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Iteru [2.4K]
3 years ago
11

A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of

35 miles per gallon of gas. During one particular week, the two cars went a combined total of 1450 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
Mathematics
1 answer:
PIT_PIT [208]3 years ago
3 0

Answer:

et x = gallons consumed by car 1

Let y = gallons consumed by car 2

We set up our equations:

35x+40y = 1850        eq1

x+y = 50                   eq2

Substituting eq 2 into eq 1,

35x+40(50-x) = 1850

35x+2000-40x = 1850

-5x+2000 = 1850

-5x = -150

  x = 30

Substitute value of x into eq 2.

x+y = 50

30+y = 50

     y = 20

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Upvote

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1

Step-by-step explanation:

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(-18x^2+12x-2)*(x^3+12x^2+48x+64)
prohojiy [21]
<h2>Answer:</h2>

-18x^5-204x^4-722x^3-600x^2+672x-128

<h2>Explanation:</h2>

( - 18 {x}^{2}  + 12x - 2)

( {x}^{3}  + 12 {x}^{2}  + 48x + 64)

There are multiple ways to solve this for example the foil method or the box method. I prefer to do the box method.

First we are going to set it up

After we set it up we have to solve it so first we are going to multiply

{x}^{3}  \times  - 18 {x}^{2}  =  - 18 {x}^{5}

We have to add the exponent

- 18 {x}^{2}  \times 12 {x}^{2}  =  - 216 {x}^{4}

- 18 {x}^{2}  \times 48x =  - 864 {x}^{3 }  \\  - 18{x}^{2}  \times 64 =  - 1152 {x}^{2}  \\ 12x \times  {x}^{3}  = 12 {x}^{4}  \\ 12x \times 12 {x}^{2}  = 144 {x}^{3}

12x \times 48x = 576 {x}^{2}  \\ 12x \times 64 = 768x

- 2  \times  {x}^{3}  =  - 2 {x}^{3}  \\  - 2 \times 12 {x}^{2}  =  - 24 {x}^{2}  \\  - 2 \times 48x =  - 96x \\  - 2 \times 64 =  - 128

Now we have to add them

-18x^5 stays because there is nothing to add to

Now we add the rest

-216 {x}^{4}  + 12 {x}^{4}  =  - 204 {x}^{4}

- 864 {x}^{3}  + 144 {x}^{3}  +  - 2 {x}^{3}  = -  722 {x}^{3}

768x - 96x = 672x

And -128 stays the same

- 1152 {x}^{2}  + 576 {x}^{2}  - 24 {x}^{2}  =  - 600 {x}^{2}

The answer is

-18x^5-204x^4-722x^3-600x^2+672x-128

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Step-by-step explanation:

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