Polynomials
What is the vertex of:
f(x)=2x^2-8x+7
(2,-1)
Solve:
-10e^(x+10)=-30
ln(3)-10
Simplify:
(5x^2+10x-15)/(25x-25)*(5x+10)/(4)
((x+3)(x+2))/4
Convert into degrees:
-(10pi)/3
-600^o
In a swim final of 8 competitors, what is the probability of correctly guessing the podium finish?
1/336 or 0.003
Which conic sections have foci?
Parabolas, Hyperbolas, and Ellipses
Sketch a graph of
f(x)=x(x+3)(x-1)(x-4)
Graphs vary.
Solve:
16^(3x+2)=64^(-2x)
-1/3
Simplify:
2/(x-4)+2/(x-6)
(4(x-5))/((x-6)(x-4))
Determine the amplitude, period, and any shifts for:
-3sin(4theta-pi)+5
a=3, period=pi/2, HS=pi/4, VS=5
If you toss a coin 12 times, what is the probability of getting 5 heads?
.193
Sketch a graph:
((x-1)^2)/9-((y+3)^2)/16=1
Graphs vary.
Solve:
2x^6-3x^4-18x^2+27=0
+-sqrt(6)/2, +-sqrt(3), +-isqrt(3)
Solve:
log_8(x)+log_8(x+2)=1
2
Solve:
(x+1)/x^2=1/x+1
+-1
Solve the triangle:
B=58^o, C=44^o, b=33
A=78^o, c=27, a=38.1
A spinner has 5 equally sized regions: red, yellow, blue, green, and purple. If the spinner is spun twice, what is the probability of getting the same color on both spins?
0.20
Write an equation for the ellipse:
V: (-2,8), (-2, -14), CV: (7, -3), (-11, -3)
((x+2)^2)/81+((y+3)^2)/121=1
Solve:
5x^4-19x^2-4=0
+-(isqrt(5))/5, +-2
Solve:
-10+3(x-1)^(2/3)=38
-63, 65
Solve:
(x-5)/(2x^2)=(x-6)/(6x^2)+(2)/(3x^2)
13/2
Solve the triangle:
a=10, b=18, c=25
A=19.4^o, B=36.7^o, C=123.9^o
In a bag of M&M's, there are 12 blue, 10 black, 8 green, 7 yellow, and 9 orange. If you grab a handful of 5 M&M's, what is the probability of getting one of each color?
0.044
Solve:
-3x^2+2y^2-13x+3y-13=0; x+y+3=0
(-2,-1)
Solve:
x^3+8x^2+14x+4=0
-2, -3+-sqrt(7)
Solve:
sqrt(5x-1)-3=sqrt(2x-4)
2, 10
Solve:
x/(x^2-2x+1)-1/(x-1)=1
0,2
Solve:
3cos(theta)-1-cos^2(theta)=cos^2(theta)
2pi, pi/3, (5pi)/3
Weights of bananas are normally distributed with an average of 0.25 lbs and standard deviation of 0.04 lbs. What is the probability that in a bunch of 7 bananas, at least 3 weigh 0.3 lbs or more?
0.030
Solve:
6x+6y-3z=3; -5x+4y+4z=-25; -3x+y+2z=-11
(1, -2, -3)