Algebra Questions

For the following matrix A 1 1 1 1 1 1 1 1 1 a Find the eigenvalues Explain how you can determine one eigen value A without any calculations b For each eigenvalue find the corresponding eigenvector s c Starting with the eigenvectors you found in b construct a set of orthonormal vectors using the Gram Schmidt procedure

olve the following system of linear equations using the substitution method 4x3 x 5x1 49 10x2 13x 30x3 10x 4x 5 4x

Compute the determinant of the following 3x3 matrix 4 1 51 8 8 7 10 7 5

Marco purchased a large can of chili that has a diameter of 18 cm and a height of 23 cm Determine the volume of the chili in the can in the following units a liters b fluid ounces Click the icon to view a set of conversion tables a The volume of the chili in the can is liters Type an integer or a decimal Round to three decimal places as needed

Rewrite the ratio so that the units in the numerator and the denominator are the same Use values in terms of the smaller measurement unit Then write the ratio in fraction notation expressing the fraction in simplest form 44 hours 4 days Write the ratio with the smaller measurement unit 44 hours 4 days Do not simplify JOT I C

Explain how to use the rate 5 ounces Choose the correct answer below to write a unit rate O A Multiply the numerator and the denominator by the quantity in the numerator B Divide the numerator and the denominator by the quantity in the denominator C Multiply the numerator and the denominator by the quantity in the denominator D Divide the numerator and the denominator by the quantity in the numerator

Write the rate as a fraction in simplest form 370 robberies per 100 000 residents Select the correct answer below and fill in the answer boxes to complete your choice Simplify your answers OA The rate written as a fraction in simplest form is OB The rate written as a fraction in simplest form is residents robberies robberies residents

Find the quotient of 7 8 10 7 8 10 Type an integer or a decimal

Find the product 0 05x0 01 0 05x0 01 Type an integer or a decimal

Multiply 4 5 0 1 4 5x0 1 Type a whole number or a decimal

20 21 Part 1 Evaluate G 1 20 1 point Part 2 Evaluate G 2 40 1 point Part 3 Calculate G 1 G 2 4 G 1 10

The function f is defined as follows f x 3 int x a Find the domain of the function b Locate any intercepts c Graph the function d Based on the graph find the range A The intercept is 1 0 B The intercepts are x 0 for 0 x 1 C There are no intercepts c Choose the correct graph below A o Ly O B 37 O C 5 Q N O D

If f x int 3x find a f 3 9 b f 2 3 c f 1 4 a f 3 9 11 Simplify your answer b f 2 3 6 Simplify your answer c f 1 4 9 Simplify your answer

Square function Constant function Absolute value function Identity function

Find the average rate of change of f x x 9x 3 over the following intervals a From 5 to 4 b From 3 to 5 c From 5 to 6 a The average rate of change from 5 to 4 is 52 b The average rate of change from 3 to 5 is

At a particular restaurant 63 of all customers order an appetizer and 58 of all customers order dessert If 49 of all customers order both an appetizer and dessert what is the probability a randomly selected customer orders an appetizer or dessert or both Write your answer as a decimal not as a percentage 0

local college 91 of the male students are smokers and 609 are non smokers Of the female students 284 are smokers and 426 are non smokers A male dent and a female student from the college are randomly selected for a survey What is the probability that both are non smokers not round your answer E

A box has 11 candies in it 3 are butterscotch 2 are taffy and 6 are peppermint Each candy falls into only one of these categories Linda wants to select two candies to eat for dessert The first candy will be selected at random and then the second candy will be selected at random from the remaining candies What is the probability that the first candy selected is butterscotch and the second candy is taffy Do not round your intermediate computations Round your final answer to three decimal places E G

An automobile manufacturing plant produced 38 vehicles today 15 were vans 11 were sedans and 12 were trucks Each vehicle falls into only one of these categories Plant managers are going to select two of these vehicles for a thorough inspection The first vehicle will be selected at random and then the second vehicle will be selected at random from the remaining vehicles What is the probability that two sedans will be selected Do not round your intermediate computations Round your final answer to three decimal places

Of the people who fished at Clearwater Park today 36 had a fishing license and 4 did not Of the people who fished at Mountain View Park today 27 had a license and 3 did not No one fished at both parks Suppose that one fisher from each park is chosen at random What is the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license Do not round your answer O

Given the function f x 2 x calculate the following values f x 1 f x f 3

Ten balls numbered from 1 to 10 are placed in a bag Some are grey and some are white as shown below 345 8 Answer the following questions Write each answer as a fraction A ball will be randomly selected a What is the probability that the selected ball is white 0 b What is the probability that the selected ball is white given that the in loss than 92 00

f f x int 3x find a f 3 9 b f 2 3 c f 1 4 30 Simplif

ind the average rate of change of f x x 9x 3 over the following intervals a From 5 to 4 b From 3 to 5 c From 5 to 6 The average rate of change from 5 to G

