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Probability

300

142. There are 212 students enrolled in geometry at West Valley High School.  Of these students, 64 are freshman, and 112 are sophomores.

a. If a random geometry student is chosen, what is the chance (in percent) that the student is a freshman or sophomore?

176/212=83%

400

142. There are 212 students enrolled in geometry at West Valley High School.  Of these students, 64 are freshman, and 112 are sophomores.

114 of the geometry students perform in band and 56 perform in chorus.  There is a 75% chance that a geometry student performs in either band or chorus.  What is the probability a geometry student performs both in band and in chorus? 

75%=114/212+56/212-x

x=5.2%

Trig

100

143 a.

For each diagram, write an equation and solve for the value of each variable.

tanx=5/8

x=32

200

143. b. 

For each diagram, write an equation and solve for the value of each variable.

costheta=10/11

theta=24.62

300

143. c. 

For each diagram, write an equation and solve for the value of each variable.

sintheta=4/5 

theta=53.1

400

143. d. 

For each diagram, write an equation and solve for the value of each variable.

cosy=9/10

y=25.8

Factoring

100

137. Completely factor the following expressions, if possible.

a. 4k²+14k+12

2(2k+3)(k+2)

200

137. Completely factor the following expressions, if possible.

b. 3x²-75

3(x-5)(x+5)

500

137. Completely Factor

c. 2x³y+8x²y+6xy²

2xy(x²+4x+3y)

Quadratic

100

139. What are the coordinates of the x-intercept of y=x²−2x−15?

(5,0) and (-3, 0)

200

139. What are the coordinates of the y-intercept of y=x²−2x−15?

(0, -15)

300

Write an equation to match each of the representations below

a. 

y=(x-1)(x+1) or y=x²-1

400

Write an equation to match each of the representations below

b. 

y=-(x-5)(x+2) or y=-x²+3x+10

500

141. Solve the quadratic equations by completing the square. Leave your solutions in exact form.

a. x²−6x−12=0

(x-3)²=21

x=3+-sqrt(21)

x=7.58 or -1.58

Quadratic #2

100

138. Factor and use the Zero Product Property to solve the following equations.

a. 0=x²−7x+12

x=3, 4

200

138. Factor and use the Zero Product Property to solve the following equations.

b. 0=6x²-23x+20

x=5/2, 4/3

300

138. Factor and use the Zero Product Property to solve the following equations.

c. 0=x²-9

x=-3, 3

400

138.  Factor and use the Zero Product Property to solve the following equations.

1. 0=x²+12x+36

x=-6

500

141. Solve the quadratic equations by completing the square. Leave your solutions in exact form.

b. x²-3=4x

(x-2)²=7

x=2+-sqrt7

x=4.65 or -0.65