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Rainbow [258]
2 years ago
6

Please help!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
Paraphin [41]2 years ago
6 0

Answer:

100 degrees

Step-by-step explanation:

Angle 1  + Angle 2 = 180 degrees (linear pair theorem)

Angle 2 = Angle 6 (verticle angles theorem)

Thus, we can substitute the given values of angle one and angle six into the following equation:

Angle 1 + Angle 6 = 180

4x - 20 + 5x - 25 = 180

9x - 45 = 180

9x = 225

x = 25 degrees

Angle 2 = Angle 6

5x - 25 = Angle 6, so 5x - 25 = Angle 2

5(25) - 25 = Angle 2

100 degrees = Angle 2

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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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