Algebra Questions

What are the roots of the polynomial equation x x 7 x 9 0 Select each correct answer 0 9 0 7 0 DO 2

How many A B floor boards 2 1 4 inches wide are needed to cover a floor 15 feet wide 34 64

Section A of a theater contains 12 rows of 15 seats each Section B contains only 10 rows but has the same total number of seats as Section A How many seats are in each row of Section B A B 8 9

Ex 3 The volume in cubic inches of a rectangular box can be expressed as the product of its three dimensions LxWxH and with the function V x x 16x 79x 120 The length of the box is x 8 Find possible width and height expressions

1 Find the quotient x 3 x 5x 6x 9 x3 0 3 x 5x 6x 9 x 3 0 6x 9

Ex 2 Find the quotient 8x3 27 4x 6x 9

Dept 109 85 Garden Shop Menswear PAYMENT Appliances Billing Date 2 16 71 Description Previous Payments Balance Credits 285 92 a Check c Find the new balance Charges 42 75 145 98 Unpaid Balance Payment Credit 74 40 35 50 Finance Charge 4 29 Date b 1 25 1 25 2 01 2 02 New Purchases Ref 6004 7018 8014 3113 Maria Azario received the charge account statement partially shown above a Find payments and credits b Find new purchases New Balance

EXTRA CREDIT Determine whether y 5 x 2x is a one to one function Make sure you support your answer mathematically

Solve the following system of equations graphically on the set of axes below 10 9 8 7 Plot two lines by clicking the graph Click a line to delete it 6 y x 5 5 2x y 7 4 3 2 1 y 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10

2023 Kuta Software LLC All rights reserved Radicals and Rational Exponents 2 Write each expression in radical form 1323 A 3x C 5x 33 1 3 6x A 6x C 4x A 7n 5 C 6n Write each expression in exponential form 4 3n 6 10k A 10k 4 C k Simplify 7 n 3 A n C n B x D x 9 9a A a C 6a B 3x D 7x B 3n 4 D 7n B 5k D 6k B 9n D n B 3a D 6a 2023 Kuta Software LLC 22 x A 4x C x 5 5 6 A C 26 8 8 49n6 A 25n6 C 27n B 3x D x B b D b B 7n D 3125n 15 All rights reservde Made with Infinite Algebra 2

Find the quotient and remainder using synthetic division for The quotient is The remainder is Question Help Video 1 Video 2 x 4x 9x 15 x 2

x 5x 6 x 2x

Solve each rational equation algebraically x 6 x 6 x 3x 2 3x 3

35 x y 8 x y 5 S x y Yan t The Answer is 44 Yan t The Answer is 39

9x 45 x 7x x 10x 25 x2 2x 35

Vanessa and Nancy plan to make a birthday cake Working together Vanessa and Nancy can complete the birthday cake in 2 hours If Nancy works alone it will take her 3 times as long as it would take Vanessa to complete the birthday cake The equation below represents this situation 2 XIN 2 3x How many hours would it take Nancy to complete the birthday cake if she worked alone 1

1 2 2 3 1 2 5x Step 1 2 3 4 10 5 6 7 00 8 9 10 Work 1 5x 5x 5x 5 x 0 5x 5 5x 5x5x 5x 5x 5x 5x 5x 5 5x 25x 25x 5x 25x 20x 0 5x 5x 1 0 4 x 0 x 5 The solution is ONLY x 45 explain the reasoning behind each step Reason

Kevin can clean a large aquarium tank in about 7 hours When Kevin and Lara work together they can clean the tank in 4 hours Write and solve a rational equation to determine how long to the nearest tenth of an hour it will take Lara to clean the tank if she works by herself Explain whether the answer is reasonable Round to the nearest tenth of an hour

the problem Cesar and Natalie want to clean their house Working together Cesar and Natalie can clean their house i 3 hours If Natalie works alone it will take her twice as long as it would take Cesar to clean the house alone How many hours would it take Natalie to clean their house if she worked alone

What is a possible first step to solving the rational expression 3 x 2 3 2x 4 2x 4 Find the common denominators Cross multiply Use the quadratic formula Add the numerator and denominators

x 1 2

x x x 2 4 x2 2

Find the quotients and any excluded value 4x 8x x 2x 1 16x 32 x 1

1 3x x 2 x 2 6

Solve each rational equation algebraically 1 1 1 2 1 12 x 2x x2

Solve each rational equation algebraically 8 x 1 x 3 X 6 E

Find the product and any excluded values 4x 20x 9x 3 xX 5

Find the LCD for each set of rational expressions 3x 12 x 4x 5 and 6x 18 7x 7

Rewrite the function in the form g x a k and graph it Also state the domain and range using inequalities 4x 15 2x 6 to 10

Find the quotients and any excluded values x 11 2x 6 4x x 2x 3

20 x 7x 5x 40x x 15x 56

Put the numbers into the boxes to represent the sum of the rational expression given below 10x 1 3x 1 16x 6 3x 1 2 26 6 x 0 0x 0 Solution Box 3 6 5

Find the LCD for each set of rational expressions and 2x 16

Combine the rational expression into a single fraction and reduce it in lowest terms X x 2x 24 11 x 3x 28

x x 3 3 x 3

x x 9 3x 27 x 1

1 x 3x 4 1 x2 2x 8

Find the products and any excluded values x 9 X 8 x2 5x 24 2x2 18x

2 x 9 x 3

1 Itz

iven the rational expression shown below select all of the statements that are true about the completely simplified form of this rational expression 3 X 4 3x 2 3x 2x A The denominator is 3x 5x 2 B The denominator is 3x 2x C The numerator is x 7 D The numerator is 2x 4

Simplify the following expressions x 1 x 1 x Se

2x 7x 4 x 10x 24

Simplify the given expressions 5x 5 x 8x 7

9x 1 3x2 5x 2

Simplify the following expressions

Amy has purchased a basic letterpress kit for 140 She plans to make wedding invitations She estimates that the cost of the paper and envelope for each invitation is 2 Model this situation with a rational function that gives the average cost of a wedding invitation when the cost of the kit is included in the calculation Use the graph of the function to determine the minimum number of invitations that brings the average cost below 5 2w 140 W Given C w represents the average cost in dollars of a wedding invitation when the cost of the kit is included graph it using key features Then select two choices that are true about the function C w A There is a zero at 2 B There is an asymptote at x 0 C There is an asymptote at y 2 D There is a y intercept at 2 Average cost dollars 876543N 0 c W 20 40 60 80 Number of invitations A zero implies an x intercept

35 n 4n 4 2n 2 2 1 8n 5 4 3 2 1 0 1 3 4 5 36 4 6 4n 6n 4n 2 8 4n 7 6 5 4 2 1 0 2 3

31 8 6a 3 2 26 2a 7 6 4 3 2 1 0 1 2 3 32 5 7b s 6 46 6 H 1 0 1 2 3 4 5 6 7 8

33 21 3 x 4 2 5x 1 3 2 1 0 1 2 3 4 5 6 7 34 67 7 5x 3 6 6 5x 10 8