College Algebra Test Prep

solve the system by Gaussian elimination −x+2y−4z=8 3y+8z=−4 −7x+y+2z=1

x=0 y=44/7 z=8/7

Solve the quadratic by factoring 3x^2+18x+15=0

x=0,-1,-5

find the exact solution for; if no solution, write no solution e^2x-e^x-110=0

x=ln (11)

what is the equation for the line that is parallel to the equation and points below? perpendicular? (-3,2); 3x+5y=2

y=(-3/5x)-(19/5) y=(5/3x)+7

solve the system of 3 equations using substitution or addition 3x+2y−z=−10 x−y+2z=7 −x+3y+z=−2

(-1,-2,3)

use substitution to solve the system of equations 10x+5y=-5 3x-2y=-12

(-2,3)

use addition to solve the system of equations 3x+2y=-7 2x+4y=6

(-5,4)

find f^-1 (x) f(x)= 1/ (x+2)

(1/x)-2

Find (f+g)(x) and (f/g)(x) for the function below; domain f(x)= x^2 +3x +2, g(x)= 5x+10

(f+g)(x)=x^2+8x+12; D: (-infinity, -6)u(-6,-2)u(-2, infinity)( (f/g)(x)= (x+1)/5; D: (-infinity, infinity)

2^3 * (8+4-10)

16

Factor the polynomial x^2+10x+25

(x+5)(x+5)

use the definition of a log to solve 6-2log(6x+4)=4

1

[(x-3)/(x^2+3x+2)] / [(x^2-9)/(x+2)]

1/(x+1)(x+3)

order of operations 6(4+3)÷2*3+1

64

find the domain of this function f(x)= [(x-4)] / [(x^2-4x-12)]

Domain: (-infinity, -2)u(-2,6)u(6, infinity)

a man has 72ft of fencing to put around a rectangular garden. If the length is 3 times the width, write the equation to solve this..

P=3w

Find the distance and midpoint between two points (-4,5), (-2,3)

d=√8; midpoint=(-3,4)

Find (f∘g)(x) and (g∘f)(x) for the function below; domain f(x)=4-x, g(x)=-4x

f(g(x))= 4+4x; D: (-infinity, infinity) g(f(x))=-16+4x; D: (-infinity, infinity)

Find (f∘g)(x) and (g∘f)(x) for the function below; domain f(x)=√(x+2), g(x)=1/x

f(g(x))=√[(1/x)+2]; D: (0, infinity) g(f(x))= 1/ (√(x+2)); D: (-2, infinity)

use the definition of a log to solve -5log7(10n)=5

n=1/70

is this function one-to-one? f(x)= (x-2)^2

no

write an equation for a line passing through (-2,1) and (4,2)

y= (1/6)x+ (4/3)

simplify i^3145

√-1

write the system of linear equation from the augmented matrix [1 0 -3| 7] [0 1 2| -5] [0 0 0| 0]

x-3z=7 y+2z=-5

solve the quadratic by the quadratic formula 16x^2+4x-1

x= (-1 +- √5)/8

Solve the quadratic by completing the square x^2+8x-5=0

x= -4 +- √21

solve the quadratic by the method of your choice x^2=10x+3

x= 5 +- 2√7

simplify 8/ (2-3i)

(16+24i)/13

Find f^-1(x) f(x)= 9+10x

(x-9)/10

simplify i^-3

-(1/i)

Find the slope of the line f(x)= -3x+7

-3

rewrite log17(4913)=x as an equivalent exponential equation

17^x=4913

solve the log below 2log4(2)-4log4(2)+log4(1/64)

2

simplify (3+2i)(4-5i)

22-7i

expand the log below log [(r^2s^11/t^14)]

2log(r) + 11log(s)-4log(t)

expand the log below log √a^6b^-3

3log(a)-(3/2)log(b)

perform the given operation and simplify (6a^2+3a+10)−(6a^2−3a+5)

6a+5

factor 4x(x-1)^4 + 3(x-1)^3

[(x-1)^3]*[(4x(x-1)+3)]

simplify (x/y)+(2/x)

[(x^2)/(xy)] + [(2y)/(xy)]

use the matrices below to preform the indicated operations A= [-8 -5] [4 4] B= [-7 -3] [6 -1] C= [8 4] [-1 -5] A+B-C

[-23 -12] [11 8]

write the augmented matrix from the system of linear equations x+3z=12 −x+4y=0 y+2z=−7

[1 0 3| 12] [-1 4 0| 0] [0 1 2| -7]

perform the operations with the given matrices A= [4 -2] [1 3] B= [6 7 -3] [11 -2 4] C= [6 7] [11 -2] D=[1 -4 9] [10 5 -7] [2 8 5] A+C

[10 5] [13 1]

perform the operations with the given matrices A= [4 -2] [1 3] B= [6 7 -3] [11 -2 4] C= [6 7] [11 -2] [14 0] D=[1 -4 9] [10 5 -7] [2 8 5] 10A-6C

[4 -62] [-56 42]

definition of a function

any value of x having only 1 y value

verify that f and g are inverse functions f(x)= 1/(x-2) g(x)= (1/x)+2

inverse; f(g(x))=x; g(f(x))=x

condense the log below 4log(a)- 1/2log(b)+ 2log (c)

log (a^4)/((b^1/2)*(c^2))

rewrite a^(-2/5)=b as a logarithmic equation

log(a)b=-2/5

condense the log below 3log7(v)+6log7(w)−(log7(u))/3

log7 ((v^3w^6)/(3√u))

find the slope of a line that passes through (8,12) and (-9, 1)

m=-11/-17

perform the given operation and simplify (m−2)(m^2+2m−3)

m^3 - 7m + 6

is this relation a function? {(4,8),(7,3),(7,8),(6,5)}

no explanation: the y value 8 is shared by two x values; (4,8) and (7,8)

determine whether the ordered pair is a solution to the system of equations (-1,1) 3x-y=4 x+4y=-3

not a solution

verify that f and g are inverse functions f(x)=3x-2 g(x)= -1/3x+2/3

not inverse; f(g(x))=-x; g(f(x))=-x+4/3

perform the operations with the given matrices A= [4 -2] [1 3] B= [6 7 -3] [11 -2 4] C= [6 7] [11 -2] [14 0] D=[1 -4 9] [10 5 -7] [2 8 5] CD

undefined; dimensions do not match # of columns in the first matrices must match the # of rows of the second matrix

find the vertex, x-intercepts, and y-intercepts x^2+6x+3

vertex: (-3,-6) x: (-3 +- √6, 0) y: (0,3)

find the vertex, x-intercepts, and y-intercepts x^2-6x+5

vertex: (3,-4) y: (0,5) x: (1,0) or (5,0)