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DerKrebs [107]
3 years ago
15

Candice drives a total of 48 miles each day to work and get back home. She works five days a week. Her car gets 21 miles per gal

lon of gas. About how many gallons of gas does she need to drive to work and back home each week
Mathematics
1 answer:
slega [8]3 years ago
5 0

Answer:

Total gallon of fuel used = 11.428 gallons

Step-by-step explanation:

Given -

The total distance travelled by car in one gallon of gas = 21 miles

Total distance travelled each day = 48 miles

Number of days days in a week in which Candice drive is 5 days

Total miles travelled per week = 48*5 = 240 miles

Total gallon of fuel used = \frac{240}{21} = 11.428 gallons

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Solution:

Given expression:

$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}

To find which expression is equal to the given expression.

$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}

Expand the term -\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right):-3 g^{4}-6 g^{3}+7 g^{2}+12

         $=\frac{5 g^{4}+5 g^{3}-17 g^{2}+6 g- 3 g^{4}-6 g^{3}+7 g^{2}+12}{g+2}

Arrange the like terms together.

         $=\frac{5 g^{4}- 3 g^{4}+5 g^{3}-6 g^{3}-17 g^{2}+7 g^{2}+6 g+12}{g+2}

         $=\frac{2 g^{4}- g^{3}-10 g^{2}+6 g+12}{g+2}

Factor the numerator 2 g^{4}-g^{3}-10 g^{2}+6 g+12=(g+2)\left(2 g^{3}-5 g^{2}+6\right)

         $=\frac{(g+2)\left(2 g^{3}-5 g^{2}+6\right)}{g+2}

Cancel the common factor g + 2, we get

         =2 g^{3}-5 g^{2}+6

Hence option C is the correct answer.

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