The usual toll charge to use the bingham tunnel is 50 cents. if you pur-

chase a special sticker for $5.50, the toll is only 35 cents. at least how

many trips through the tunnel are needed before the sticker costs less than

paying for each trip separately?

At least 37.

Step-by-step explanation:

First, write an equation for the problem.

5.50+0.35x<0.50x

Where X is the number of trips through the tunnel.

Then, solve.

550+35x < 50x         Multiply all terms by 100

550 < 15x                  Subtract 35x from both sides

36 2/3 < x                  Divide both sides by 15.

Therefore, the number of trips through the tunnel must be greater than 36 to have having the sticker cost less than paying for each trip separately.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.