Derrick’s Dog Sitting and Darlene’s Dog Sitting are competing for new business. Derrick's Dog Sitting charges $12 plus $5 per hour. Darlene's Dog Sitting charges $18 plus $3 per hour.

Which is an equation to find the number of hours for which the total cost will be the same for the two services?
a 12 + 5h = 18 + 3h
b 12h + 5 = 18h + 3
c 12 + 5h = 18
d 8h = 30

Solution:

Let "h" be the number of hours

Given that,

Derrick's Dog Sitting charges $12 plus $5 per hour

Cost : 12 + 5(number of hours )

Cost : 12 + 5h eqn 1

Darlene's Dog Sitting charges $18 plus $3 per hour

Cost: 18 + 3(number of hours)

Cost: 18 + 3h eqn 1

For eqn 1 = eqn 2,  the number of hours for the total cost will be the same for the two services

Therefore,

12 + 5h = 18 + 3h

Thus option A is correct

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

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step-by-step explanation:

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