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GaryK [48]
3 years ago
12

a counter top is in the shape of a trapizoid . the lengths of the base is 70 1/2 and 65 1/2 inches long. the area of the counter

top is 1,224 square inches . write and solve an equation to find the height of the countertop.

Mathematics
1 answer:
Grace [21]3 years ago
4 0
I attached a photo of the work below :-) 

Area of a trapezoid= [(a+b)÷2]h
1,224 in²= [(65.5 in+70.5in)÷2]h
1,224in²= (136÷2)h
1,224 in²= 68h
(1,224 in²÷68)= 68h÷68 (elimination)
h= 18 inches

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Answer:

x = 0, x = 4

Step-by-step explanation:

12x - 21 = 5x + 7(x - 3)

First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.

Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.

Factor out a 5x --> 0 = 5x(x - 4)

If you want to solve for x, set 5x = 0 and x - 4 = 0.

For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.

For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.

Plug the values back into the original equation to check if it works

12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21

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