are (-8/3, 20).

Step-by-step explanation:

1. The top of the chair lift occurs at ( y = 20 ).

2. The coordinates of the point are denoted as (x, 20).

Now, you are given the equation ( 20 = 12x + 52 ). To find the x-coordinate, you need to solve this equation for x.

Subtract 52 from both sides:

[ 20 - 52 = 12x]

Simplify:

[ -32 = 12x ]

Now, divide both sides by 12 to solve for x:

`\[ x = (-32)/(12) \]`

Simplify the fraction:

`\[ x = -(8)/(3) \]`

So, the x-coordinate is
`\( -(8)/(3) \)`. Now you can write the coordinates of the chair at the top of the chair lift as
`\( \left(-(8)/(3), 20\right) \)`.