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3 years ago

2L + 2W = 88 L = W + 12 What are the dimensions?

Mathematics

1 answer:

liraira [26]3 years ago

8 0

Answer:the length of the rectangle is 28

The width of the rectangle is 16

Step-by-step explanation:

The given equations are set up to determine the dimensions of a rectangle. L represents the length of the rectangle. W represents the width of the rectangle. Let us label

2L + 2W = 88 as equation 1.

We would substitute L = W + 12 into equation 1, it becomes

2(W + 12) + 2W = 88

2W + 24 + 2W = 88

4W + 24 = 88

4W = 88 - 24 = 64

W = 64/4 = 16

Substituting W = 16 into L = W + 12, it becomes

L = 16 + 12 = 28

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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

solniwko [45]

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

The linear equation of the function is: $g(P) = 22.9P+7$ .
The inverse function is: $g^{-1}(c) = \frac{1}{22.9}(c - 7)$ .
A practical domain is from 0% to 100%
A practical range is from 7 to 29.9

A. Input quantity

The input quantity is the percentage of frozen citrus crop

B. Output quantity

The output quantity is the cost of box of oranges

C. The linear function

We have:

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

Calculate the slope of the function

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

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

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

$m = 22.9$

The linear equation is calculated as follows:

$c -c_1 = m(P-P_1)$

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

$c-11.58 = 22.9P-4.58$

D. Rewrite as y = mx + b

We have:

$c-11.58 = 22.9P-4.58$

Collect like terms

$c = 22.9P - 4.58 + 11.58$

$c = 22.9P+7$

The function is:

$g(P) = 22.9P+7$

E. A practical domain

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: $[0\%,100\%]$

F. A practical range

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.

H. The inverse formula

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

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

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

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

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3 years ago

5% of the toddlers in a preschool class drink water with their lunch. How many toddlers are in the class if 3 drink water with t

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Answer:

There are 60 toddlers in the preschool class

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Percentage of the toddlers in a preschool class drink water with their lunch = 5

Number of the toddlers in a preschool class drink water with their lunch = 3

2. How many toddlers are in the class?

We'll solve the question, using the Direct Rule of Three, this way:

Percentage Toddlers

5 3

100 x

*******************************

5x = 3 *100

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x = 300/5

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Answer:

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