Basic Math Questions and Answers

Hana paid $1,200 for the carpet in her living room. The room has an area of 251.2 square feet. What was her unit cost of carpeting in dollars per square foot? Round to the nearest cent.

Given that the polynomial f(x) has degree 4, which of the following most accurately describes the number of turning points of f(x)? Select the correct answer below: The graph of f(x) has at least 5 turning points. The graph of f(x) has at least 4 turning points. The graph of f(x) has at most 5 turning points. The graph of f(x) has at most 3 turning points. The graph of f(x) has at most 4 turning points. The graph of f(x) has at least 3 turning points.

Simplify the expression (-2) 16/(-2)5

George and Dale have been assigned the same number of math problems for homework. George has finished 20 problems, and Dale has finished 4 problems. If Dale has three times as many problems remaining as George does, how many problems was George originally assigned? math problems

Mike is baking cookies. Her recipe calls for 2/3 of a cup of milk. Mike decides she wants to tripe the recipe. How much milk is needed? Your answer: 2/9 4 1/2 1 2

Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after seconds is given by E(t) = 4000 - 60t. The equation tells us that Terry started

Suppose that $2000 is invested at a rate of 3.3%, compounded annually. Assuming that no withdrawals are made, find the total amount after 7 years. Do not round any intermediate computations, and round your answer to the nearest cent.

Write the equation of a line parallel to the line: y= -x+2 that goes through the point (5, 5). Write your equation in slope intercept form, using reduced fractions for the slope and intercept if necessary.

In this problem we aim to graph the function g(x) = -3^(-x-1) +3 by using transformations. (a) Let f(x) = 3^x. Determine the general flip shift form for the exponential function, af (b(x-c))+d= (b) Write g(x) in flip-shift form: (c) Graph f(x) = 3^x. On the same xy-plane, apply the transformations suggested by your answer from part (b). Graph each step. Mark the x and y intercepts and the horizontal asymptote

Given the polynomial functions m(x) and r(x), find m(x)+r(x). m(x) = x² + 3x²-x-2 r(x) = 2x^4 + 3x³ - 2x²-x+2 x+3x³5-x² - 4 -x^4-3x³ + 5x² - 4 3x^4 + 3x³ + x² - 2x 3x^4 + 6x³ - 3x² - 2x

If a preimage is (0,1), (4,0), (4,1), what are the points after a translation of 3 units up and then a reflection over the y-axis? (0,3), (4,3), (4,4) (0,4), (-4,3), (-4,4) (-3,0), (-3,4). (-4,4) (0.-1). (4,0), (4,-1)

A father put a dollar on the first square of an 8x8 checkerboard. On the second square, the father doubled $2, on the third $4, the fourth $8 and so on. At what square would the value be more than $1 million for the first time? The first time a square would have a value of more than $1 million would be on square

A company offers one free book download to anyone that registers. The total number of people that register can be modeled by the function f(x) = 8x³ +70x² + 145x + 182, where is the number of months passed since starting the company. The number of free books available to choose from can be modeled as 2x + 13. Write an expression that can be used to determine the average number of people that download each of the free books.

What is the range of the polynomial function f(x) = -x^4-2x³+x+1? (-∞, 1.25] All real numbers. (-∞, 3.688] (-∞, 1.25)

The Cooking Club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces to sell. How many pies did the club make? Let x =

Kerwin pulls with a force of 25 Newtons on the handle of a wagon to move it along level ground. If the handle makes an angle of 35° with the horizontal, how much work would Kerwin do by pulling the wagon 150 meters? Round your answer to two decimal places.

A large community college has professors and lecturers. The total number of faculty members is 136. The school reported that they had 6 professors for every 11 lecturers. How many professors does the community college employ?

Factor the following expression completely: 8z^15 + 12z^10 - 2z^6

Solve the following expression when g=7 and e = 5 4e+g²-3e-9-g

Solve the following expression when v = 10 and e = 5 2v ÷ e + 3

A rock is thrown downward from the top of a cliff with an initial velocity of 3 feet/sec. (Remember, the acceleration of a falling object is 32 ft/sec².) Select the function that describes the relationship between the velocity (v) of the rock and time (t). A. v=16t+3 B. v = 32 C. v = 32t +3 D. v = 32t E. v= 16t² +3t

Find the average rate of change of the function f(x) = x^2+ 6x from x₁ =3 to X₂ = 9. The average rate of change is (Simplify your answer.)

An online furniture store sells chairs for $50 each and tables for $550 each. Every day, the store can ship a maximum of 32 pieces of furniture and must sell no less than $4100 worth of chairs and tables. If 24 chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.

1Magic Mountain sells a refillable soda cup for $18.50. Each refill costs $1.75. Last month, you spent $46.50 on the cup and refills. How many refills did you buy? a) Step 1: Define a variable: Let x = b) Step 2: Write an equation: Cost of soda cup plus Refill Cost cost for the month c) Solve your equation for x:

Cooper is a salesperson who sells computers at an electronics store. He makes a base pay amount of $60 per day regardless of sales and he earns a commission of 1.5% of the dollar amount of all sales that he makes. Write an equation for P, in terms of x, representing Cooper's total pay on a day on which he sells x dollars worth of computers. Answer: P =

Subtract the following polynomials (Write answers in descending order): 8. (-x²+x-4)-(3x²-8x - 2) 9. (8x²-3x) - (5x-5-8x²) 10. (-x²-5x-3)-(-7x² - 8x-8) 11. (-2x³ + x)-(7x-3-7x³) 12. (3x³ + 3x² +9) - (5x³-7x² + 6x-9) 13. (5x³ + 5x² + 5) - (6x³ - 6x² + 8x - 5) 14. (5x³ + 3x² + 5) - (7x³-9x² + 8x - 5)

Factor the following expression completely: x(x + 1) - 3(x + 1)

Ms. Fowler had $80 to purchase school supplies for her class. She bought 32 glue sticks and 32 boxes of crayons. Each glue stick cost $1.40, and each box of crayons cost $0.59. How much money did Ms. Fowler have left after these purchases? Bubble in your answer.

