Question

1. Aubrey is driving on a long road trip. She currently has 14 gallons of gas in her car. Each hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 6 hours? How much gas would be left after tt hours?

2. Find the sum of -8x^2+3 and -9x^2+3x-3−

3.Simplify the expression to a polynomial in standard form:

(-3x-5)(-x^2+x-5)

Answer 1

Answer:

See solutions below

Step-by-step explanation:

1) Total amount of gallons = 14 gallons

If she uses up 0.75 gallons of gas each hour then;

1 hour = 0.75gallons

after driving 6 hours, amount of gallons used will be;

6 hours = x

Divide both expressions

1/6 = 0.75/x

x = 6 * 0.75

x = 4.5gallons

Amount of gas left = 14 - 4.5 = 9.5 gallons of gas

Hence 9.5 gallons of gas will be left after 6 hrs

Similarly;

1 hour = 0.75gallons

after driving t hours, amount of gallons used will be;

t hours = x

x = 0.75t

Amount of gas left after t hours = (14 - 0.75t) gallons of gas

2) We are to find the sum of -8x^2+3 and -9x^2+3x-3

-8x^2+3 + (-9x^2+3x-3)

= 8x^2+3 -9x^2+3x-3

Collect like terms

=  8x^2 -9x^2+3x + 3-3

= -x^2 + 3x

Hence the sum is -x²+3x

3) Expressing in standard form;

(-3x-5)(-x^2+x-5)

Expand

= 3x³-3x²+15x+5x²-5x+25

Collect like terms

= 3x³-3x²+5x²+15x-5x+25

= 3x³+2x² + 10x + 25

Hence the product in polynomial form is 3x³+2x² + 10x + 25