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irga5000 [103]
3 years ago
9

The United States is about the only country that still uses the units feet, miles, and gallons. However, you might see some car

specifications that give fuel efficiency as 7.6 km per kilogram of fuel. Given that a mile is 1.609 km, a gallon is 3.785 liters, and a liter of gasoline has a mass of 0.729 kg, what is the car’s fuel efficiency in miles per gallon?
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
3 0

Answer: 4.5 \text{ miles per gallon}

Step-by-step explanation:

Given :  The fuel efficiency of car = 7.6 km per kilogram

We also given that

1 mile = 1.609 km

Then, \text{1 km}=\dfrac{1}{0.609}\text{ mile}

1 gallon = 3.785 liters

\text{1 liter}=\dfrac{1}{3.785}\text{ gallon}

1 liter of gasoline = 0.729 kg

Then, \text{1 kg}=\dfrac{1}{0.729}\text{ liter}

\Rightarrow\ \text{1 kg}=\dfrac{1}{0.729}\times\dfrac{1}{3.785}\text{gallon}

Now, the fuel efficiency of car will be :

7.6\times\dfrac{1}{0.729}\times\dfrac{1}{3.785}\times\dfrac{1}{0.609}\\\\=4.52275317827\approx4.5 \text{ miles per gallon}

Hence,  the car’s fuel efficiency in miles per gallon= 4.5

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Please Help, Geometry Work due Tomorrow
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Answer:

1) x= 7

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3)(5,2)

Step-by-step explanation:

problem 1:

1) Distribute

4(x-5)=x+1

4x-20=x+1

2) Add 20 to both sides of the equation

4x-20=x+1

4x-20+20=x+1+20

3) Simplify

*Add the numbers

4x=x+21

4) Subtract x from both sides of the equation

4x=x+21

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5) Simplify

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6) Divide both sides of the equation by the same term.

3x=21

3x/3=21/3

7) Simplify

*Cancel terms that are in both the numerator and denominator

*Divide the numbers

Result: x=7

-------------------------------------

problem 2:

a

1) Use the sum-product pattern

Identify a, b, and c in your equation and then find two numbers that when multiplied together equal c and when added together equal b.

x²-9x+8=0

2) Factor

* Write your equation in factored form

(x-8)(x-1)=0

3) Create two separate equations

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x-1=0

4) solve

*rearrange and isolate the variable to find each solution

x=8

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b.

1) move terms to the left side

2x²+7x-4=x²+10x

2x²+7x-4-(x²+10x)=0

2) distribute

2x²+7x-4=x²+10x

2x²+7x-4-x²-10x=0

3) combine like terms

2x²+7x-4-x²-10x=0

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4) Multiply by 1

1x²+7x-4-10x=0

x²+7x-4-10x=0

5) combine like terms

x²+7x-4-10x=0

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6) Use the sum-product pattern

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7) Factor

Write your equation in factored form

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9) Solve

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x=4

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-=----------------------

problem 3:

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x-y-3

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x-(2)=3

x=5

(5,2)

4 0
2 years ago
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