Basic Math Questions and Answers

When f(x) = 6x²-2x - 6, evaluate f(-3) f(-3) =

The number of streetlights in a town is growing linearly. Four months ago (n = 0) there were 130 lights. Now (n = 4) there are 146 lights. If this trend continues, how many months will it take to reach 200 lights?

Express the fact that x differs from 11 by less than 6 as an inequality involving absolute value. Solve for x. Express the given sentence algebraically as an inequality involving absolute value.

Write the first five terms of the sequence. f(0) = 3: f(n) = f(n-1) 2 f(0) = f(1) = f(2)= f(3) = f(4) =

Identify all the numbered angles that are congruent to the given angle. List the numbers of any angles that are congruent to the given angle.

What words describe how Anthony should build the next model in his series of concrete representations of this situation? O The pool should be 3 squares by 5 squares, and the border should be 4 squares by 6 The pool should be 3 squares by 5 squares, and the border should be 4 squares by 7 squares. squares. O The pool should be 3 squares by 5 squares, and the border should be 5 squares by 7 squares.

The position of a model train, in feet along a railroad track, is given by s(t) = 2.5t + 17 after t seconds. (a) How fast is the train moving? ft/sec (b) Where is the train after 4 seconds? feet along the track (c) When will the train be 32 feet along the track? t= sec

(a) Write an equation representing the fact that the product of two consecutive odd integers is 195. Use x to represent the smaller integer. (b) Solve the equation from part (a) to find the two integers. Part 1 of 2 (a) The equation is (x + 15) (x - 13) = = 0 Part: 1 / 2 Part 2 of 2 (b) Find the pair(s) of consecutive odd integers. If there is more than one pair, use the "or" button. and or X

A pump removes 1000 gallons of water from a pool at a constant rate of 50 gal/min. Write an equation to find the amount of water, w, in the pool after t minutes. How long will it take for the pool to become half-empty?

bstitution to Identify Solutions of Inequalities Read and try to solve the problem below. Pilar has a gift card for a sporting goods store. She has $42.50 left on the card. She plans to buy one pair of yoga socks for $8. There are four other items that she is looking at. Use the inequality x + 8 = 42.50, where x is the price of an item, to determine which of the other four items Pilar can buy. Yoga Socks 58.00 BUT HER Bike Helmet 530.00 ** BUT NOW Baseball Bat $38.50 BUT NOW Running Shoes 535.50 BUY NOW Swim Goggles $28.50 SUY NOW

Is the graph of the function f(x) = 9x5 + 7x symmetric with respect to the origin? O Yes, the graph is symmetric about the origin. O No, this graph has no symmetry. O No, but the graph is symmetric about the x-axis. O No, but the graph is symmetric about the y-axis.

An insurance policy on an electrical device pays a benefit of $5500 if the device fails during the first year. The amount of the benefit decreases by $1100 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.42. Find the expected benefit under this policy,

Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces? O(-3,-18) O (-0.5, -3) O (0,0) O (0.5, 3)

(1) Cora cut 3 shelves of equal length using 2/3 of a yard of wood. How long was each shelf? ◄) Write your answer as a fraction or as a whole or mixed number. D yards

Two lengths of stereo speaker wire total 32.5 ft. One length is 2.9 ft longer than the other. How long is each length of speaker wire?

Select the correct third step and reasoning: O -4; Division Property of Equality O x = 2; Division Property of Equality O x = -4; Multiplication Property of Equality O X x = 2; Multiplication Property of Equality X =

Given that an investment into a college fund is represented by A = 12, 000e(0.023.12) match each value to the correct description of the value in the context of the question. The amount of money in the av The amount of money in the account at the end of the time given. The initial amount of money invested into the college fund The amount of years the money is invested. The interest rate. The interest is compounded continuously.

