Jerry gets price quotes from two different pool cleaning services for the cost of cleaning the pool. Company A charges $7 plus an additional $3 per hour. Company B charges $10 plus an additional $2 per hour. The total price quote for each company is the same amount. How many hours do the companies estimate it will take to clean the pool?

Step-by-step explanation:

Step one:

given data

price quotes from Company A

charges= $7

additional charges per hour= $3

let the number of hours be x

and the total be y

the linear function for the total is

y=3x+7

price quotes from Company B

charges= $10

additional charges per hour= $2

let the number of hours be x

and the total be y

the linear function for the total is

y=2x+10

if the total quote is the same , then

3x+7=2x+10

solve for x, collect like terms

3x-2x=10-7

x=3 hours

coins of silver or gold

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1