Basic Math Questions and Answers

A mirror should be centered on a wall. The mirror is 36 inches wide and the wall is 18 feet wide. Which equation helps determine the distance x on each side of the mirror? A) X + 3 + x = 18 B) X = 18 + 3 C) X + 36 + x = 18 D) 3 + x + 3 = 18

27) A-Plus Advertising charges a fee of $27 plust $0.10 per flyer to print and deliver flyers. Print and More charges $0.25 per flyer. For how many flyers is the cost at A-plus Advertising less than the cost at Print and More?

Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, the ends of these mats are right triangles. If the height of the mat is 28 inches shorter than the length of the mat and the hypotenuse is 8 inches longer than the length of the mat, what is the length of the mat?

To rent a certain meeting room, a college charges a reservation fee of $14 and an additional fee of $4 per hour. The chemistry club wants to spend less than $50 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room? Use / for the number of hours. Write your answer as an inequality solved for t.

Differentiate the function, and find the slope of the tangent line at the given value of the independent variable. f(x) = 5x + 4/x, x = -5 The derivative of the function f(x) = 5x + 4/x is The slope of the tangent line at x = -5 is

A company pays its sales people a base salary of $38,500 per annum plus a commission of 12% on all sales. Stephen, one of the company's salespeople, made sales worth $105,000 in his first year. a. Calculate the commission Stephen earned during the year. Round to the nearest cent b. Calculate the total salary Stephen earned during the year.

A store pays $39.27 for a quilt. The store marks up the price by 26%. What is the new price? Round your answer to the nearest cent: $

Identify the zeros and y-intercept for the following function graphed below. a. zeros: (0, -3), (0, 5); y-intercept: (90, 0) b. zeros: (-3, 0), (5, 0); y-intercept: (0, 90) c. zeros: (5, 0); y-intercept: (0, 90) d. zeros: (0, 90); y-intercept: (5, 0)

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 70 workers to build a 80 story building? It will take years

On the planet Golgafrincham there are two systems for measuring temperature. Using the Celia scale, water freezes at 0° C and boils at 50° C. Using the Furryhat scale, water freezes at 10° F and boils at 110° F. Both systems divide the temperatures in between into equal increments. Let x be the temperature in degrees Celia and y be the temperature in degrees Furryhat. a. Find a formula which converts temperatures measured in Celia into Furryhat. y(x) = b. Find a formula which does the inverse. c. What temperature is the same in both Celia and Furryhat?

A student has student loans of $96,000. He would like to pay it back in 10 years. (10 points) a) Calculate the monthly payments if his loan has a fixed APR of 8%. b) What is the total amount that the student paid for his college education (principal and interest)?

The average cost of a 4-year college education is projected to be $130,000 in 20 years. How much money should be invested now at 8% compounded quarterly to provide $130,000 in 20 years?

Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous f(x)= (2x-2) / (x2+2x-3) is discontinuous at x =

A student has student loans of $96,000. He would like to pay it back in 10 years. a) Calculate the monthly payments if his loan has a fixed APR of 8%.

For each sum or product, determine whether the result is a rational number or an irrational number. Then choose the appropriate reason for each. Result is Rational Result is irrrational reason (a) 2/11 + 17/19 (b) 16+√13 (c) 20 + 8/9 (d) √2+38

If y=ex is reflected about the x-axis, what is the formula for the resulting function? y = help (formulas)

Suppose that $10,000 is invested at an APR of 6% for 4 years. a) Determine the accumulated balance assuming that interest is compounded annually. b) Determine the accumulated balance assuming that interest is compounded monthly. c) Determine the accumulated balance assuming that interest is compounded continuously.

Patricia receives a gross pay of $1,850 bi-weekly from his employer. If his employer changed his pay period to monthly instead of bi-weekly, calculate the monthly payment that he would receive. Round to two decimal places

Alexander, a sales representative at a jewelry store, receives a 1.50% commission for the first $12,000 in sales he makes, 3.50% for the next $25,000, and 6.50% thereafter. If he was paid $2,000.00 in commissions last month, calculate the amount of sales he made.

A school superintendent purchase a new car for $26,788. A. If the sales tax is 7.75%, find the amount of sales tax. The sales tax is B.The superintendent makes a $3000 down payment and the license fee is $145. Find the amount the superintendent must finance. The amount financed is C. Assuming the superintendent gets the loan for the amount in part B at an annual interest rate of 8.1% for 5 years, determine the superintendent's monthly car payment. The monthly payment is

If you drive 23 miles south, make a turn and drive 39 miles east, how far are you, in a straight line, from your starting point? Round your answer to the nearest tenth of a mile. If a 12-foot ladder is leaned against the top of a 10-foot high wall, how far will the base of the ladder be from the bottom of the wall? Round your answer to the nearest tenth of a foot.

Cabinet X costs $60, requires 12 sq ft of floor space, and holds 24 cu ft of files. Cabinet Y costs $50, requires 6 sq ft of floor space, and holds 24 cu ft. To get maximum storage, how many of each should be purchased with a budget limit of $600 and floor space of 96 sq ft?

Which of the following is true about the graph of f(x) = 6x³ - 12x² + 6x - 7? a) f(x) has a local minimum at the point (1/3 , -55/9) b) f(x) is decreasing on the interval (1/3, 1). c) f(x) has a local maximum at the point (1, -7). d) f(x) is increasing on the interval(2/3 ,infinity) e) f(x) has a point of inflection at the point (1, -7).

