Algebra Questions

The number of items in millions that a company sold from 1998 through 2004 is modeled as N x 0 1x x 3x 4 and the average price per item in dollars as P x 0 2x 5 where x represents the number of years since 1998 Write a polynomial R x that can be used to model the total revenue for 81 this company Hint R x N x P x

15x 2

actoring the polynomial by group x 3x 3x 9

4x316x 20x

10x 490x

Factor the polynomial by grouping x3 3x x 3

2 64x 81

Factor the following polynomials or identify it as irreducible 8x 125 Below is a list cube roots 1 1 8 2 27 3 64 4 125 5 216 6 343 7 512 8 729 9 1000 10

30x6 72x4

Factor the polynomial 3x3 7x 4x or identify it as irreducible

A rectangle has a length of 2x 9 and a width of x2 3x 4 What is the polynomial that models the are of the rectangle A x 5x 13 B 2x 15x 19x 36 C 2x 3x 35x 36

2 12x 21X 8X 14 72x 56x 36x 28

Simplify by performing the following polynomial multiplications 4x 2 6x x 2

A biologist has found that the number of branches on a certain rare tree can be modeled by the polynomial b y 4y y where y is the number of years after the tree reaches a height of 6 feet The number of leaves on each branch can be modeled by the polynomial y 2y 3y y Write a polynomial describing the total number of leaves on the tree

A rectangle has a length of x and a width of 5x 4x What is the polynomial that models the perimeter of the rectangle A 10x 2x 2x 8 B 10x3 8 C 5x4x 4x

Perform the following polynomial multiplications 3 2x 4 7x 5x

x 6 4x 8x 3

2x 23x 11 5 9x x

1080 cubic V Lwh 1080 22 2x 19 2x x 49x38x 4x 418 82 4x x 418 1 19 1080 418 Xx 1080 82x 4x3

According to the data from the U S Census Bureau for 1990 2009 the number of commercially owned automobiles in the United States can be modeled by the function A x 1 4x 130 6x 1831 3x 128141 where x is the number of years after 1990 and A x is the number of automobiles in thousands The number of privately owned automobiles in the United States can be modeled by the function P x x 24 9x 177 9x 1709 5 where x is the number of years after 1990 and P x is the number of automobiles in thousands Create a polynomial that represents the total number of automobiles owned

Which graph is sketched to the right A g x x 1 x 2 x 3 B g x x 1 x 2 x 3 C g x x 1 x 2 x 3 6 4 2 6 1 4 2 0 2

7x x 4x 10x 6x 6x x

6x5 13x 2x 11x 10x 9x

6x58x4 3 8x5 6x 3x

9x 8x 2x 2x 1 x 4

13x6 x5 6x4 7x5 6x4 5x

Add or subtract the following polynomials 4x4 3x 14 3x4 14x 8

7x 13x8x5 20x 2x5 9x

8x 3x 1 x4 4x4 x 17

17x 8x 9x7 4 2x 11x 8x 12

Given the graph of the polynomial function write the function as g x in intercept form y 4 2 O 2 X

Which angle has a cosine value of O ZA O ZB LC B 2

Mia is standing 210 yd from a radio tower The angle of elevation from where she is standing on the ground to the top of the tower is 11 How tall is the radio tower Round the final answer to the nearest tenth Enter your answer in the box A

A wooden board is leaning against a house The base of the board is 10 feet from the base of the house and the base of the board forms a 35 angle with the ground What is the length of the wooden board Enter your answer rounded to the nearest tenth in the box 17 3 ft

What is the value of cos C of 60 8 B 15

logam x and logany Prove log mn log m log n Drag the statements and reasons into the boxes to correctly complete the proof Statements 2 a m and a n 3 mn a a 4 mn a z y 5 log mn log a z y 7 6 log mn x y log a 8 log mn logm log n log mn log m log n Reasons 1 Given 2 Definition of logarithms 3 Multiplication 4 Exponent rules 5 6 Power property of logarithms 7 Logarithm property log m 1 8 Substitution log m x and log n y log mn x y log mn a x y

What is 3 In a Inb Inc written as a single logarithm 3ab In O In 3abc In ab C

What is log 21 written in expanded form O2loga log 21 O loga log 21 2 log 21 2 logr O 2log 21 log a

Solve for z In 63 In z ln 7 Enter your answer in the box Z 9

What is the logarithmic form of 9 81 O logg 2 81 O logs1 9 2 log 81 2 O log 2 9

Which expression correctly shows how to rewrite log115 using a log base of 8 log118 log 8 O log 5 log 11 log 11 log 5 log 8 log 8

3 7 to search 4 O O 5 6 Which of the following equations has NO SOLUTIONS O 7 8 2 4 3 2 O 2 34 4 2 224 Et 9

Solve for x In 5x 3 2 x Ox O x 1 e 3 5 5 e2 3

Which of the following is a complex number that is not in the set of real numbers O 8 O 2 5 C O T 3 7i

22 2a 2 2 4 4 6 4 6 a 2 3a 5 6 r 2 5r 1 3 5 v 4 6 v 7 3

Kiran and Mai are trying to figure out if this equation is an identity a b 4 a 4a b 6a b 4ab b Kiran picks several different values for a and b to test For each pair he tries the left side and the right side have the same value Since his tests all worked Kiran thinks the equation is an identity Who do you think had a better argument for why the equation is an identity Explain Mai started by using the distributive property the expression on the left side She then arranged the result to look the same a the right side Since she can write both sides the same way Mai thinks the equation is an identit

3 5 Solve show work Write your answers as complex numbers your answers should have P in them 3 x 3 25 0 4 x 6x 12 0

Find all values of x that make the equation true Find all values of r that makro the equation truo x 6 3x 9 X X 1 x 3 Sh Show your thinking

n true X x 6 3x 9 x 1 x 3

Which figure below is a graph of r x Letter 10 8 6 10 8 6 4 represents the function r x because 6 Y 2 2 2 2468 6 8 469 2 4 2 4 6 8 6 8 Describe why X 10 8 d 6 10 8 6 4 6 4 22 4 6 8 6 4 2 4 22 6 8 2 4