Basic Math Questions and Answers

Find the real and complex zeros of the function f(x) = x³ - 14x² + 3x - 42 Express your answer as a list separated by commas. Do not use a Provide your answer below: sign in your answer; instead, list the zeros separately.

Find the principal root of this equation: tan(z) - 1 = 0 X= . Give your answer in radians. • Do not use decimal approximation. Use 'pi' to represent .

3. An open box of maximum volume is to be made from a square piece of material, 9 inches on a side by cutting equal squares form the corners and turning up the sides. Find the dimensions of the squares. Find the maximum Volume.

Use the point-slope form of a linear equation to write the equation of the line in slope-intercept form. m=- 2/3 through (7,3) Enter the correct expression in the box to complete the linear equation.

g(x)=x-2 h(x)=4x-2 Find (g- h)(x) A) 4x² - 10x+4 B) 12x³-9x² + 4x-3 C) 2x³-5x² +8x-20 D) 2x² - 13x+15

During a game of marbles, a player is trying to win a 2 g marble that is at rest. The player flicks a 1.25 g marble at a velocity of 8 at the larger marble that is sitting still. After the collision, the smaller marble has a velocity of 1 m S What is the velocity of the 2 g marble after the collision? Round your answer to the nearest whole number m

The manager of an 80-unit apartment complex knows from experience that at a rent of $1000 per month, all units will be rented. However, for each increase of $25 in rent, he can expect one unit to be vacated, Let x represent the number of $25 increases over $1000. Complete parts (a) through (e) below. (a) Express, in terms of x, the number of apartments that will be rented if x increases of $25 are made. (For example, with three such increases, the number of apartments rented will be 80-3=77.) The number of apartments that will be rented if x increases of $25 are made is

If you throw a stone up in the air off a bridge that is 20 feet above a creek, the path of the stone can be modeled using the equation h = -16t² +50t + 20, where h is the height of the stone and t is the time in seconds. How long will it take the stone to reach the water below?

Write a quadratic equation with integer coefficients having the given numbers as solutions. -√29, √29

The function f(x) = 5x+7/X + 5 is one to one (a) Find its inverse and check your answer. (b) Find the domain and the range of f and f

The number of seconds, t it takes for an object to fall a distance of d feet can be found using the formula t = √2d/g, where g is the constant acceleration due to gravity, 32-ft/sec². How many feet does an object fall in 2 seconds?

You start driving west for 3 miles, turn right, and drive north for another 2 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.

Each person has a 2.5 x 10-7 chance of winning one lottery game. Another lottery game gives you a 5 times better chance of winning. What are your chances of winning the second lottery game? (Hint: Write 5 in scientific notation)

Find the principal root of this equation: √3 tan(x) = -1 X = Give your answer in radians. Do not use decimal approximation. Use 'pi' to represent .

A ratio is... where two or more values are compared in lowest terms. when two numbers are written as a division problem. where two numbers are written as a fraction in lowest terms. all of these.

For the function on the right, determine whether the function is one-to-one. 30 Hours 35 Hours 45 Hours 75 Hours Is the function one-to-one?

Your digital camera has a 512 megabyte memory card. You take pictures at two resolutions, a low resolution requiring 4 megabytes of memory per photo and a high resolution requiring 8 megabytes of memory per photo. Write an equation to model the amount of each kind of photo you can take.

Simplify √24 to the form a√b. a = b =

Which have a 1:3:4 ratio? 2:6:8 6:18:20 3.5:10.5:14 1.5:3.5:4.5

A farmer has 520 feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence? The rectangle with the maximum area enclosed by the fence has a length of ft and a width of

For the function below, find a) the critical numbers; b) the open intervals where the function is increasing; and c) the open intervals where it is decreasing. f(x) = x+5/x+2 a) Find the critical number(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical number(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no critical numbers.

From the window of an airplane, you can see a farmhouse directly below. If the plane is traveling at an altitude of 3 miles, how far from the farmhouse will the airplane be after it has traveled 4 miles at the same altitude?

Graph the circle given below by moving the key point: (x + 1)² + (y+3)² = 16 To graph the circle, drag the center point to the desired location, and then drag the radius point until the radius is the desired number of units.

