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3 years ago

y − 4 = three fourths(x + 8) in point-slope form, identify the equation of the same line in standard form.

1 answer:

3 0

Standard form is ax+by=c, we like a and b to be integers, we also like a to be positive
basically get x and y on one side

so
y-4=(3/4)(x+8)
distribte the 3/4
y-4=(3/4)x+6
minus 3/4x from both sides
-(3/4)x+y-4=6
add 4 to both sides
(-3/4)x+y=10
times both sides by -4
3x-4y=-40

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True or false A chance event with probability 1 is certain to happen

Gnesinka [82]

Answer:

True, since 1 is 1/1, which is 100%

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Step-by-step explanation:

7 0

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

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

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

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

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

Read more about linear equations at:

brainly.com/question/19770987

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3 years ago

Given the function defined in the table below, find the average rate of

AURORKA [14]

Answer:

Average rate of change = $\frac{2}{5}$

Step-by-step explanation:

Average rate of change of a function 'f' in the interval a ≤ x ≤ b is given by,

Average rate of change = $\frac{f(b)-f(a)}{b-a}$

We have to find the average rate of change in the interval 20 ≤ x ≤ 65

From the table attached,

f(65) = 32

f(20) = 14

Average rate of change = $\frac{32-14}{65-20}$

= $\frac{18}{45}$

= $\frac{2}{5}$

Therefore, average rate of change in the given interval is $\frac{2}{5}$ .

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3 years ago

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Harrizon [31]

Answer:

Step-by-step explanation:

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-2/21. the y intercept would be 5, considering the x is 0 on the first pair of coordinates. so y=-2/21x+5, or A

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3 years ago

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Maksim231197 [3]

Answer:

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