Basic Math Questions and Answers

Graph the given equation. -3 y = 2³x+3 4

On moving day, Guyton needs to rent a truck. The length of the cargo space is 11 ft, and the height is 2 ft less than the width. The brochure indicates that the truck can hold 385 ft³. What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid. x-2 11 ft

Find the inverse of the one-to-one function f(x) = 5x/6 + 25. (Use integers or fractions for any numbers in the expression.)

6. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy's wake as a line. m/1 = (2x + 2y)° and m/2 = (2x + y)°. Find x and y. X = y =

Solve the systems of equations. y = x + 3 y = -x + 1 x= y=

To use the quotient rule, write the given function as a quotient of two functions.

Express the fact that x differs from 10 by less than 5 as an inequality involving absolute value. Solve for x. Express the given sentence algebraically as an inequality involving absolute value.

Simplify the complex fraction: (3x5/4y6)/(x4/3xy)

The land area of the entire United States is 3,531,905 square miles. Use the current population of the United States to estimate the population per square mile. Explain.

Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a statement. There were 22,869 children, 49,563 men, and 2,872 more women than men at the fair. How many people were at the fair?

Jenny is solving the equation 3x+5-4x42 using algebra tiles. She cannot decide if she should add 3 negative x-tiles or add 2 negative unit tiles to both sides first. Which explains which Jenny should do first? She should add 3 negative x-tiles first because that is the only way to isolate the variable. She should add 2 negative unit tiles first because that is the only way to get to the correct solution. She can do either one first because zero pairs will be created to isolate the variable either way, She should do neither one first because the first step is to add 4 negative tiles to both sides.

Graph the function f(x) = − −x+2, and then find and graph its inverse. 3 f-1(x) = (Simplify your answer.)

The scores and their percents of the final grade for a statistics student are given. An error occurred grading the final exam. Instead of getting 94, the student scored 99. What is the student's new weighted mean? Homework Quiz Project Speech Final Exam The student's new weighted mean score is 20 (Simplify your answer.) Score 83 85 99 87 94 Percent of Final Grade 5 30 20 10 35 Weighted Mean Weighted Score 4.15 25.5 19.8 8.7 32.9 91.05 0

Substitution property of Equality: If AB = 20, then AB + CD = Symmetric property of Equality: If m1=m42, then Addition property of Equality: If AB = CD, then AB + EF = Multiplication property of Equality: If AB = CD, then 5. AB= Subtraction property of Equality: If LM = XY, then LM - GH = = 2 Distributive Property: If 5(x+8) = 2, then Transitive Property of Equality: If mz1 = m22, and m22=m23, then Reflexive Property of Equality: m<ABC=

Betsy, a recent retiree, requires $6,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 3% per year. How much money should be invested in each to realize exactly $6,000 in interest per year? The amount of money invested at 13% = $ The amount of money invested at 3% = $ Question 8, 1.6.19

A cell phone company charges $40 for a smart phone and $20 per month for its data package. Find the cost C(t) of operating a phone for t months. Use the function to find the cost of the plan for 2 months. Find the cost C(t) of operating a phone for t months.

A credit card company estimates that the average cardholder owed $7440 in the year 2005 and $9420 in 2010. Suppose average cardholder debt D grows at a constant rate. a. Express D as a linear function of time t, where t is the number of years after 2005. b. Draw the graph. c. Use the function in part (a) to predict the average cardholder debt in the year 2015.

When drawing a card from a deck, the P(face card and hearts) is: O 1/13 O 3/26 O 3/52 O 1/52

The distance, d, of an object in free fall for an amount of time in seconds, t, is given by the equation d = 9.81². Write the distance d as a function of t, and find the distance an object falls after 5 seconds The distance d as a function of t can be written as

Simplify s-³s-9 and write your answer without using negative exponents.

A taxi company charges an initial fee of $3 and a rate per mile of $0.71. Write C, the cost for a taxi ride, as a function of m, the number of miles ridden. Find the cost of a 11-mile taxi ride. The cost C for a taxi rides as a function of m can be witten as C(m). The cost is $ *****

Graph f(x)=2x.

A population of 420 bacteria is introduced into a culture and grows in number according to the equation below, where ti measured in hours. Find P'(t). P'(t) = P(t) = 420 3+ 5t 72 +² bacteria/hour Find the rate at which the population is growing when t = 3. (Round your answer to two decimal places.) P'(3) = bacteria/hour

Evaluate the discriminant and determine the number and type of solutions to the equation. 6x²-2x+8=0

A cell phone company charges $30 for a smart phone and $20 per month for its data package. Find the cost C(t) of operating a phone for t months. Use the function to find the cost of the plan for 8 months. Find the cost C(t) of operating a phone for t months. C(t)= (Simplify your answer.)

If we are told that (2x - 1)(5x + 3) = 0, then what can we infer? By the zero product property we know: And therefore we know that: • Do not use decimal approximations in your answer. Use fractions instead.

