Yay Algebra!
Solve the following rational inequality:
(x-2)/(x+2) [<=] 0
(20)
Factor and find all possible solutions:
x3-9x2+20x=0
(16)
x= {0, 4, 5}
Use synthetic division to determine if the given value for k is a zero of this polynomial. If not, determine p(k).
p(k)=2x4-12x3-6x2+99x-44
k=4
(7)
yes, it is a zero
Find the center and radius of the circle:
(x-2)2+(y-9)2=81
(3)
radius: 9
center: (2,9)
The amount of water used to take a shower is directly proportional to the amount of time that the
shower is in use. A shower lasting 24 minutes requires 9.6 gallons of water. Find the amount of
water used in a shower lasting 5 minutes.
2 gallons
Find the degree and coefficient of the following polynomial:
g(x)=(8x+3)(x-3)(3x+8)
(8)
degree: 3
leading coefficient: 24
Solve the following rational equation and simplify your answer:
(5x)/(x+1)=(4x)/(x+2)
(4)
x= {-6,0}
Solve the following rational equation and simplify your answer:
(2)/(x+2) = 1 - (4)/(x+6)
(17)
x= {-2, 4}
Find the solution of the following inequality:
2x2<3x+5
(14)
(-1 , 5/2)
The square root of 10x - 9 = 9
{9}
Solve the following rational inequality:
(5-2x)/(3x+2)>0
(5)
( -2/3 , 5/2 )
Simplify the Following radical:
cube root(-64x9y12)
(1)
-4x3y4
Suppose that y varies inversely as the cube of x, and that y=14 when x=7. What is y when x is 9?
(2)
y=6.59
Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
zeros: -7, -1, 1
degree: 3
(6)
f(x)=x3+7x2-x-7
x^2 - 4x + 4 + y^2 - 10y + 25 = 64
A) (x - 2)^2 + (y - 5)^2 = 64
(2, 5), r = 8
Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents:
[z-12(z4x)3] / [8yx3]
(18)
1/8y
Complete the square and write the equation in standard form. Then give the center and radius of the circle:
x2 - 4x + 4 + y2 - 10y + 25 = 64
(15)
(x-2)2 + (y-5)2 = 64
center: (2,5)
radius: 8
f(x)= (x+1)/(x2+x-2)
(12)
x=-2
x=1
Find the horizontal asymptote for the following function:
f(x) = (2x2+3x+1) / (x3-2x2-3x+1)
(19)
y=0
Show 26
f(x) = -x^2(x - 3)(x - 1)
D
Construct a polynomial with the stated qualities:
second-degree, zeros of -4 and 2, approaches -infinity as x approaches -infinity
(9)
-x2+2x+8
Solve the following radical equation. If needed write your answer as a fraction reduced to the lowest terms:
cube root(19-7y) - cube root(2y-2) = 0
(11)
17/9
The perimeter of a square varies directly as the length of a side of the square. If the perimeter of the square is 288m when one side is 72m, what is the perimeter of the square when the side is 96m?
(10)
384 meters
The graph of a third-degree polynomial p(x) has zeros -3, 0, 5 and it passes through point (2,5). Find its leading coefficient of a.
(13)
-1/6
Give the equation of the horizontal asymptote, if any, of the function.
f(x) =25x^5 - 5/x - x^3
No horizontal asymptotes