pablo will rent a car for the weekend. he can choose one of two plans. the first plan has an initial fee of $55.96 with additional costs of $0.12 per mile driven. the second plane has an initial fee of $63.96 and costs an additional $0.08 per mile driven. how many miles does pablo drive to make the miles the same?

200 miles

Step-by-step explanation:

First, set up the equations.

plan 1: initial fee of $55.96, $0.12 per mile

plan 2: initial fee of $63.96, $0.08 per mile

We want to know at what distance will the cost be the same. So, set the equations equal to each other.

0.12x + 55.96 = 0.08x + 63.96

Combine the variables.

0.04x + 55.96 = 63.96

Combine the constants.

0.04x = 8

Divide by 0.04 to isolate x.

x = 200 miles

Check by plugging x back into each equation.

y = 0.12(200) + 55.96

y = 24 + 55.96

y = $79.96

y = 0.08(200) + 63.96

y = 16 + 63.96

y = $79.96

You are correct!

sine

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.