What is x in the similar triangles? Please help:)

Answer:

x = 18

Step-by-step explanation:

Since both right triangles are similar, therefore:

[tex] \frac{2x - 6}{20} = \frac{39}{x + 8} [/tex]

Cross multiply

[tex] (2x - 6)(x + 8) = 39*20 [/tex]

[tex] 2x(x + 8) -6(x + 8) = 780 [/tex]

[tex] 2x^2 + 16x - 6x - 48 = 780 [/tex]

[tex] 2x^2 + 10x - 48 = 780 [/tex]

Subtract 780 from both sides

[tex] 2x^2 + 10x - 48 - 780 = 0 [/tex]

[tex] 2x^2 + 10x - 828 = 0 [/tex]

[tex] 2x^2 + 46x - 36x - 828 = 0 [/tex]

[tex] 2x(x + 23) - 36(x + 23) = 0 [/tex]

[tex] (x + 23)(2x - 36) = 0 [/tex]

x + 23 = 0

x = -23

Or

2x - 36 = 0

2x = 36

x = 18

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1. Do Charlotte's calculations make sense? Why or why not? Make sure to address each step in your answer and use complete sentences to explain your reasoning.

2. Charlotte is redecorating the master bedroom in her house. She has purchased a new bedroom set and also plans to paint the room and put in new flooring. The room is rectangular, with dimensions of 16 feet (length) by 13 feet (width). The walls in the room are 9 feet tall, and the room contains two doors and two windows.

Charlotte has decided to put new carpet in the bedroom. The carpet she chose costs $1.85 per square foot, not including the cost of labor or other related materials. She was given the following information by the local flooring store where she is purchasing the carpet.

She is required to purchase a piece of carpet that includes a 3-inch overlap on all sides. Labor and material costs will relate to the area of this piece.
The labor costs are $23 per hour, per person.
A two-person carpet crew can lay 50 square feet of carpet each hour.
The crew that will complete the job at Charlotte's house will be a four-person crew.
There is an additional $75 fee to cover the cost of equipment, materials, and supplies.
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Length:
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feet.

3. Charlotte is redecorating the master bedroom in her house. She has purchased a new bedroom set and also plans to paint the room and put in new flooring. The room is rectangular, with dimensions of 16 feet (length) by 13 feet (width). The walls in the room are 9 feet tall, and the room contains two doors and two windows.

Charlotte has decided to put new carpet in the bedroom. The carpet she chose costs $1.85 per square foot, not including the cost of labor or other related materials. She was given the following information by the local flooring store where she is purchasing the carpet.

She is required to purchase a piece of carpet that includes a 3-inch overlap on all sides. Labor and material costs will relate to the area of this piece.
The labor costs are $23 per hour, per person.
A two-person carpet crew can lay 50 square feet of carpet each hour.
The crew that will complete the job at Charlotte's house will be a four-person crew.
There is an additional $75 fee to cover the cost of equipment, materials, and supplies.
Recall that the area of a rectangle is found by multiplying the length and width of the rectangle. What is the area of the piece of carpet that Charlotte must purchase? Note: Express your answer as a decimal number and do not round.

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