Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f (x) = 5-12x+3x^2, [1, 3]

thomas started a lawn-mowing business in Florida, in which he has x lawns on his route. his costs are $6 per lawn for fertilizer and $14 per lawn for labor. a) if he charges $25 per lawn, write a polynomial that represents his weekly profit.

What is the product of (p3) (2p2 - 4p) (3p2 - 1) ? A) 6p7 + 4p4 B) 6p7 - 2p5 - 12p5 + 4p3 C) 6p7 - 12p6 - 2p5 + 4p4 D) 6p12 - 14p6 + 4p3

Margarita is driving at the speed of s-4/s^2-9s+20 miles per hour. The distance Margarita covers in s-5/4 hours is miles. Give your answer in simplest form.

What is 23/35 simplified?

Tracy deposited $59 into a bank account that earned 3.5% simple interest each year. If no money was deposited into or withdrawn from the account, how much money was in the account after 1 1/2 years? Round your answer to the nearest cent.

How does the volume of a sphere with radius 2cm compare to the volume of a sphere with radius 1cm

6 yards to 36 yards. Find the percent of change. Round to the nearest tenth of a percent if necessary.

Mark, evan, and cayla are playing a game. there are 3 blue marbles, 2 red, and 1 green marble. if mark pulls a blue marble he gets $1. if evan pulls a red marble, he gets a $2. if cayla pulls a green marble, she gets $3.

How do you reduce 12/30 by 1/2

Maria's age of 17 years less than Orlando's age. The sum of their ages is 33 find their ages.