Simplify
(15x^2 -12x+4)/(4x)
(15x)/4-3+1/x
Solve for b.
A=(h(a+b))/2
b=(2A)/h-a
Show that 4 is a zero of f(x)=2x^3-13x^2+26x-24 by using synthetic division.
Show your work and verify that the remainder is zero.
(3x^2-12)/(x^2+2x-8)div(6x+18)/(x+4)
(x+2)/(2(x+3)
Solve for Z.
1/x=1/y+1/z
z=(xy)/(y-x)
Cindy can paint a room in 6 hours. With Scott's help, they can paint the same room in 4 hours. How long does it take Scott to paint the room by himself?
12 hours
(1-(3x)/4)/(2+x/4)
(4-3x)/(x+8)
x/(x-4)=3-4/(x-4)
x=8
The weight of a ball varies directly with the cube of its radius. A ball with a radius of 2 in. weighs 1.5 pounds. Find the weight of a ball of the same material with a 3-inch radius.
5.1 pounds
x/(x^2-9)+3/(x^2 -6x+9)-1/(x+3)
(6x)/((x+3)(x-3)^2)
(x^2+8)/x-1=(2(x+4))/x
x=3
Hooke's law states that the distance a spring stretches varies directly to the weight attached to the spring. If a 40lb weight attached to a spring stretches the spring 5 inches, then find the distance that a 65lb weight attached to the same spring stretches it.
8 inches
(x^-1y^-1)/(x^-1+y^-1)
1/(x+y)
6p^-2-5p^-1+1=0
{3, 2}
A small plane and a truck leave the same town at sunrise and head for a town 450 miles away. The speed of the plane is 3 times the speed of the truck, and the plane arrives 6 hours ahead of the truck. Find the speed of the truck.
50 mph
Final Jeopardy
The horsepower to drive a boat varies directly as the cube of the speed of the boat. If the speed of the boat doubles, then determine the corresponding increase in horsepower.