Basic Math Questions and Answers

1 Identify the rules of exponents showing in the problem 2 Simplify the expression 83

Consider the following function y 2 3 1 Select all statements that are true The function is showing decay O The range is 1 infinity The horizontal asymptote is y 1 The y intercept is 1 0

Consider the following function y 5 8 Select all statements that are true The Range is 8 0 The domain is all real numbers O The y intercept is at 0 8 The function is showing growth

Verify the identity sin 0 1 cot 0 To verify the identity start with the more complicated side and transform it to look like the other side Choose t correct transformations and transform the expression at each step sin 0 1 cot 0 sin 0 Apply the appropriate even odd identity Apply a Pythagorean identity Apply a quotient identity

18 Samantha thinks that the equation x 4 y 3 25 is equivalent to the equation x 4 y 3 5 Is she correct Are the two equations equivalent Explain how you know If they are not equivalent explain Samantha s mistake

Find the roots the solutions when y 0 of each of the following polynomial functions y x 6x 8 a b f x x 6x 9 C y x 4x

20 Sketch a graph of y x 7 a How many roots does this graph have What are the roots of the function b

8 24 Start with the graph of y 3 then write new equations that will shift the graph as described below Down 4 units a b Right 7 units

Which of the following best explains why union membership affects the salaries of different genders O Unions allow women to be paid more than men O Unions negotiate only on behalf of certain members O Union membership is primarily dominated by men Unions set standard rates for work regardless of gender

Condense 5 In 2 7 ln x 4lny Remember to write logarithms in the form log b y type your answer

To condense the expression log 2x log y you need to use the choose your answer choose your answer Quotient Product A Property of Logarithms

Dack 20 minutes Morgan Vaugh Question 6 1

Match 6 log3 2 with the logarithm that has the same value log 12 Olog3 64 log 3 log 36

Match log 6 log3 2 with the logarithm that has the same value log 12 log 36 log 3 log 64

If m MPL 63 find each measure N M a mJK b mNJ c mJL d mKNM e mMJL f mJLK

Find the inverse y 3 10 O log x 10 Olog 10 Olog a 10 O log 10

Find the inverse y log x 3 10 O 6 10 3 O 6 10 6 3 10 6 10 3 O

Find the inverse y log x 7 0 32 7 0 4 0 4 0 3 7

Find the inverse y log 2x Of 0 5 0 10 2 10 O 5 47

Divide the following Give your answer in the form quotient 2013 13x2 19x 5 4x45 S remainder divisor if necessary

Assessment 5 Word Problem Practic P If you have questions about these problems schedule a time to meet with a tutor 1 Lori is having a Twin XL size quilt r

In Lesson 1 4 you learned about a water footprint Part of a person s water footprint is the water used for cleaning In this question you will calculate the cost of water for laundry and bathing You will use the City of New York 2022 rate of 10 61 100 cubic feet of water Calculate the cost of each of the following based on this rate Use the conversion factor of 7 48 gallons per cubic foot a A standard washing machine uses approximately 50 gallons of water per load A household washes one load of laundry per week for 52 weeks Find the total cost per year yr b According to one study the average American shower lasts for 8 2 minutes and uses 17 2 gallons A person showers once a day for a year 365 days Find the total cost per year Submit Question yr Question Help Message instructor

Score 33 33 100 10 20 answered Question 17 A person standing close to the edge on top of a 112 foot building throws a ball vertically upward The quadratic function h t 16t 96t 112 models the ball s height about the ground h t in feet t seconds after it was thrown a What is the maximum height of the ball Question Help Video feet b How many seconds does it take until the ball hits the ground seconds

NASA launches a rocket at t 0 seconds Suppose its height in meters above sea level as a function of time is given by h t 4 9t 184t 430 How high above sea level does the rocket get at its peak Round your answer to 2 decimal places The rocket peaks at meters above sea level

Question 14 We are standing on the top of a 1344 feet tall building and launch a small object upward The object s vertical position measured in feet after t seconds is h t 16t 128t 1344 What is the highest point that the object reaches feet

13 An electronics store is selling personal CD players The regular price for each CD player is 90 During a typical two weeks the store sells 50 units Past sales indicate that for every 1 decrease in price the store sells five more units during two weeks Calculate the price that will maximize revenue

3 A deck consists of 40 cards of which 9 are red Cards are dealt at random without replacement until 3 red cards have appeared Let X be the number of cards dealt Find the distribution of X

Question 8 Find the domain and range of the function f x 4x 3 The domain is TE The range is y E Enter your answer in interval notation Enter your answer in interval notation

Given the function in standard form determine all the indicated information WITHOUT USING YOUR CALCULATOR OR DESMOS COM f x 2x 42 5 1 Does the parabola open up or down O Concave up O Concave down 2 Is the vertex a maximum or a minimum Maximum Minimum 3 What is the y intercept Write answer as an x y ordered pair b 4 What is the x coordinate of the vertex Hint use formula z 2a H 5 What is the y coordinate of the vertex Hint Substitute plug in the x coordinate you

Which of the following is the axis of symmetry of y 2x 6x 3 Or 6 Ox 3 Or I 1 32 32