Solve by using the square root property. Express the solution set in exact simplest form. (z+3)²=28

A savings account had an initial deposit of $50 with $20 deposited each month after it was opened. The total amount in the account can be found by the function A(t) = 20t+50, where t is the time in months after the account was opened. If the total amount in the account is $390, find the length of time the account has been open. After months, the total amount in the account is $390. (Simplify your answer.)

A certain substance has a half-life of 4 minutes. A fresh sample of the substance weighing 90 mg was obtained. After how many minutes will there be 23 mg of the substance remaining? 1.9 minutes 7.9 minutes 5.5 minutes 31.6 minutes

A business uses straight-line depreciation to determine the value y of a piece of machinery over a 10-year period. Suppose the original value (when t= 0) is equal to $42,000 and its value is reduced by $4200 each year. Write the linear equation that models the value y of this machinery at the end of year t. The linear equation models the value y of the machinery at the end of year t (Type an equation. Do not factor.)

A group of test subjects is divided into twelve groups; then four of the groups are chosen at random. [Select] Par Idei or c [Select] Simple Random Stratified Systematic Cluster Convenient ✓ crete, quantitative continuous,

Mr. Morrison bought a cart to move boxes for $49.80 and furniture straps for $19.78. He helped the Greene family move and got paid $400. How much profit did Mr. Morrison make?

WHAT IF? The surface of a city playground is being covered with rubber mulch, which is shredded rubber made from recycle tires. A city worker measures the dimensions of the playground as shown. The recommended depth of the mulch is 4 inches. A 1-ton bag of mulch contains about 3 cubic yards of mulch. How many bags of mulch are needed to cover the surface of the playground? 40.5 ft bags 66.75 ft

Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92? x+y = 15.98 x+y= 43.92 43.92x-2.99y = 12.99 2.99x+12.99y = 43.92

An internet provider charges a $150 set-up fee and a $70 monthly fee. Find the cost C(t) of having a contract with this provider for t months. If a person has paid $1130 to the internet provider, how many months has he had a contract with them? Find the cost C(t) of having a contract with this provider for t months. C(t)= (Simplify your answer.)

Convert 96°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. C= (F-32) F=C+32

The state of Michigan recorded an all-time high snowfall of 355.9 inches during the winter of 1978-79. Its lowest snowfall of 81.3 inches was recorded during the winter of 1930-31. How much more snowfall did Michigan receive during the winter of 1978-79 than in 1930-31?

For a ride on a rental scooter, Dante paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Dante's ride was $9.92. For how many minutes did Dante ride the scooter? minutes X 5 P

Frank invests $2,500 in an account that has an annual interest rate of 5.4% compounded continuously. Hannah invests $3,000 in an account that has an annual interest rate of 3.2% compounded quarterly. Which of the following statements is true when comparing the amount of money in the two accounts after 10 years? After 10 years Hannah has about $164 more than Frank. After 10 years Frank and Hannah have the same amount of money in their accounts. After 10 years Frank has about $164 more than Hannah. After 10 years Frank has about $500 more than Hannah.

Graph r(x) = -8. Use the graphing tool to graph the function.

The tangent line to the graph of y = g(x) at the point (4, 3) passes through the point (9, 4). Find g(4) and g'(4).

A class of 195 students went on a field trip. They took 7 vehicles, some cars and some buses. Each car holds 5 students and each bus hold 45 students. If x represents the number of cars and y represents the number of busses determine which of the following systems of equations model this scenario. x+y=195 7x + 5y = 45 x+y=7 5x + 45y = 195 x+y = 45 5x + 7y = 195 x+y = 745 x + 5y = 195

Using a calculator, simplify the following to the ten-thousandths place: A) log(768) B) In (135) 2.8853 4.9052 C) log4(225) 3.907 D) log (225) 5.4161

Is this equation an identity? 19p+ 16 = 2p + 17p + 16 yes no

Write the inequality using interval notation and illustrate the inequality using the real number line. -4≤x≤8

The population of Winnemucca, Nevada, can be modeled by P=6191(0.98)' where t is the number of years since 1990. What was the population in 1990? 6191 By what percent did the population change each year? [Select]

Determine if the following relation is a one-to-one function. S={(-6, -6), (4,4), (3,7), (7,3)} Is S a one-to-one function? Yes No

Use the Remainder Theorem and the Factor Theorem to determine whether (x+3) is a factor of the polynomial f(x) = 2x³ + 6x²+x+3. O It is not a factor because f(-3) = 0. O It is a factor because f(-3)-0. O It is a factor because f(3) = 0. It is not a factor because f(3) = 0.

How much water must be evaporated from 32 ounces of a 7% salt solution to make an 8% salt solution? To obtain a solution that is 8% salt,ounce(s) of water must be evaporated. (Simplify your answer)

Find the inverse of the one-to-one function. f(x) = 6x+5