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Black_prince [1.1K]
2 years ago
10

Find the value of x,y and z (hint:both are the parallelogram )

Mathematics
1 answer:
allochka39001 [22]2 years ago
4 0
<h3>In question a, </h3>

Interior angles are supplementary

So, x+50 = 180

x = 180-50

<h3><u>x = 130</u></h3>

Alternate angles are congruent

x = y = z

<h3><u>y = 130</u></h3><h3 /><h3><u>Z</u><u> </u><u>=</u><u> </u><u>130</u></h3>

<h3 /><h3>In question b, </h3>

Alternate angles are congruent

<h3 /><h3><u>y</u><u> </u><u>=</u><u> </u><u>120</u></h3>

Interior angles are supplementary

So, y + 40 + z = 180

120 + 40 + z = 180

160 + z = 180

z = 180 - 160

<h3><u>z = 20</u></h3>

Alternate angles are congruent

z = x

<h3><u>x = 20</u></h3>

.... Hope this will help....

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A devastating freeze in California's Central Valley in January 2007 wiped out approximately 75% of the state's citrus crop. It t
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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>.</em>
  • <em>The inverse function is: </em>g^{-1}(c) = \frac{1}{22.9}(c - 7)<em> .</em>
  • <em>A practical domain is from 0% to 100%</em>
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<u>A. Input quantity</u>

The input quantity is the percentage of frozen citrus crop

<u />

<u>B. Output quantity </u>

The output quantity is the cost of box of oranges

<u>C. The linear function</u>

We have:

(P_1,c_1) = (20\%,11.58)\\(P_2,c_2) = (80\%,25.32)

<em>Calculate the slope of the function</em>

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

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

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

m = 22.9

<em>The linear equation is calculated as follows:</em>

c -c_1 = m(P-P_1)

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

c-11.58 = 22.9P-4.58

<u>D. Rewrite as y = mx + b</u>

We have:

c-11.58 = 22.9P-4.58

Collect like terms

c = 22.9P - 4.58 + 11.58

c = 22.9P+7

<em>The function is:</em>

g(P) = 22.9P+7

<u>E. A practical domain</u>

The domain is the possible values of P.  Because P is a percentage, its possible values are 0% to 100%.

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

<u>F. A practical range</u>

When P = 0%

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

When P = 100%

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

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

G. The meaning of g^{-1}(12)

The inverse function of g(P) is g^{-1}(P)

So:

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

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We have:

c = 22.9P+7

Subtract 7 from both sides

c - 7 = 22.9P

Make P the subject

P = \frac{1}{22.9}(c - 7)

So, the inverse formula is:

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

Substitute 12 for c

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

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

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

Read more about linear equations at:

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