Find the derivative of the function without using the Quotient Rule. 12/13x² Step 1 Rewrite the equation so the variable is not in the denominator. y =12x/13

Your college professor tells you he will give a 30 % -30% -40% split on grades between homework, quizzes, and test. However whichever category you have the highest average in will be the 40% category. What will your final grade be if your homework average is 57, you quiz average is 97, and your test average is 86? Type your answer...

We want to solve the equation x² - 8x +15=0 First, factor x² - 8x + 15: By the zero product property we know: And therefore we know that: Do not use decimal approximations in your answer. Use fractions instead.

The first 50 people who walk into a sporting event are polled on their television preferences. [Select] Simple Random Stratified Systematic Cluster Convenient

Tutorial Exercise Find two positive real numbers whose product is a maximum. The sum of the first and three times the second is 60. Step 1 Let x be the first number and y be the second number. Write an equation describing the sum in this problem. y = X + Submit Skip (you cannot come back)

Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles she needs to sell to earn $100. 1.25x + 1.49 = 100 What error did Barbara make in writing the equation? O Barbara's equation did not consider the number of bottles of water. O Barbara's equation did not consider the number of bottles of iced tea. O Barbara's equation did not use the correct price for the bottles of iced tea. O Barbara's equation did not use the correct total for sales.

Phoebe has a job singing in a café. Phoebe makes an hourly rate of $4.25 plus tips. Last week Phoebe worked 25 hours and made $220.50. How much in tips did Phoebe earn last week?

A shower uses 2.5 gal of water each minute. Yolanda wants to be sure each shower she takes uses no more than 15 gal of water. She writes the inequality 2.5m ≤ 15, where m is a number of minutes. Which values from 0 to 100 are solutions of the inequality? What do the solutions tell you? Explain your reasoning.

Roun#10 the nearest hundredth, if necessary. Complete the statement. to 3.2 km = cm

Plot the point (3/2,-9/2) in a rectangular coordinate system.

An airplane flying at an altitude of 30,000 feet flies up to avoid a storm. Immediately after passing the storm, the airplane returns to its original altitude. a. What integer represents the airplane's change in altitude to avoid the storm? b. What integer represents the airplane's change in altitude immediately after passing the storm? c. Use Appropriate Tools Draw a number line to represent the airplane's change in altitude.

Jude worked at the student café. On Wednesday, they worked for 3 hours and made their hourly rate plus $7 in tips. Write an expression that represents the amount of money Jude made on Wednesday, where x represents their hourly rate.

Solve the inequality algebraically Graph the solution set. Verify your results using a graphing utility. |2x+1|-3≥-1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution is the empty set.

Determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. Express numbers as integers or simplified fractions. k²+16k+n

You have a choice to invest in one of three different college funds to save up for college. You need to save at least $14,000 for your first year. In which of the three accounts do you choose to invest your money given that you have $10,000 to invest and you would like to accrue as much interest as possible? Account 1: An annual interest rate of 3.5% compounded quarterly for 10 years. Account 2: An annual interest rate of 3.6% compounded continuously for 10 years. Account 3: An annual interest rate of 3.2% compounded annually for 10 years. You choose account #1 You choose account #2 You choose account # 3 You choose to look for a different savings account because none of the options help you save $14,000.

McKenna and Lara work for their uncle Eddie, who repairs skateboards and bicycles. Uncle Eddie is leaving for a vacation to the Amazon. He asks the girls to order 54 new wheels for the 21 skateboards and bicycles in his repair shop. How many bicycles and how many skateboards are in Uncle Eddie's shop? From the list of facts, circle those you need to solve Lara and McKenna's problem. McKenna and Lara's uncle is named Eddie. There are 21 skateboards and bicycles in the shop. Uncle Eddie went on a trip. A bicycle has two wheels, and a skateboard has four wheels. 54 new wheels are needed.

Solve the problem. Supply and demand functions, S(x) and D(x), are given for a particular commodity in terms of the level of production x. In each case: S(x) = 4x + 200 and D(x) = -6x + 460 a. For what values of x is there a market shortage? b. For what values of x is there a market surplus? Show all your work.

