Paul is comparing two high-speed Internet service providers (ISPs) for his business. The graph represents the cost of each ISP as a function of t, the duration in months of a service contract. A coordinate grid showing Internet Service Provider Cost, with Service Contract in months along the horizontal axis, and Total Cost in dollars along the y-axis. Two lines are graphed. One line is labeled I S P A and passes through (0, 180) and (12, 300). The second line is labeled I S P B and passes through (0, 0) and (12, 300).

If C(t) = 180 + 10t represents ISP A and C(t) = 25t represents ISP B, how long would the service contracts need to be for the total costs to be the same?

6 months
8 months
10 months
12 months

8

Step-by-step explanation:

12 months

Step-by-step explanation:

Theres an awful amount of needless information to get through.

Only the last paragrph is needed.

C(t) = 180 + 10t

C(t) = 25t

Set the equations equal

25t = 180 + 10t

Subtract 10t from both sides

15t = 180

Divide both sides by 15

t = 12

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)