Which one of the library of functions discussed has no intercepts Choose the correct answer below O A The square root function O B The reciprocal function O C The constant function D All of them had an intercent

Reciprocal function Square root function Cube root function Cube function Square function Constant function Identity function Absolute value function Drag the function to the appropriate area below

Complete the sentence below When functions are defined by more than one equation they are called When functions are defined by more than one equation they are called functions functions

Complete the sentence below The function f x x is decreasing on the interval

10 Solve the equation by completing the square x 13x 30 0 To complete the square what number should be added to both sides of the equation 169 4 Question 3 1 5 55 Setup Solve Part 2 of 2 Type an integer or a simplified fraction The solution set is Type an integer or a simplified fraction Use a comma to separate answers as needed www

There used to be a program in the Salt Lake valley where the electric company would pay customers who installed solar panels and contributed electricity to the grid A homeowner installed a solar panel system and made a contract with Rocky Mountain Power to sell them electricity Create a model which shows the cost of the system to the homeowner over time Here is information to use in this model This Salt Lake area gets an average of 8 hours of sunlight each day The system consists of 29 panels that each produce 380 Watts of power for each hour of sunlight 380 Watts 0 38 kilowatts The cost of the system was 21 200 Y The homeowner uses an average of 20 kWh each day for their home The rest they sell to Rocky Mountain Power at a rate of 0 13 for each kWh kilowatt hour a Find a linear equation that gives the total cost y of the panels after x days of use Enter the equation in slope intercept form y mx b You may write the slope as a decimal OR an unsimplified expression Recommendation Use the given information to determine how much the homeowner receives from Rocky Mountain Power each day Negating this will give you the slope b In how many days will the payments from Rocky Mountain Power pay for the system Round UP to the nearest day c In how many years will the payments from Rocky Mountain Power pay for the system Round UP to the nearest year Use 365 days 1 year

Solve each question Round your answer to the nearest hundredth 6 Asanji can wax a floor in 9 minutes One day his friend Maria helped him and it only took 5 63 minutes How long would it take Maria to do it alone A 10 91 minutes C 12 82 minutes By 15 04 minutes Dy 12 18 minutes 7 7 Working alone it takes Julio 12 hours to pick forty bushels of apples Molly can pick the same amount in 9 hours Find how long it would take them if they worked together A 6 29 hours C 4 23 hours zoom i B 6 51 hours D 5 14 hours

5 Solve each question Round your answer to the nearest hundredth 6 Asanji can wax a floor in 9 minutes One day his friend Maria helped him and it only took 5 63 minutes How long would it take Maria to do it alone A 10 91 minutes C 12 82 minutes 8 Darryl can wax a floor in 10 minutes Asanji can wax the same floor in 15 minutes How long would it take them if they worked together A 6 19 minutes C 5 41 minutes B 15 04 minutes D 12 18 minutes A 4 24 hours C 3 7 hours B 7 14 minutes D 6 minutes 10 Working alone it takes Abhasra eight hours to mop a warehouse Jack can mop the same warehouse in nine hours If they worked together how long would it take them B 3 17 hours D 3 13 hours 7 9 7 Working alone it takes Julio 12 hours to pick forty bushels of apples Molly can pick the same amount in 9 hours Find how long it would take them if they worked together A 6 29 hours C 4 23 hours A 16 42 minutes C 14 58 minutes B 6 51 hours D 5 14 hours 91 Working together Norachai and Scott can sweep a porch in 7 24 minutes Had he done it alone it would have taken Scott 14 minutes Find how long it would take Norachai to do it alone B 14 99 minutes D 11 45 minutes

8 Darryl can wax a floor in 10 minutes Asanji can wax the same floor in 15 minutes How long would it take them if they worked together A 6 19 minutes C 5 41 minutes B 7 14 minutes D 6 minutes 9 9 Working together Norachai and Scott can sweep a porch in 7 24 minutes Had he done it alone it would have taken Scott 14 minutes Find how long it would take Norachai to do it alone A 16 42 minutes C 14 58 minutes B 14 99 minutes D 11 45 minutes D

An acid solution was made by mixing I gal of a 30 acid solution and 9 gal of al 20 acid solution What is the concentration of the mixture A 25 C 18 B 20 D 21

1 06 02 HC Let 135 Part A Determine tan using the sum formula Show all necessary work in the calculation 5 points Part B Determine cos using the difference formula Show all necessary work in the calculation 5 points AA AFE E OD BU Font Family I