In 2005, Bhutan had a population of about 2200000 and was growing at a rate of 2.11 percent per year. Let P(t) be the population t years after 2005 assuming growth continues at this rate. (a) Write a formula for P. P(t) = (b) According to your formula, what will the population of Bhutan be in 2008?

What is the equation of the line that goes through (-3,-1) and (3,3)? A. 3x+2y=15 B. 3y + 2x = 15 C. 3x-2y=3 D. 2x-3y=-3

Factor the following expression completely: 6x^18 + 16x^12 +6x^7

Given f(x) = f(x)= 1/2 (-x+4)²-3 a. Identify all the transformations of the toolkit function f(x) = x². b. Graph using transformations by first graphing the toolkit function, then the progression of transformations (in the correct order). c. Determine the domain of the function in interval notation.

A large tank contains 90 litres of water in which 22 grams of salt is dissolved. Brine containing 11 grams of salt per litre is pumped into the tank at a rate of 8 litres per minute. The well mixed solution is pumped out of the tank at a rate of 2 litres per minute. (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(t) be the amount of salt in the tank after t minutes. Which of the following is a differential equation for x(t)?

The density of steel is 8,050 kilograms per cubic meter. A construction company is using a steel beam in the shape of a rectangular prism that measures 12 meters long, 1/5 of a meter wide, and 1/3 meter deep. What is the mass of the steel beam? 6,440 kilograms 8,050 kilograms 1,610 kilograms 3,220 kilograms

Solve the System by Elimination/Addition 3x -3y = 6 5x + 6y = -1

Given v(x) = x³ +12x² +36x+9 and dv/dx = 3x² +24x+36, select the local maximum and minimum of v(x). A. Local Max: (6,873); Local Min: (2,137) C. Local Max: (-6,9); Local Min: (-2,-23) E. Local Max: (-6,873); Local Min: (-2,137) B. Local Max: (2,137); Local Min: (-6,9) D. Local Max: (6,873); Local Min: (-2,-23)

Suppose that a population P(t) follows the following Gompertz differential equation. dP/dt = 3P(20 - In P), with initial condition P(0) = 110. (a) What is the limiting value of the population? (b) What is the value of the population when t = 2?

The number of research articles in Physical Review that were written by researchers in the United States from 1983 through 2003 can be approximated by A(t) = -0.01t² + 0.24t+ 3.4 hundred articles (t is the time in years since 1983). (a) Find an appropriate domain of A. (Enter your answer using interval notation.) Is t ≤ 20 an appropriate domain? Yes No (b) Compute A(16). hundred articles. What does the answer say about the number of research articles? Since t= 16 represents, the answer tells us that, in , approximately x 100 = T research articles in Physics Review were written by researchers in the U.S.

An inground swimming pool contains 2.3 x 10^4 units of water. Which unit of measure was used? teaspoons cubic centimeters fluid ounces gallons

The height h (in feet) of a water balloon can be modeled by h(x) = -3x² + 24x + 11, where x is the horizontal distance (in feet) from the launch pad. The launch pad is adjusted so that the water balloon lands exactly 9 feet away from the launch pad. Write a function that models the new path of the water balloon. Use Extra Example 5. The launch pad is adjusted so that the water balloon lands 8 feet from the launch pad. V/rite a function to model the new path of the water balloon.

Use technology to graph the pairs of functions on the same set of axes with -3 ≤ x ≤ 3. f₁(x) = 1.6^x, f₂(x) = 1.8^x Identify which graph corresponds to which function. f₁(x) starts lower than f₂(x), but finishes higher than f₂(x). f₁(x) is identical to f₂(x). f₁(x) starts higher than f₂(x), but finishes lower than f₂(x). f₁(x) is always lower than f₂(x). f₁(x) is always higher than f₂(x).

Factor the following expression completely: xy + 4y - 6x - 24

Factor the polynomial f(x)=x³-3x²-9x+27 and find all its real zeros using the Zero Product Property. f(x) = (x - 3)² real zero at x=3 (multiplicity 2) f(x) = (x - 3)³ real zeros at x=3 (multiplicity 3) f(x) = (x - 3)²(x + 3) real zeros at x=-3.3 (multiplicity 2) f(x) = (x - 3)(x + 3)(x - 2) real zeros at x=-3.3

Factor the following expression completely: 70p+q - 10 - 7qp

The value V of an item after 7 years is given by the following formula, assuming linear depreciation, V = C-Crt, where C is the original cost and r is the rate of depreciation expressed as a decimal. If you buy a car for $7830 and it depreciates linearly at a rate of 17% per year, what will be its value after 9 months? Round your answer to the nearest cent.

What electrical changes occur in muscles as they get tired? Student subjects hold their arms above their shoulders until they have to drop them. Meanwhile, the electrical activity in their arm muscles is measured. This is an uncontrolled experiment. an observational study. matched pairs experiment. a randomized comparative experiment.

If f(x) is a linear function, f(-1) = 1, and f(5) = -3, find an equation for f(x). f(x) =

Factor the following expression completely: 24p + q-3-8qp

Determine whether y is a function of x. x² + y = 3 Yes, y is a function of x. No, y is not a function of x. It cannot be determined whether y is a function of x.

The domain of the piecewise function is (-∞,∞). f(x) = x+4 if x < -2 x-4 if x ≥ -2 a. Graph the function. b. Use your graph to determine the function's range. a. Choose the correct graph below.