For a given input value x, the function h outputs a value y to satisfy the following equation. 6x + y = 4x + 11y Write a formula for h(x) in terms of x. h(x) =

Christine is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges an initial fee of $77.50 and an additional 30 cents for every mile driven. Company B charges an initial fee of $45 and an additional 80 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using m for the number of miles driven.

Identify the transformation equation below for the following function: f(x) = x²→ shifted 2 units right & up 2 units Select one: a. f(x) = (x + 2)² + 2 b. f(x) = (x - 2)² + 2 c. f(x) = (2x)² - 2 d. f(x) = 2(x)² +2

Simplify the following rational expression by subtracting, then identify the simplified form below. 6/x2-1 - 3/x+1 Select one: a. x²+1 / (x-3)(x+3) b. 3x²/ (x-1)(x+1) c. x-3 / (x²-1)(x²+1) d. -3x+9 / (x-1)(x+1)

List the roots of the parabola: y = -x² + 20x - 7 In other words, list the solutions of the equation: 0= -x² + 20x - 7 x= Your answers must be in exact form, do not give their decimal values. Separate multiple roots with a comma.

This polynomial is not factorable, so you need to use the complete the square method. Solve the equation for x. x² + 2x - 12 = 0

An exponential function f(x) = ab^x passes through the points (0, 4000) and (3, 108). What are the values of a and b? a = b=

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.) y = 18(1.15)^x y = 18(0.15)^x y = 20.7(1.15)^x y = 20.7(0.15)^x

Write an expression that represents the total cost of making roughly 16 coffees at home and occasionally going to Starbucks (use x to represent the number of mochas). What does each part of your expression represent? Don't forget to define your variable.

Mr. Parker had $86 to buy school supplies for his class. He bought 32 boxes of pencils and 32 packages of notebook paper. Each package of paper cost $1.09, and each box of pencils cost $0.75. How much money did Mr. Parker have left?

f(x)=√(x-4) Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.

Greg is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A has no initial fee but charges 70 cents for every mile driven. Company B charges an initial fee of $55 and an additional 20 cents for every mile driven. For what mileages will Company A charge more than Company B? Use m for the number of miles driven, and solve your inequality for m.

Bloomington is a growing industrial town. Every year, the level of CO₂ emissions from the town increases by 6%. If the town produced 186,000 metric tons of CO₂ this year, how much will be produced 5 years in the future? If necessary, round your answer to the nearest whole number.

The rabbit population in a forest area grows at the rate of 9% monthly. If there are 160 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use y-160(2.7)^0.09t 481 455 468 467

You want to start a summer business to earn money. What will you do? You have to consider how much money you can afford to invest in this business, how much it will cost you to make each item, and how much you're going to charge for each item. Research something that would be reasonable to make and sell with the start- up investment you have determined. a. What is the total amount of money you are willing to invest in this business? b. What item are you going to make and sell? Why? c. Describe how your business will work. How much will it cost you to make each item? How much will you sell each item for? d. Do you think your business will be profitable? Explain your answer.

A geneticist conducts an experiment with peas, one sample of offspring consisted of 458 green peas and 149 yellow peas. Based on these results, estimate the probability of getting an offspring pea that is green. Report the answer as a percent with one decimal place accuracy. (You need not enter the "%" symbol) Probability Is the result reasonably close to the value of 3/4 that was expected? yes no

Raina is choosing between two exercise routines. In Routine #1, she burns 21 calories walking. She then runs at a rate that burns 10.25 calories per minute. In Routine #2, she does only running, burning 15.5 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3 mph greaterbthan the speed of the eastbound train. After 3.5 hours, they are 567 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions. AnswerHow to enter your answer (opens in new window) westbound train: eastbound train:

James receives a gross pay of $1,550 bi-weekly from his employer. If his employer changed his pay period to monthly instead of bi-weekly, calculate the monthly payment that he would receive.

A fish tank of 82 fish is made up of three types of fish. There are 41 betta fish, 18 goldfish and some rainbow fish. How many rainbow fish are in the tank?

Amanda is earning extra money over the summer mowing lawns around her neighborhood. She would like to earn at least $450. She charges $15 for a small yard and $26 for a larger yard. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. . x = the number of small yards mowed . y = the number of larger yards mowed 15x - 26y> 450 26x + 15y > 450 15x + 26y ≥ 450 15x + 26y≤ 450

Kenneth invested his savings in shares of a new company. The company's share price dropped by $1.00 at the end of the first year, and by a further $0.75 at the end of the second year. The share price was $21.63 at the end of the second year. a. Calculate the original share price (at the beginning of the first year). b. Calculate the percent change in the share price over the two-year period.

Marwin is selling handmade toys in an online craft boutique. She hopes to earn more than $150 by selling toy planes for $8 each and toy tractors for $12 each. Use the following variables to write an inequality that represents the scenario. . x = the number of toy planes . y = the number of toy tractors

Vail Ski Shop received a $1,210 invoice dated July 17 with 3/10, 2/15, n/60 terms. On July 31, Vail sent a $494 partial payment. a. What credit should Vail receive? (Round your answer to the nearest cent.) b. What is Vail's outstanding balance? (Round your answer to the nearest cent.)

Find five solutions of the equation. Select integer values for x, starting with - 2 and ending with 2. Complete the table of values below. y = − x + 4

A video rental company offers a plan that includes a membership fee of $5 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $25 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? Write a system of equations, graph them, and type the solution.

Macy of New York sold LeeCo. of Chicago office equipment with a $7,100 list price. Sale terms were 1/10, n/30 FOB New York. Macy agreed to prepay the $20 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?