4 06 05 06 06 HC Students were asked to prove the identity cot x cos x csc x sinx Two students work is given Student A Step 1 Step 2 COS X sinx Step 3 cos x sinx COS X CSCX sinx Step 4 1 1 sin x sinx sinx CsCx sinx eex sinx sin x sinx Student B Step 5 csc x sinx cscx sinx Step 1 cotxcos X Step 2 cotx cosx W cscx sinx Step 4 cotx cos x sin sin Step 5 cotx cos x 1 sinx sinx sinx Step 3 cotxcos x 1 sin x sinx cos x sinx COSX sinx COSX Step 6 cotx cosx cot x cos x Part A Did either student verify the identity properly Explain why or why not 10 points Dart B Name two identities that were used in Student A s verification and the steps they appear in 5 points

3 06 06 HC The difference in length of a spring on a pogo stick from its non compressed length when a teenager is jumping on it after 8 seconds can be described by the function f 6 2c0s8 5 Part A Determine all values where the pogo stick s spring will be equal to its non compressed length 5 points Part B If the angle was doubled that is became 28 what are the solutions in the interval 0 2n How do these compare to the original function 5 points Part C A toddler is jumping on another pogo stick whose length of their spring can be represented by the function o 0 1 sin 5 At what times are the springs from the original pogo stick and the toddler s pogo stick lengths equal 5 points BU Font Family AA A OFE

What are the key features of the function below 2 A 2 lo Positive Intervals X Negative Interval and Type your answer in interval notation without spaces use inf for infinity For example 2 inf Type your answer in internotation without spaces use inf for infinity For example 2 inf

What are the key features of the function below Domain Range X Intercepts Y Intercept 2 JO ty X 4 Type your answer in interval notation without spaces use inf for infinity For example 2 inf Type your answer in interval notation without paces use inf for infinity For example 2 inf Type your answers as coordinate points without spaces from left to ri Type your answer as a coordinate point without spaces For example 17 6

Question 1 Imagine reflecting triangle ABC across line MN Then answer the questions about the reflected figure B Part A N

The Venn diagram below shows the 9 students in Mr Martinez s class The diagram shows the memberships for the Softball Club and the Tennis Club Note that Abdul is outside the circles since he is not a member of either club One student from the class is randomly selected Let A denote the event the student is in the Softball Club Let B denote the event the student is in the Tennis Club a Find the probabilities of the events below Write each answer as a single fraction P A P B P A and B P A or B P P R P A and B Abdul ola X Softball Donna Josh Isabel Eric Charlie Tammy Kaitlin Tennis Michael

a Find f 0 f 0 b Find f 1 f 1 c Find f 3 3 5 8 75 2 10 5 0 5 2 4 powered by desmos

1 Graph on graph paper or a coordinate plane lined paper will not earn credit List the domain and range in interval notation a 1 if x 0 f x 2x if 0 x 3 6 if x 3 b f x x 51 c f x 2x 41 6

company is ordering booklets to promote their business The manufacturer charges 0 50 for each booklet when 50 or fewer are ordered 0 45 for each booklet when 51 to 100 booklets are ordered 0 40 for each booklet when 101 to 250 booklets are ordered and 0 35 for each booklet when 251 or more booklets are ordered Each order consists of a 10 shipping charge no matter the size of the order a What is the cost of purchasing 50 booklets b What is the cost of purchasing 252 books Check PARKING The rates at a short term parking garage are 5 00 for 2 hours or less 10 00 for 4 hours or less 15 00 for 6 hours or less and 20 00 for 8 hours or less Draw a graph that represents the charges State the domain and range Domain Range Check

x Function A 0 1 10 20 700 750 1200 1700 e the sentences to compare the two functions A appears to grow exponentially es the quantities for Function A Function B 600 624 888 1315 rounded value Function B appears to grow exponentially As will eventually exceed the quantities for Function B

Match the function with the correct domain a f x x b f x x c f x x d f x x e f x x f f x 10 9 f x log x h f x Domain 1 00 Domain 2 0 U 0 Domain 3 0 Domain 4 0 Function a Function b Function c Function d Function e Function f Function g Function h Choose Choose Choose Choose Choose Choose Choose Choose

1 Describe each transformation as it relates to the parent graph a y x 3 b y x 5 c y 4lx d y 2x e y 2 x 1 4 2 Use the graph of each translated parent function to write its equation na 10 O IN dhy

Match the function with the correct range a x x b f x x c f x d f x x e f x x f f x 10 g f x log x h f x Range 1 x Range 2 00 0 U 0 Range 3 0 Range 4 0 Function a Function b Function c Function d Function e Function f Function g Choose 11 Choose Choose Choose Choose Choose G Choose

Match the graph with the correct name and parent function A E B Rational f x F Absolute Value f x x 1 X C G Choose Choose Quadratic f x x Choose Radical Square Root f x x Choose Linear Identity f x x Logarithmic f x log x Exponential f x 10 Cubic f x x Choose Choose Choose Choose D H f Thy

eneral Form f x a x h k h is negative the graph shifts h units to the h is positive the graph shifts h units to the k is positive the graph shifts h units to the k is negative the graph shifts h units to the a there is a vertical stretch there is a vertical compression negative in front of the grouping symbol reflects the graph across the a