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3 years ago

11

The number of miles driven varies directly with the number of gallons of gas used. If 8 gallons of gas are used to drive 204 mil

es, how many miles can be driven on 18 gallons of gas?

1 answer:

Alik [6]3 years ago

8 0

Answer:

3672

Step-by-step explanation:

If 8 gallons of gas were used to drive 204 miles multiply 18x204=3,672 miles

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The degree of 4 – x2

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Answer:

Step-by-step explanation:

If the given is x^2 then the degree is 2.

Degree: 4 - x^2 = 2.

It is what is on the x to the highest power. If the question was

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3 years ago

Element X decays radioactively with a half life of 12 minutes. If there are 200 grams of Element X, how long, to the nearest ten

Semenov [28]

Answer:

It would take 24 minutes for the element to decay to 50 grams

Step-by-step explanation:

The equation for the amount of the element present, after t minutes, is:

$Q(t) = Q(0)e^{-rt}$

In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.

Half life of 12 minutes

This means that $Q(12) = 0.5Q(0)$

So

$Q(t) = Q(0)e^{-rt}$

$0.5Q(0) = Q(0)e^{-12r}$

$e^{-12r} = 0.5$

$\ln{e^{-12r}} = \ln{0.5}$

$-12r = \ln{0.5}$

$12r = -\ln{0.5}$

$r = -\frac{\ln{0.5}}{12}$

$r = 0.05776$

If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?

This is t when Q(t) = 50. Q(0) = 200.

$Q(t) = Q(0)e^{-rt}$

$50 = 200e^{-0.05776t}$

$e^{-0.05776t} = 0.25$

$\ln{e^{-0.05776t}} = \ln{0.25}$

$-0.05776t = \ln{0.25}$

$0.05776t = -\ln{0.25}$

$t = -\frac{\ln{0.25}}{0.05776}$

$t = 24$

It would take 24 minutes for the element to decay to 50 grams

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3 years ago

How many solutions exist for the given equation? <br><br> 3(x-2) =22 -x

kenny6666 [7]

Answer:

one solution

Step-by-step explanation:

3(x-2) =22 -x

Distribute

3x - 6 = 22-x

Add x to each side

3x+x-6 = 22-x+x

4x+6 = 22

Subtract 6 from each side

4x+6-6 = 22-6

4x= 16

Divide by 4

4x/4 = 16/4

x=4

There is one solution

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2 years ago

Which is the best interpretation of the solution set for the compound inequality? 3(2x + 1) > 21 or 4x + 3 4 D. all real numb

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D

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