Basic Math Questions and Answers

Use the Factor Theorem to determine whether x-3 is a factor of P(x) = -x4+x3+5x²-4. Specifically, evaluate P at the proper value, and then determine whether x-3 is a factor.

Use the ALEKS graphing calculator to find the vertex and x-intercept(s) for the quadratic function. f(x)=-3.38x²-5.2x-2

How long will it take for a $4000 investment to grow to $7148 at an annual rate of 9.4%, compounded quarterly? Assume that no withdrawals are made.

13. Diego wants to purchase a used car that sells for $6,399. The dealer has offered him $299 on his trade-in car. The total cost of the car Diego wants to buy will be a. $4,543 b. $6,100 c. $6,399 d. $6,698

A building 160 feet tall casts a 90 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.) 61° 56° 29° 34°

12. Harrison loaned his friend Mattson $100 for one year at a simple interest rate of 5%. The total amount of money that Mattson will pay back at the end of the year is a. $5.00 b. $100.00 c. $105.00 d. $120.00

A chemistry student needs 20.0 g of diethylamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of diethylamine is 0.706 g/cm^3 . Calculate the volume of diethylamine the student should pour out.

If θ=210°, find the exact value of each expression below. (a) 2 sin θ = (b) sin (-θ) = (c) sin 2θ =

Which situation is an example of exponential decay? The amount of a radioactive element is decreasing at a rate of 35% per year. The weekly earnings of a part-time job that pays $8 per hour is increased by a weekly bonus of $25. The amount deducted for taxes decreases an annual salary by about 22%. The number of ants in an ant farm is increasing at a rate of 108% per week.

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $125. Two adults and three children must pay $89. Find the price of the adult's ticket and the price of a child's ticket. The price of a child's ticket is $. The price of an adult's ticket is $

A sports arena can hold 18,500 people, plus or minus 1200 people. A. Write an absolute value equation to represent the number of people that can attend an event. B. Explain the steps to solve the equation.

Match each action with its effect on the set of scores shown. Use each action only once. 90, 85, 35, 70, 67, 76, 90, 79, 94, 100, 87, 61, 56, 80, 67, 65 The greatest change on the mean because it is an outlier The mode of the data changes to 67. The median of the data changes to 79. The range of the data changes to 59. The mean of the data changes to 73.87.

Find the unit vector in the direction of (7,5). Write your answer in component form.

Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Alexa will earn $20 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties on 8 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa's songs were played. Define the variables that you use to write the system.

Find the solution to the system by the addition (elimination) method. Check your answers. 10x + 7y = 21 5x +9y = 27 What is the solution to the system? (Type an ordered pair.)

The base of a 13-foot ladder is 3 feet from a building. If the ladder reaches the flat roof, how tall is the building? The height of the building is

Graph the solution of the following system. x-2y ≥ -6 3x + y ≤ 6

Point T is at (-6, 2). What are the coordinates of T' after R(x-axis) o R(y-axis)? If a figure is translated with the rule T<-6, 3>, what translation moves the image back to the original position?

Against the wind a small plane flew 280 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air? The speed of the plane in still air was mph. The speed of the wind was mph.

Consider the line - 6x+7y=4. Find the equation of the line that is perpendicular to this line and passes through the point (1, 5). Find the equation of the line that is parallel to this line and passes through the point (1, 5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

Use the frequency histogram to complete the following parts. (a) Determine the number of classes. (b) Estimate the greatest and least frequencies. (c) Determine the class width. (d) Describe any patterns with the data. classes. (a) There are (Type a whole number.) (b) The least frequency is about (Round to the nearest whole number as needed.) The greatest frequency is about (Round to the nearest whole number as needed.) (c) The class width is (Type an integer or a decimal. Do not round.) (d) What pattern does the histogram show?

The population density of an area can be computed by dividing the total population by the total land area. The population density of Rhode Island is 870.5 people/square mile and the population is 1,055,046. What is the area of Rhode Island?

Make a box-and-whisker plot that represents the data. Describe the plot, in the area provided, by giving Q1,Q2,Q3, and Q4. If there are any outliers be sure to identify them. Newly planted tree heights (in inches): 16, 10, 10, 18, 18, 6, 24, 16

A technical machinist is asked to build a cubical steel tank that will hold 540 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m.

Which of the following is a true statement? a. A horizontal translation changes the x-coordinate of the endpoints of a figure but the y-coordinate remains the same. b. A vertical translation changes the x- coordinate of the endpoints of a figure but the y-coordinate remains the same. c. A horizontal translation changes the y-coordinate of the endpoints of a figure but the x-coordinate remains the same. d. A vertical translation changes both coordinates of the endpoints of a figure.

A space plane skims the edge of space at 4000 miles per hour. Neglecting altitude, if the circumference of the planet is approximately 20,000 miles, how long will it take for the plane to travel around the planet? How long will it take for the plane to travel around the planet? It will take__for a plane to travel around the planet. (Type an integer or a decimal.)

