Basic Math Questions and Answers

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.

At a golf club the demand equation for the number of members of the club, q is given by q=-10p+200 where p is the yearly price for membership in the club a) Find the revenue function b) What would be the yearly price that would maximize revenue

Add the following polynomials (Write answers in descending order): 1. (7j³-2) + (5j³-j-3) 2. (8a5-4) + (3a² + a-2) 3. (6m5 + 1) + (2m5 + 9m - 1) 4. (3m5 + 1) + (9m5 +3m - 2) 5. (-5x²-x+4) + (-3x² - 5x+2) 6. (-4x + 4x³ + 7) + (3x³-9-3x) 7. (3x² - 2x + 1) + (-x² + 3x + 1)

Graph the equation y = -x² + 12x - 35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation -² + 12x - 35 = 0.

For a recent year, the monthly snowfall (in inches) for Chicago, Illinois, for November, December, January, and February was 2, 8.4, 11.2, and 7.9 respectively. How much snow would be necessary in March for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months?

A car rental agency advertised renting a car for $24.95 per day and $0.28 per mile. If Shawn rents this car for 2 days, how many whole miles can he drive on a $150 budget? miles (Round down to the nearest whole mile.)

The dollar value v (t) of a certain car model that is / years old is given by the following exponential function. v (t)=32,000(0.95)^t Find the initial value of the car and the value after 11 years. Round your answers to the nearest dollar as necessary. Initial value: Value after 11 years:

Tell whether each sentence below is true or false. The formula for calculating the sum of any finite geometric sequence is n/2 (a₁ + an). Standard deviation is a popular (and accurate) measure of the spread or distribution of a group of data.

Solve the polynomial inequality. (x + 1)(x-2)(x - 5) >0 (-∞, -1) U (2,5) (-1,2) U (5,∞) [-1,2] U [5,∞) (-∞, -1] U [2,5]

A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size. After 6 hours there will be 5760 bacteria. (a) Express the population after t hours as a function of t. population: (function of t) (b) What will be the population after 2 hours? (c) How long will it take for the population to reach 1090?

Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product? The pair of numbers whose difference is 14 and whose product is as small as possible is (Use a comma to separate answers.)

Factor the polynomial f(x)= x³ - 2x² - 9x +18 given that x=2 is a zero of f(x). f(x) = (1-3)(x + 3) f(x) = (x-2)(x-3)(x+3) f(x) = (x + 2)(x − 3)(x+3) f(x) = (x-2)(x - 3)²

PLAT has vertices P(-1,1), L(0.2), A(1,2), T(0,1). P'L'A'T' is the image of PLAT for the translation (x,y) → (x+3, y-2), Show that PP', LI', AA', and TT' are all parallel. Two segments are parallel if are Find the coordinates of the images of the vertices by each x-coordinate andy-coordinate and each

A cylinder with surface area 300 square inches and a height equal to 10 inches has what volume? Round to the nearest cubic inch. 391 cubic inches. 782 cubic inches 498 cubic inches 738 cubic inches

You start a small baking business, and you want to earn a profit of at least $250 in the first month. The expenses in the first month are $155. What are the possible revenues that you need to earn to meet the profit goal? Write and solve an inequality to model this situation.

Factor the following expression completely: -4w² - 4w - 6w-6

Katie was asked to solve the following inequality and show all of her work. She made an error when solving. x/3 +2≤6 x + 2 ≤ 18 X ≤ 16

Members of the student council are taking a trip to the state legislature. The student council must pay a $1000 entry fee plus $140 per student. What is the average total cost per student if 25 students attend? Do not include the dollar sign ($) in your answer. Provide your answer below: