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4 years ago

5

The figure is to be rotated 1/4 (90 degrees) turn about point P.

1 answer:

Mariulka [41]4 years ago

7 0

The answer is C. <span>7 units. just turn it to the position of 90 degrees.</span>

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3 years ago

A triangle has side lengths of 200 units and 300 units. Write compound inequality for the range of the possible lengths for the

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3 years ago

A devastating freeze in California’s Central Valley in January 2007 wiped out approximately 75% of the state’s citrus crop. It t

inna [77]

The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

<em>The linear equation of the function is: </em> $g(P) =22.9P +7$ <em>, while its inverse is: </em> $g^{-1}(c) = \frac{c - 7}{22.9}$ <em>.</em>
<em>The domain is from 0% to 100%, while the range is from 7 to 29.9</em>

<em />

Given that:

$c = g(P)$

<u>Input and Output quantity</u>

The input quantity is the <em>percentage of frozen citrus crop</em>, while the output quantity is the <em>cost of box of oranges</em>

<u>Linear Function</u>

The given parameters can be written as:

$(P_1,c_1) = (20\%, 11.58)$

$(P_2,c_2) = (80\%, 25.32)$

Calculate the slope (m)

$m = \frac{c_2 - c_1}{P_2 - P_1}$

So, we have:

$m = \frac{25.32 - 11.58}{80\% - 20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

The equation is then calculated using:

$c =m(P - p_1) + c_1$

So, we have:

$c =22.9(P - 20\%) + 11.58$

$c =22.9P - 4.58 + 11.58$

$c =22.9P +7$

So, the function is:

$g(P) =22.9P +7$

<u>The domain and the range</u>

The domain is the <em>possible input value (i.e. possible values of P).</em>

Because P is a percentage, its possible values are 0% to 100%.

Hence, the domain of the function is: $[0\%,100\%]$

The range is the <em>possible output value (i.e. possible values of c).</em>

When P = 0% and 100%

$c = 22.9 \times 0\% + 7 = 7$

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

<u>The meaning of </u> $g^{-1}(12)$ <u />

$g^{-1}(12)$ is an inverse equation, where 12 represents the <em>cost of box of oranges.</em>

So, $g^{-1}(12)$ represents the percentage of frozen citrus crop, when the cost is $12.

<u>The inverse formula</u>

We have:

$c =22.9P +7$

Make P the subject

$22.9P = c - 7$

Divide by 22.9

$P = \frac{c - 7}{22.9}$

So, the inverse function is:

$g^{-1}(c) = \frac{c - 7}{22.9}$

<em>This is used to calculate the percentage of frozen citrus crop, when the cost is known.</em>

<em />

$g^{-1}(c) = \frac{c - 7}{22.9}$

Substitute 12 for c

$g^{-1}(12) = \frac{12 - 7}{22.9}$

$g^{-1}(12) = \frac{5}{22.9}$

$g^{-1}(12) = 22\%$

Read more about linear equations at:

brainly.com/question/19770987

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2 years ago

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3 years ago