a) Mary has y apples. She ate two-thirds of them. Then Jilly gave Mary 5 more apples. Now mary has 8 apples altogether. Write an equation representing this situation.

y – (2/3)y = (1/3)y = y/3

y/3 + 5 = 8

b) Mary spent $1 per apple. Jill spent $6 per pineapple. Altogether they spent $15… Write an equation representing this situation.

let x = # of apples

let y = # of pineapples

x($1) + y($6) = $15

b) Mary spent $1 per apple. Jill spent $6 per pineapple. Josh spent $3 per half gallon of ice cream. Altogether they spent $25… Write an equation representing this situation.

let x = # of apples

let y = # of pineapples

let z = # of half gallon cartons of ice cream

x($1) + y($6) + z($3) = $25

3. Write a system of equations having

a) A unique solution.

2x + 6 = 9

b) An infinite number of solutions.

y = 2x + 3

A line or parabola has an infinite number of solutions…

c) No solution.

|x-2| = -1

Solve the following equations.

1) x = 3x – 5

x = 3x – 5

2x = 5

x = 5/2

2) x/3 = 6

x

— = 6

3

cross multiply and you get…

x = 18

3) y/3 + 5 = 8

multiply the whole equation by 3 to get rid of the fraction…

3 * (y/3 + 5 = 8)

y + 15 = 24

y = 9

4) -8 = 2x/9

-8 = 2x / 9

multiply both sides by “9”

9 * (-8 = 2x / 9)

-72 = 2x

x = -36

Find f(1) for f(x) = x3 + x2 – 1

substitute 1 for every x you see…. since you are looking for f(x) when x = 1….

Given f(x) = x^3 + x^2 – 1

Therefore, f(1) = 1^3 + 1^2 -1 = 1 + 1 -1 = 1

So f(1) = 1

Hope this helps!!!