Sketch the graph of the rational function below. Include any vertical asymptotes and describe the end behavior of the rational function. r(x) =x²+3x-4/(x-2)²(x+4)(x - 1)

The average price of a movie ticket in the United States from 1980 to 2000 can be modeled by the expression 2.75 +0.10z, where z is the number of years since 1980. Which part of the expression corresponds to the cost of movie tickets in 1980? A.2.75 + 0.10 B 2.75 C.10 D. 0.102

A car is 180 inches long. A truck is 75% longer than the car. How long is the truck? 135 inches 240 inches 255 inches 315 inches

Under which angle conditions could a triangle exist? Check all that apply. 3 acute angles 2 acute angles, 1 right angle 1 acute angle, 1 right angle, 1 obtuse angle 1 acute angle, 2 obtuse angles 2 acute angles, 1 obtuse angle

What is the author's purpose in writing this paragraph? to persuade the reader that the Grimm brothers were influential to entertain the reader with excerpts from thenGrimms' tales to inform the reader that the text will take a secondnlook at the Grimms' original tales to show the reader that the Grimms have receivedbmany honors

Suppose you saw a sign at your local bank that said, "7.4% rate compounded semiannually - 7.9% Annual Percentage Yield (APY)." Is there anything wrong with the sign? Explain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Yes. The number of compounding periods is incorrect. Interest should be compounded daily. B. Yes. The APY is incorrect. The correct APY is (Round to the nearest hundredth as needed.) C. No. The information on the sign is correct.

A file that is 251 megabytes is being downloaded. If the download is 17.3% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.

A population numbers 10,000 organisms initially and grows by 11.3% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a bt where

A population numbers 19,000 organisms initially and decreases by 3.2% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a b where

The admission fee at an amusement park is $20 for children and $35 for adults. On a certain day, 287 people entered the park, and the admission fees collected totaled $7465. How many children and how many adults were admitted?

Graph the exponential function. f(x) = 2*

7. At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could he used to determine the price of each book?

A family went to a baseball game. They parked the car in a parking lot which charged $5. The cost per ticket was $20. Write an equation for the total cost of going to the baseball game, where y is the total cost and x is the total number of people. If the family spent $145, how many people went to the game?

Six boxes of paper were delivered to Chandra. This is 30% of her total paper order. How many boxes of paper did she order?

The school store sells binders for $5 and notebooks for $4. The store needs to sell $80 worth of these two items combined each week. Write a linear equation in standard form that describes the linear relationship. Let x represen the number of binders sold and let y represent the number of notebooks sold.

Which problem would result in this quotient? 4,800 ÷ 10² 400,800 103 400,800 ÷ 10² 408,000 + 103

Brent Pickett borrowed $5000 from his brother Dave. He agreed to repay the money at the end of 3 years, giving Dave the same amount of interest that he would have received if the money had been invested at 3.75% compounded quarterly. How much money did Brent repay his brother?

Divide using synthetic division. State what the remainder means. You must use synthetic division as shown in class for full credit. SHOW ALL STEPS FOR FULL CREDIT! (3x4 - 3x² + 2x - 8) ÷ (x-2)

In the diagram below, NO is parallel to KL. OL = 1.8, MN = 2.7, and MO= 2.2. Find the length of NK. Round your answer to the nearest tenth if necessary.

If two sides of a triangle have lengths of 8 in and 12 in, what are the possible lengths for the third side? 8<x<12 6<x<14 none 4<x<20 -4<x<10

A water storage tank is in the shape of a hemisphere (half a sphere). If the radius is 29 ft, approximate the volume of the tank in cubic feet.

Mr. Rivas bought a can of paint. He used of it to paint a bookshelf. He used 3/8 of it to paint a bookshelf. He used 1/4 of it to paint a wagon. He used some of it to paint a birdhouse and has 1/8 of the paint left. How much paint did he use for the birdhouse?

Suppose that you are thinking about buying a car and have narrowed down your choices to two options. The new-car option: The new car costs $29,000 and can be financed with a four-year loan at 5.73%. The used-car option: A three-year old model of the same car costs $14,000 and can be financed with a four-year loan at 7.26%.

The balance on Ramon Felipe's credit card on January 14, his billing date, was $269.71. For the period ending February 14, Ramon had the following transactions to the right. a) Find the average daily balance for the billing period. b) Find the finance charge to be paid on February 14. Assume an interest rate of 1.2% per month. c) Find the balance due on February 14.

The sun is approximately 1.5 × 108 kilometers from Earth. The moon is approximately 4 x 105 kilometers from Earth. How many times farther away is the sun than the moon from planet Earth?

During each second of braking, an automobile slows by about 10 miles per hour. a. Plot the points (0, 60) and (6, 0). What do the points represent? b. Draw a line through the points. What does the line represent? c. Write an equation of the line.

A local bus travels 7 mph slower than the express. The express bus travels 60 miles in the time that it takes the local bus to travel 50 miles. Find the speed of each bus.