Quadratic equations Questions and Answers

3x 8x 4 3x 10x 8

Given the rational expression shown below select all the statements that are true about the completely simplified form of this rational expression 4x 5 x 2 2 x 3 x 3 A The numerator is 6x 1 B The denominator is 2 x 3 C The numerator is 5x 3 D The denominator is 3x 5

x 8 x2 9x 8 Simplify the given expression

Which function is graphed to the right A f x 3 1 x 2 B f x 2 c f x x 2 6 5 4 3 2 1 6 0 1 2 TV TY 2 4

equation algebraically 619 6 3x

1 3 x 4 2 2

3 5 9 V 4 V 12 3 7p 5 27 4 7 5t 13 25 6 14 13y 20y 21

Kelsey is 5 years older than her sister Misty The product of their ages in years is 84 How old is Misty Drag the answers into the boxes to correctly complete the statements The equation years old where m is the Misty s age in years can be used to solve this problem Misty is

The length of a rectangle is 3 inches shorter than its width The perimeter of the rectangle is 50 inches What are the length and width of the rectangle Drag the answers into the boxes to correctly complete the statements The equation the rectangle is 5 73 8 73 11 12 5 where w is the width of the rectangle can be used to solve this problem The length of inches and the width of the rectangle is 14 2 w 3 2w 50 2 w 3 2w 50 inches w w 3 50

What type of exponential function is f x 0 75 2 1 What is the function s percent rate of change Select from the drop down menus to correctly complete each statement The function is an exponential Choose function The percent rate of change of the function is Choose

Which graph represents the polynomial function y 2 22 11x 12x 36 100 80 60 40 20 10 8 6 4 2 100 20 40 60 80 100 100 80 60 40 20 N 6 8 10 10 10 8 6 100 80 60 40 20 60 80 100 60

he movement of the progress bar may be uneven because questions can e worth more or less including zero depending on your answer What are the values of cos Y and cot X in the triangle below 1 3 5 34 cos Y COS Y cos Y cos Y 3 34 5 34 3 34 5 34 9 9 N cot X cot X cot X cot X 9 5 3 5 3 3 5 315

The population of bacteria in a petri dish triples every 10 minutes The population of the bacteria is initially 400 organisms What unit is most appropriate for the time at which the number of bacteria is 600 O hour O bacteria per hour O minute bacteria per minute

As the concert came to its end the number of people in a stadium decreased every 10 minutes The function p x 0 65 96 models the number of people in hundreds of thousands where x represents the number of 10 minute periods since the trend has been observed What do the values in the function represent Select each correct answer There were 650 000 people in the stadium when the trend began The number of people in the stadium decreased by 96 each 10 minute period since the trend began There were 65 000 people in the stadium when the trend began The number of people in the stadium decreased by 4 each 10 minute period since the trend began

What does the fundamental theorem of algebra state about the equation 2x2 6x 10 0 O The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2 The roots are x 3 i 11 The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2 The roots arex 3 i 11 The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the 3 II polynomial is 2 The roots are x O The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2 The roots are a 3 11

Which graph represents the system of inequalities 3x 5y 10 x y 1 5 4 3 2 1 2 5 4 3 2 1 1 2 3 45 2 3 2 5 4 3 2 1 2 3 5 4 3 2 1 2 3 2 3

What is 2 log logy 2 log z written as a single logarithm O log O log 21 2yz 7 yz O log 22 log no zz

Solve for x 6x 2x 1 0x 0 x ti 7 Hivi Ox 1 5 Ox 1 7 6 1 i 5 6

What is the exact angle measure in radians 420 OT

Simplify 2 32 10 243 2x2 72 15 z2 9 O O 2 52 6 1 1 6 2x 3 r 5r 0 2x 3 1 x 6 2x 3

Right triangle ABC has its right angle at C AC 12 and BC 5 Which trigonometric ratios are correct Select each correct answer tan B sin B sin A cos A

Multiply 6x 15xy 20

Solve the system of equations using the substitution method y 1 x 2x 5y 6 Enter your answer in the boxes

Solve for x x 1 x Ox 25 0x 28 0 x 25

Solve for u m2 r k y 0 1 O 0 k y r 172 771 ky r m k y r ky r m

What is the simplest radical form of the expression x y x6 y 10 ng v Or y x y

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

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

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

x 1 2

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

1 3x x 2 x 2 6

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