Oscar charges $25 for the first hour of tutoring and $15 for each additional hour or fraction of an hour counting as a whole hour. The rates that Latoya charges for x hours of tutoring are modeled with the function shown.

f(x)=30x,0≤x≤3

20x,3 6

(Imagine this stuff above as a piecewise function)

Complete to make a true sentence.

will charge $ more to tutor for 5.5 hours.

Answer and explanation:

Since Oscar charges $25 for the first hour and $15 for every additional hour or fraction of an hour, his function would be :

f(x)= 25x 0 is less than or equal to x and x is less than or equal to 1

Latoya charges $30 for the first three hours and $20 for every additional hour or fraction of an hour. The function :

f(x)= 30x

0 is less than or equal to x and x is less than or equal to 3

Given that each taught their students for 5.5 hours, their charges would be :

For Oscar,

The first hour = 25×1= $25

4.5 hours left= 15×4.5= $67.5

Total charge for 5.5 hours= $67.5+$25= $92.5

For Latoya,

The first three hours= 30×3=$90

2.5 hours left= 2.5×20= $50

Total charge for 5.5 hours= $90+$50= $140

Therefore Latoya will charge $47.5 more to tutor for 5.5 hours.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15