College Algebra Ch 1

Linear Equations & Complex

100

Add

(12 + 3i) + (-15 - 8i)

-3 - 5i

200

Simplify:

sqrt(-9)sqrt(-18)

-9sqrt2

300

Simplify

(3+i)/(4-2i)

1/2+ 1/2i

400

Solve

6(3x-1)=8-(10x-14)

x=1

500

Solve

2[x-(4+2x)+3]=2x+2

x=-1

Story Problems

100

A rectangular room is twice as long as it is wide. If the perimeter 42 feet, find the dimensions of the room.

14 ft by 7 ft

200

I have 4 liters of 10% alcohol solution. How much 25% do I need to add to it to get a 15% solution?

2 Liters

300

I invest $125,000 into two accounts for a year and earned $3500. One account pays a 3% and the other at 2.5%. How much money did I invest in each account?

$75,000 @ 3%

$50,000 @ 2.5%

400

I threw a ball upward at an initial velocity of 18 ft/sec as I was standing on top of a 20 foot building. How long will it take the ball to hit the ground?

1.81 sec

500

My garden is in the shape of a right triangle. The longer leg is 3 yards longer than the short leg. The hypotenuse is 3 yards less than twice the short leg. Find the length of each side of my garden.

9 yards

12 yards

15 yards

Quadratic Equations

100

Solve by factoring:

x^2-6x-16=0

x=-2

x=8

200

Solve by factoring

6x^2-x=2

x=2/3 , x= -1/2

300

Solve by using the square root property

(x+2)^2=36

x=4, x=-8

400

Daily Double!!

Solve by using the Quadratic Formula

-2x^2+4x+5=0

500

Solve by Completing the Square

x^2-8x+11=0

4+-sqrt5

Other Types of Equations

100

Solve

x^-2+x^-1-6=0

x=-1/3,x=1/2

200

Solve:

sqrt(x-4)=sqrt(2x-9

x=5

300

Solve

5/(x-2)+8=5/(x-2)

No Solution

400

Solve

(x-4)^(2/3)=64

x=516

x=-508

500

Solve

3/(x-2)+4/(x+2)=(4x)/(x^2-4)

x=2/3

Inequalities and Absolute Value

100

Solve and graph

11<2x-5<=21

8<x<=13

200

Solve

|x-4|+3=9

x=10, x=-2

300

Solve

|2x-5|>=-17

Infinitely many solutions

400

Solve

x^2-5x-14>0

(-oo,-2),(7,oo)

500

Solve

5/(x+4)<=1

(-oo,-4),[1,oo)