Math Study Guide

Solve the system by the addition method x+4y=-24 5x+3y=-35

(-4,-5)

Solve the system of equations by the substitution method 4x+2y=162 x-4y=0

(36,9)

Simplify by reducing the index of the radical ⁸√25x²

(5x)^¼

Solve the equation using the quadratic formula x²+3x+1=0

-3±√5÷2

For the given function f and g, find the indicated composition f(x)=-2x+2 g(x)=3x+2 (g°f)(x)

-6x+8

Rewrite the polynomial 15x²+9-8x⁴+3x³-9x in standard form. Then, identify the leading coefficient, degree, and number of terms

-8x⁴+3x³+15x²-9x+9 leading coefficient:-8 degree:4 number of terms:5

Evaluate the function at the given value of the independent variable and simplify f(x)= x²+6÷x³-5x f(x)=4

-½

Solve the Problem A car rental agency charges $175 per week plus $0.25 per mile to rent. How many miles can you travel in one week for $225?

200

Solve the formula for the specified variable A=½h(a+b) solve for a

2A/h-b=a

Divide using synthetic division -2x³-10x²-5x+12÷x+4

2x²-2x+3

Divide and express the results in standard form 5÷3-i

3/2+eye/2 eye= the imaginary number symbol

Perform the indicated operations and write the result in standard form 5√-64 + 4√-4

48i

Divide using long division 4x³-47x-33÷x+3

4x²-12x-11

Find the Product (2x-7)²

4x²-28x+49

Divide by using long division 6x+5x³-3÷x-2

5x²+10x+26 R49

Add or subtract and write the result in standard form -6-(-5-4i)-(-7-7i)

6+11i

Find the product (6x-2)(x³-3x+1)

6x⁴-2x³-18x²-2

Perform the indicated operations (7x⁴+5xy-y³)-(x⁴+9xy+5y³)

6x⁴-4xy-6y³

Simplify using properties of exponents 70x^3/2÷10x^2/3

7x^5/6

Find the Product (7x-1)(x²-5x+1)

7x³-36x²+12x-1

Add. Write your answer in standard form (6x³-7x²)+(x³+2x²-9)

7x³-5x²-9

Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line -2x+6≥-3x+8

[2,+oo)

Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line 7≤3x-2≤13

[3,5] check study guide for the graph

Solve the problem When making a long distance call from a certain pay phone, the first three minutes of a call costs $2.75. After that, each additional minute or portion of a minute of that call costs $0.50. Use an inequality to find the number of minutes one can call long distance for $3.75

m≥5

Determine whether the equation defines y as a function of x x+y²=4

no

Divide using synthetic division x²-7x+10÷x-3

x-4 R-2

Solve and Check the equation (x+6)^3/2=8

x=-2

Solve the equation by completing the square x²-14x+13=0

x=1 x=13

Solve the equation by the square root property. (x-5)²=16

x=1 x=9

Solve the equation by factoring x²+2x-48=0

x=6 x=-8

Solve the polynomial equation by factoring and then using the zero product principle x³+6x²-x-6=0

x=6 x=±1

Solve the radical equation and check all proposed solutions √7x+18=x

x=9 x=-2

Solve the absolute value equation or indicate that the equation has no solution 3|x-3|=18

x=9 x=-3

Write an expression that represents the width of a rectangle with length x-7 and area of x³-13x²+40x+18

x³-13x²+40x+18÷x-7

Simplify the exponential expression 2⁻⁸x⁻⁴y²÷2⁻⁵x⁻⁷y⁴

x³÷8y²

Simplify the exponential expression (xy⁵÷x³y)⁻²

x⁴÷y⁸

Use the given conditions to write an equation for the line in slope-intercept form Passing through (5,3) and (4,6)

y=-3x+18

y=-√x-9

yes

Express the interval in set-builder notation and graph the interval on a number line (-1,4]

{x/-1<x≤4} check study guide for the graph

Find the inverse of the one-to-one function f(x)=4x+8

¼x-2=y