Given 110 9 8 matches the given graph 3 2 27 10 9 8 7 6 5 4 3 2 1 72 3 4 5 649 99 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Write the quadratic equation that

Which equation is correctly rewritten to solve for y 12y d 19y t

Graphing Quadratic Functions Complete each of the following steps for the Quadratic Function f x x 2x 1 1 Identify the coefficients a b and c a b 2 Graph the function on your calculator 3 Does the graph open up or down and why Select an answer 4 Write the Vertical Intercept as an Ordered Pair 5 Plot the Vertical Intercept on the graph using the point tool 6 Draw the function neatly on the graph using the poly tool by plotting the highest or lowest point and one other point 10 9 8 7 6 155 h f x x 2x 1 3 2 Clear All L 10 C 32 987 7 7 T 2 3 4 5 699 6 75 2 9 3 9 10 8 Draw 5 6 7 8 9 IC

Question 20 The follow table shows total dollar sales in thousands for a local retailer for various years 2019 2020 2021 2022 2023 74 102 130 158 Year Sales 46 a What was the the sales for 2020 b By how much did sales increase by each year S c Find a linear function that models the above data Let x 1 correspond to 2019 and let S x be in thousands S I X thousand d Use S z to predict sales in 2025 S If needed round answer to 5 decimal places Enter DNE for Does Not Exist oo for Infinity thousand thousand

14 The LaGelleys have 25 000 that they want to invest in a certificate of deposit Granite Trust offers a 4 year certificate of deposit that earns interest at 3 50 compounded quarterly Hancock Cooperative Bank offers a 4 year certificate that earns interest at 3 25 compounded daily a Which CD earns more interest b By how much

If f x is a linear function and given f 4 1 and f 12 4 determine the linear function a What is the slope Be sure to leave your answer in reduced fraction form b What is the y intercept fraction form c What is f x f x Question Holp Vides Be sure to leave your answer in reduced

Raul is a saver He sets aside 100 per month during his career of 40 years to prepare for retirement He does not like the idea of investing because he prefers to minimize his risk as much as possible so he puts his money in a savings account which earns 1 5 interest per year 1 What is the total balance in the account after 40 years 4657 4 90 2 than 100 How much of the total did Raul contribute himself 3 How much money did Raul make through compound interest in this savings account 48 063 84 4 Identify one way Raul could have increased the total amount of money he made over the 40 years Explain your reasoning Look for high interest rate putting mixe a menth

Your job is to build a road joining a new development to a highway that enables drivers to reach the city in the shortest time see figure How should this be done if the speed limit is 60 km h on the road and 110 km h on the highway The perpendicular distance from the development to the highway is 30 km and the city is 50 km down the houses 30 P Q city

18 At 300 per person an airline anticipates selling 300 tickets for a particular flight At 350 per person the airline anticipates selling 250 tickets for the same flight Assume a linear relation between the cost per ticket C and the number of tickets a sold Which of the following equations can be used to model the given information OC 2 605 C 1r 600 C 1x 605 OC 2x 600 Question Help Video

Write an equation for the graph below in terms of 3 Y 2 3 2 1 2 3 2 Question Help Viden 1 Video 3

the equation in terms of 2 of the line through the points 1 and 1 121

An influencer is planning a lunch banquet The equation C 760 24g models the relation between the cost in dollars C of the lunch banquet and the number of guests g Find the cost if the number of guests is 50 The cost is Question Help Duide A dollars

Write the equation of the line show in the graph below 10 8 6 Oy Oy Y T T 5454T 24 2 45 52 3 x 4 3 10 8 6 4 M 2 4 6 8 10 2 4 6 Co 8 10

Write the equation of the line show in the graph below 6 5 4 3 2 1 6 5 4 3 2 1 1 2 3 7 6 Write your equation here 1 2 3 4 5 6

Find the x intercept and y intercept of the graph of 2x 4y 8 Then graph x intercept y intercept 0 45 4 3 2 1 0 4 3 2 2 2 3 My 2 3 Las 4 5

Lisgender individuals If a patient does not subscribe to Male or Female gender they have deviated from this norm and Female under Gender This norm has been set as the standard by are often viewed as deficient less than or abnormal This is an example of O a Weathering O b Othering c GenderQueer O d Patient Participation Oe None of the above QUESTION 11 Mental health coping strategies such as Alcoholics Anonymous and Bridges are O a Self help strategies O b Psychologist led help strategies O c Internet based strategies

13 Marsha Johnson has 50 000 to invest in a 4 year CD Fifth Central Bank offers 4 50 compounded monthly while American National offers 4 50 compounded daily However Fifth Central is giving a toaster to anyone who opens a CD What will the toaster cost Marsha if she goes with Fifth Central

Select all of the following tables which could satisfy a linear equation O I 0 5 10 15 I O5 0 8 5 12 HO Y 10 32 15 52 8 33 108 233 05 Y 0 3 5 22 250 13 10 47 15 72 y 10 10 20

Is y 84x 94 increasing or decreasing O decreasing O increasing

Question 1 increase Match the description of the relationship between inputs and outputs with the corresponding type of linear function the output values increase as the input values increase the output values decrease as the input values increase the output values neither increase nor decrease as the input values