A 1000 gram sample of radioactive matter will completely decay (be undetectable) in 10 hours. There exists a set of ordered pairs (t, m), where t is the amount of time in hours that the substance has been decaying, and m is the mass in grams that has decayed. If t 0, what is the range of m? Om 1000 OmER Om 10 00 m 1000 Om > 0

A car enters an interstate highway 15 mi south of Youngstown. The car travels due south at an average speed of 62.5 mi/h. Write an equation to model the car's distance, d, from Youngstown after traveling h hours. How far south of Youngstown will the car be after 150 minutes?

In the number: 05629 determine the most significant digit = the least significant digit = The number of significant digits = I

Luke invests $4200 in an account that has an annual interest rate of 2.8% compounded semi-annually. Todd invests $3900 into an account that has an annual interest rate of 3.3% and is compounded continuously. After 8 years what is the difference between the two accounts? Todd has approximately $1.361 more in his account than Luke after 8 years. Luke has approximately $168 more in his account than Todd after 8 years. Luke has approximately $300 more in his account than Todd after 8 years. Both Todd and Luke have the same amount of money in their accounts after 8 years.

Potassium-42 has a half-life of 12.4 hours. Approximately how much of a 1202 mg sample of potassium-42 will be left after 36.8 hours? 953 mg 153 mg 300 mg 88 mg

The perimeter of the rectangular playing field is 370 yards. The length of the field is 7 yards less than triple the width. What are the dimensions of the playing field?

Maximum Capacity A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. How many boxes of books can the delivery person bring up at one time?

6 Write the equation of the line passing through the point (7, - 7) with slope 7 The equation of the line is EE H-R

Write the equation of the line with slope 7 and y-intercept 1/8. The equation of the line is

#10 i 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. - T

Solve the problem. When starting a new job at a production facility, employees can be expected to assemble n items per hour after t weeks of work experience, where n(t) = 75 -130/t+ 20.88 Employees are paid 30 cents for each item they assemble. a. Find an expression for the amount of money A(t) earned per hour by an employee with t weeks of experience. b. How much money per hour should an employee expect to earn in the long run (as t→ ∞0)?

Use what you learned to solve these problems. Aimee works up to 50 hours a month and earns $12 per hour. She wants to save more than $240 to buy a computer. The inequality 12h 240, where h is the number of hours Aimee works this month, models this situation. Which values from 0 to 50 are solutions of the inequality? What do the solutions mean in this situation? Explain your reasoning.

In this Exercise, use what you've learned about linear functions and their properties to model real-world situations. 1. In science class, you learned about converting temperatures between degrees Celsius (°C) and Fahrenheit (°F), but recently you could not find a reference with the correct formulas. You then remembered that the relationship between °F and °C is linear. (a) Using this and the knowledge that 32°F = 0°C and 212° F = 100°C, find an equation that computes Celsius temperature in terms of Fahrenheit; i.e. an equation of the form C = "an expression involving only the variable F." (b) Analogously, find an equation that computes Fahrenheit temperature in terms of Celsius temperature; i.e. an equation of the form F = "an expression involving only the variable C."

1 point Final grades are often computed using weighted averages. Some college professors use complicated weighted averages. Your college professor tells you he will give a 33% -67% split on grades between tests and homework where whichever average is higher will be the 67%. What will your final grade be if your homework average is 56 and your test average is 71?

We want to solve the equation 10x² + x3 = 0 First, factor 10x² + x - 3: By the zero product property we know: 5x+3 = = 0 OR 2x-1=0 And therefore we know that: X= 1 3/5 -B 2 OR= • Do not use decimal approximations in your answer. • Use fractions instead.

Hiroaki has 23 keychains in his collection. He has a goal of collecting at least 30 keychains. He uses the inequality 30 ≤ 23 + x, where x is a number of keychains, to represent how he can reach his goal. Which values in the set (6,7,8} are solutions of Hiroaki's inequality? Show your work.