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Kryger [21]
3 years ago
9

A shopper’s discount club charges a monthly fee of $15 and sells gasoline for $2.05 per gallon. The gas station across the stree

t sells gasoline for $2.35 per gallon and charges no fee. Write and equation to model how many gallons of gasoline would you have to buy in one month to spend the same amount at either store
Mathematics
1 answer:
NeX [460]3 years ago
8 0

Answer:

15 + 2.05 x = 2.35 x

Step-by-step explanation:

Let x be the number of gallons you would have to buy for the two places to be the same.

At the club, there is a monthly fee of $15 that is charged once in a month. They also charge $2.05 per gallon, which is charged every gallon of gas you buy.

We can write an expression: 15 + 2.05 x

At the gas station, they charge $2.35 per gallon with no other fees.

We can also write an expression: 2.35 x

For the prices to be the same, we have 15 + 2.05 x = 2.35 x

If we were to solve, then we have:

(2.35 - 2.05) x = 15

x = 15 / 0.3 = 50 gallons

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Answer:

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Step-by-step explanation:

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Adrian cuts a block of wood as shown. What is the volume of the block of wood?
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Step-by-step explanation:

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What is the completely factored form of f(x)=x^3+4x^2+7x+6?
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we are given

f(x)=x^3+4x^2+7x+6

We will use rational root theorem to find factors

We can see that

Leading coefficient =1

constant term is 6

so, we will find all possible factors of 6

6=\pm 1,\pm 2,\pm 3,\pm 6

now, we will check each terms

At x=-2:

We can use synthetic division

we get

f(-2)=0

so, x+2 will be factor

and we can write our expression from synthetic division as

f(x)=x^3+4x^2+7x+6=(x+2)(x^2+2x+3)

f(x)=(x+2)(x^2+2x+3)

now, we can find factor of remaining terms

x^2+2x+3=0

we can use quadratic formula

\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

we can compare our equation with quadratic equation

we get

a=1,b=2,c=3

now, we can plug these values

x=\frac{-2+\sqrt{2^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}

x=-1+\sqrt{2}i

x=\frac{-2-\sqrt{2^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}

x=-1-\sqrt{2}i

so, we get

x=-1+\sqrt{2}i,\:x=-1-\sqrt{2}i

so, we can write factor as

x^2+2x+3=(x-(-1+\sqrt{2}i))(x-(-1-\sqrt{2}i))

so, we get completely factored form as

f(x)=(x+2)(x-(-1+\sqrt{2}i))(x-(-1-\sqrt{2}i))...............Answer


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3 years ago
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