Math 105 - College Algebra

Ch 1-2

100

Simplify the imaginary numbers

√(-144x²)

12xi

200

Find all real solutions of each equation.

√(x²+21)=x+3

2

300

Solve the formula for the indicated variable.

a=(n-2)(180/n); n

360/(180-a)

400

An electronic LED billboard in Times Square is 26 feet taller than it is wide. If its perimeter is 92 feet, find the dimensions of the billboard.

10ft by 36ft.

500

Solve the absolute value for x.

|(2x-4)/5|+6=8

7,3

Ch 3-4

100

Let f(x)=3x and g(x)=x²+2. Find each function.

a. f+g

b. g•f

a. x²+3x+2

b. 9x²+2

200

Graph the function

f(x)=-x²+4

y-int: (0,4)

x-int: (-2,0); (2,0)

300

Use Descartes' Rule of Signs to find the number of possible positive, negative, and nonreal zeros of the polynomial function.

P(x)=3x⁵-2x⁴+2x²-x-3

1 or 3 positive

0 or 1 negative

0, 2, or 4 nonreal

400

Use synthetic division to divide.

(3x³+7x²+2x) / (x+2)

3x²+x

500

Find f ^-1.

f(x) = x³-3

(cubed root) √(x+3)

Ch 5-6

100

log₂2048

11

200

Solve the equation.

log₆18-log₆(x-3) =log₆3

9

300

 Write the system of equations as a matrix and solve using Gauss-Jordan elimination.

x+2y+3z=-5

3x+y-2z=7

y-z=2

(1,0,-2)

400

Graph the solution set:

3x+4y≤12

3x+4y≥6

x≥0

y≥0

 

500

Use Cramer's Rule to solve for y.

3x-5y=3

-3x+y=2

-5/4

Ch 7-8

100

Find the required term in the binomial expansion.

(2a-b)⁸; 7th term

112a²b⁶

200

Evaluate the sum.

₃

∑ (4k+1)

^k=1

27

300

Find an equation in standard form of the hyperbola described. 

Center at the origin, focus at (13, 0), vertex at (5,0).

(x²/25)-(y²/144)=1

400

Solve using substitution or elimination.

2x²-3y²=9

x²+y²=27

(3√2, 3), (-3√2, 3), (3√2, -3), (-3√2, -3)

500

Write an equation in standard form of the circle described

a. Center (2, -5) passes through (7,7)

b. Ends of diameter at (-2,2) and (6,8)

a. (x-2)²+(y+5)²=169

b. (x-2)²+(y-3)²=41

SURPRISE!

100

Evaluate the determinant

| 3  -5|

|-3   1|

-12

200

Write the first six terms of the arithmetic sequences with the given properties.

first term =5. 

Third term=2

5, 7/2, 2, 1/2, -1, -5/2

300

Solve the equation. 

4^x+2-4^x= 15

(Hint:4^x+2=4^x4²)

0

400

FREEBIE!

:D

500

Simplify the expression 

i⁸⁷

-i