Basic Math Questions and Answers

Given that f(x) = 2(x - 3)² - 8, determine the true statement. The x intercepts of the graph of f(x) are (1,0) and (5,0). O The graph of f(x) is decreasing from (3, ∞). O The domain of f(x) is x > 3. O The range of f(x) is y> -8. O The graph of f(x) has a maximum point at (3, -8).

10 Given f(x) = 2x²-4, which of the following represents a point on the graph of the function? A. f(3) = 16; to eat the cake B. f(-5) = -46; they got to decorate C. f(4) = 28; the house looked festive D. f(-2) = -8; the internet was back on

Tiana cannot read traffic signs that are more than 50 m away. Which inequality represents the distances, d, at which Tiana can read traffic signs? A d > 50 B d≥ 50 C d < 50 D d≤ 50 Erik chose A as the correct answer. How might he have gotten that answer?

Jimmy brings $24 to the county fair for rides. Roller coaster rides are $2, and the spinning cup rides cost $3. But Jimmy knows that he gets queasy if he takes more than 6 roller coaster rides or more than 8 spinning cup rides. Let r represent the number of roller coaster rides and let s represent the number of spinning cup rides. In addition to r ≥ 0; s ≥ 0, which is a set of inequalities that Jimmy can use to guide his choice of rides? Ar+s≤ 24; r ≤ 6; s < 8 Br+s≤ 24 C2r + 3s ≤ 24; r ≤ 6; s ≤ 8 D 2r ≤ 6; 3s ≤ 8

A physician whose patient suffers from severe arthritis wrote a prescription for 100 mg of Celebrex twice daily for 90 days. At the end of the 90 days, the patient will have taken of Celebrex grams

A vendor at a craft show sold items for $4.50, $6.00, and $7.50. Altogether, the vendor sold 87 items for a total of $489. The vendor sold 5 more items for $6.00 than for $7.50. Which system of equations could you use to determine how many of each item were sold? Ax + y + z = 87 z = y + 5 4.5x + 6y + 7.5z = 489 B) x + y + z = 87 y = z + 5 4.5x + 6y + 7.5z = 489 x + y + z = 489 y = z + 5 4.5x + 6y + 7.5z = 87 Dx + y + z = 489

Two companies, Chocolate Bliss and Expressions in Sweets, sell a special heart shaped box of chocolate candy for Valentine's Day containing the same number of candies. Chocolate Bliss sells their box of chocolate candy for $2.00 per candy plus a $12 packaging fee. Expressions in Sweets sells their box of chocolate candy for $3.00 per candy plus a $10 packaging fee. If five boxes of Chocolate Bliss chocolate candy cost the same as four boxes of Expressions in Sweets chocolate candy, how many candies are in each box? Define the variables and write the equations. Solve for your variables: Check your work: Explain what your answer means in the context of the problem

Find the domain and range of the function. (Enter your answers using interval notation.) g(x) = x² - 8 domain range

2. Greg received a 95 on his last math test. The only question that he got wrong is listed below. (a) Read through Greg's work and circle his mistake. Evaluate: ²-2(x-3) when x = 3. Greg's work: (b) Explain what Greg did wrong. = *²-2(x-3) = 3²-2(3-3) 3²-2(0) = 9-2(0) = =7(0) = 0 (c) Revise Greg's work and state the correct value of the expression.

Solve the inequality algebraically. Graph the solution set. Verify your results using a graphing utility. |2x+3|-5≥-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.

While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars O44.70 US dollars 73.06 US dollars 136.87 US dollars O140.41 US dollars

Consider the provided five-number summary: Minimum = 4, Q₁ = 8, M = 12, Q3 = 15, Maximum = 19. Which set of seven numbers have the same five-number summary? 4, 8, 9, 12, 14, 15, 19 4, 8, 10, 12, 17, 16, 20 4, 8, 11, 13, 11, 14, 19 1, 5, 12, 11, 13, 15, 19

The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p) = -12p2 + 186p, where p is the price charged per pet (in dollars). (a) Find the revenue earned for each price per pet given below. R($2) $324 R($6) $684 R($7) $714 (b) Find the unit price that yields a maximum revenue. $ 7.75 per pet What is the maximum revenue? $ 645 x Explain.

Let P(t) represent the number of cars in a school parking lot t hours after 7 a.m. P(0) = 8 and P'(0) = 12, which of the following statements must be true? 1. The instantaneous rate of change in the number of cars in the parking lot is 12 cars per hour at 7 a.m. II. The number of cars in the parking lot is increasing at 7 a.m. III. There are 20 cars in the parking lot at 8 a.m. Onone Olonly OI and II only II and III only

It took Sharon 4 hours to drive to her grandmother's house. Her grandmother lives 140 miles from Sharon. What was Sharon's average speed for this trip? 30 mph 35 mph 136 mph 560 mph

What is the slope of the line through (-8, 9) and (5,9)? If the slope is undefined, type undefined. What is the slope of the line through (-6, 9) and (-7,10)? If the slope is undefined, type undefined.. What is the slope of the line through (-10, 1) and (-10,2)? If the slope is undefined, type undefined.

Ross had an annual earned income of $48,000 last year. He also had a passive income of $3,500, and capital gains of $4,000. What was Ross' total gross income for the year?

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.