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Alexeev081 [22]

3 years ago

6

Jenny decided to grow out her hair. Over 6 months, her hair length grew by 100%. During the next 6 months, her hair length grew

by 50%. What was the combined increase in hair length during the entire year

2 answers:

zimovet [89]3 years ago

8 0

150% in 12 months. .......

musickatia [10]3 years ago

5 0

In your mind, you could think 100% more is 200% and 50% of that is another 100% so 200% increase. Let's see on paper. x will be her current hair length.

<span>x + x + .5(x + x) </span>

<span>x + x is simply her hair length doubling. This is when it grew 100% longer. Then, from that, we have 50% more, so we have to add 50% of the x + x. </span>

<span>2x + .5x + .5x </span>
<span>3x </span>

<span>Subtract our starting length. </span>

<span>3x - x = 2x </span>

<span>The difference is 2 hair lengths, or 200% her original length of hair.</span>

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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:

Divide both sides by 2.
(p) ÷ 2 = (2w + 2l) ÷ 2
$2's$ $cancel$ $out$
$\frac{p}{2} = w + l$

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).
$\frac{p}{2} - l = w + l - l$
$l's$ $cancel$ $out$
p/2 - l = w

$a = l * w$

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

Multiply out the L.
$a = \frac{p}{2}l - l^{2}$

Plug in all your numbers a = 110 and p = 42
$110 = \frac{42}{2}l - l^{2}$
$110 = 21l - l^{2$

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.
$(l -10)(l-11) = 0$

Make each parenthesis set equal to 0.
$l-11=0$ $l-10=0$

Add.
$l = 11$ $l = 10$

By doing this you solve for both the width and length so the answer is:
w = 11 L = 10

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