Solve t=9c-8d for d. assume all variables represent positive values.

1 answer:

6 0

T = 9c - 8d
t - 9c = -8d
(t - 9c)/-1 = -8d/-1
-(t - 9c) = 8d
-1(t - 9c)/8 = 8d/8
-1/8 • (t - 9c) = d or
-(t - 9c)/8 = d

Thus d = -(t - 9c)/8.

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The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.

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$p = 2w + 2l$ $p = 42$
$a = l * w$ $a = 108$

You want to make either the length or width variable (I chose the width variable to be by itself. It doesn't matter) by itself by:

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(p) ÷ 2 = (2w + 2l) ÷ 2
$2's$ $cancel$ $out$
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Subtract both sides by either length or width depending on what variable you chose to make by itself (in this case I subtracted the length variable because I wanted the width variable by itself).
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$l's$ $cancel$ $out$
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$a = l * w$

You replace w with the equation above p/2 - l = w
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$a = \frac{p}{2}l - l^{2}$

Plug in all your numbers a = 110 and p = 42
$110 = \frac{42}{2}l - l^{2}$
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Move everything to the left side so $l^{2}$ would be positive (makes the equation easier when $l^{2}$ is positive).
$l^{2} - 21l + 110 = 0$

Factor.
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Make each parenthesis set equal to 0.
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Add.
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