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1 year ago

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A company contracts to paint 3 houses. Mr. Brown can paint a house in 6 days while Black would take 8 days and Blue 12 days. Aft

er 8 days Brown goes on vacation and Black begins to work for a period of 6 days. How many days will it take Blue to complete the contract?

1 answer:

AleksAgata [21]1 year ago

6 0

You can start with the equation of
(1/6)x8+(1/8)x6+(1/12)x X=3

Multiply by common denominator of 24 to get
32+18+2x=72

Simplify it we get
50+2x=72

Eliminate using algebra (because it’s add 50 take away the 50 on both sides)
2x=22

Because it’s X2 divide by 2 on both sides
x=11
It will take 11 days

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Evaluating for x = -2:

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Then, the AVR is:

$AVR = \frac{18-(-2)}{3-(-2)}$

$AVR = \frac{18+2}{3+2}$

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For f (x) = 3x - 8:

Evaluating for x =4:

$f (4) = 3 (4) - 8\\f (4) = 12 - 8\\f (4) = 4$

Evaluating for x = 5:

$f (5) = 3 (5) - 8\\f (5) = 15 - 8\\f (5) = 7$

Then, the AVR is:

$AVR = \frac{7-4}{5-4}$

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For f (x) = x ^ 2 - 2x:

Evaluating for x = -3:

$f (-3) = (-3) ^ 2 - 2 (-3)\\f (-3) = 9 + 6\\f (-3) = 15$

Evaluating for x = 4:

$f (4) = (4) ^ 2 - 2 (4)\\f (4) = 16 - 8\\f (4) = 8$

Then, the AVR is:

$AVR = \frac{8-15}{4-(-3)}$

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For f (x) = x ^ 2 - 5:

Evaluating for x = -1:

$f (-1) = (-1) ^ 2 - 5\\f (-1) = 1 - 5\\f (-1) = - 4$

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$f (1) = (1) ^ 2 - 5\\f (1) = 1 - 5\\f (1) = - 4$

Then, the AVR is:

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$AVR = \frac{-4+4}{1+1}$

$AVR = \frac{0}{2}$

$AVR = 0$

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from the greatest to the least value based on the average rate of change in the specified interval:

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f(x) = x^2 - 5 interval: [-1, 1]

f(x) = x^2 - 2x interval: [-3, 4]

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