Suppose H (x)= (5x-2)6. Find two functions and g such that (fog)(x) = H (x). Neither function can be the identity function. (There may be more than one correct answer.) ƒ(x) = g(x)=

A plane flying a straight course observes a mountain at a bearing of 30.2° to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time later, the bearing to the mountain becomes 40.2°. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)? 7 km 13.1 km 4.7 km 11.5 km

Chris has a job selling newspapers every morning. He receives a base pay of $10 per day and also gets 15 cents for every paper he sells. One morning he made $16.45. How many papers did he sell? A 39 B 43 C 52 D 64

Brent Pickett borrowed $4000 from his brother Dave. He agreed to repay the money at the end of 2 years, giving Dave the same amount of interest that he would have received if the money had been invested at 3.25% compounded quarterly. How much money did Brent repay his brother? Brent repaid his brother $ (Round to the nearest cent as needed.)

Read the sentence. Toni's father taught at two schools, Concordia College and University of Wisconsin-Madison. How does the underlined phrase function in the sentence? as an adverb prepositional phrase as an appositive with essential information as an appositive with nonessential information as an adjective prepositional phrase

A man uses a loan program for small businesses to obtain a loan to help expand his vending machine business. The man borrows $29,000 for 4 years with a simple interest rate of 1.3%. Determine the amount of money the man must repay after 4 years. The man must repay $

Veronica wants to cut a sheet of paper into squares with an area of 12 square inches. For the best approximation, the length of inches. If each side were exactly this length, the each side of the square pieces of paper must be approximately equal to area of each square would be square inches.

Which of the deals shown has the lesser unit price? Deal 1: 9 pairs of shorts for $89.01 Deal 2:8 pairs of shorts for $75.92 Choose the correct answer below. A. Deal 1 and Deal 2 have the same unit price. B. Deal 1 has the lesser unit price. C. Deal 2 has the lesser unit price.

A 150-pound person uses 5.1 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 210 calories? minutes in order to use at least 210 calories. A person must walk for at least (Round up to the nearest minute.)

Describe the transformation of f(x) = cosx to g(x) = cosx-4 A. (x) is shifted 4 units right to g(x). B.(x) is shifted 4 units left to g(x). C. (x) is shifted 4 units down to g(x). D. f(x) is shifted 4 units up to g(x).

The function h (t) = -16t(t-7) models the height of an object at any time t after it is launched, where t is measured in seconds. After how many seconds will the object hit the ground? 3.5 seconds 7 seconds 9 seconds 16 seconds

Gaines invested $11,000 in a money market account with an interest rate of 2.25% compounded semiannually. Three years later, Karen withdrew the full amount to put toward the down payment on a new house. How much did Karen withdraw from the account? Karen Karen withdrew $ (Round to the nearest cent as needed.)

You and your friend plan to meet for coffee in a town between your two towns. You both drive at a constant speed for 45 minutes, but your speed is 40 miles per hour and your friend's speed is 35 miles per hour. What is the total distance between your town and your friend's town? Justify your answer.

Suppose you take out a loan of $15,000 where interest on the loan accrues at an APR of 8.4% compounded monthly. a. If the loan is to be paid back in 12 years. What will the monthly payment of the loan be? b. What will the total interest on the loan be?

Use the simple interest formula to determine the missing value. p=$1275, r=?, t=2 years, i=$30.60 r= % (Do not round until the final answer. Then round to one decimal place as needed.)

A certain forest covers an area of 2300 km². Suppose that each year this area decreases by 3%. What will the area be after 13 years? Use the calculator provided and round your answer to the nearest square kilometer.

A cylinder and a sphere both have the same radius, 4. The height of the cylinder is equal to the diameter of the sphere. Select the expression that describes the volume of the cylinder that is not occupied by the sphere. (Use π=3.14) A. 39.67 B. 85.33π-128π C. 124.56 D. 128π-85.33π

A laptop computer is purchased for $2400. After each year, the resale value decreases by 25%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

Your class earned $110.00 Saturday afternoon by washing cars to raise money for a class trip. This is 1/4 of the money needed for the trip. What is the total amount needed? A $114 B $27.50 C $106 D $440

Find the average rate of change of f(x)=x²+3x+1 from x=-4 to x= 1. Simplify your answer as much as possible.

Jamie and Margie need to divide a couch and a hot tub. Using the Method of Sealed Bids, Jamie bids $530 on the couch and $160 on the hot tub, while Margie bids $490 on the couch and $180 on the hot tub. Jamie will get the couch, and Margie will take the hot tub and will also get a little bit of money from Jamie. To make the division fair, how much money will Jamie have to give to Margie?

At a festival, stunt devils are launched in large catapults and air cannons. On one launch, the height of the stunt devil in feet above the ground after t seconds is modeled by y = -16t² + 60t +8. How long does it take the stunt devil to hit the ground? 10.2 sec 15 sec 3.8 sec 16 sec

Determine the total amount and the interest paid on $4000 with interest compounded monthly for 5 years at a) 2%. b) 4%. c) 8%. d) Is there a predictable outcome in either the amount or the interest when the rate is doubled? a) The total amount accumulated at 2% is $ (Round to the nearest cent as needed.)

If a ball is thrown into the air with a velocity of 46 ft/s, its height in feet t seconds later is given by y = 46t - 16t². (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. (b) Estimate the instantaneous velocity when t = 2.