Basic Math Questions and Answers

2 The area of a rectangle is 21 ft², and the length of the rectangle is 1 ft less than double the width. Find the dimensions of the rectangle.

The year that you enter college, your freshman class consists of 760 students. According to statistical studies, about of these students will actually graduate. Approximately how many of 7 your classmates will receive their degrees?

Carry out the indicated operation and give your answer with the specified number of significant digits. 43 x 32.1; 3 significant digits 43 x 32.1≈ (Simplify your answer.)

Solve (w-5)³-48 = 0 where w is a real number. WZL-

2 What are the first two steps to graph y=x+4? What is the first step? A. Plot the point (4,0). Plot the point (0,4). B. OC. Plot the point (3,2). OD. Plot the point (2,3). What is the next step? O A. From this point, move 2 units up (the rise) and 3 units to the right (the run). OB. From this point, move 3 units down (the rise) and 2 units to the left (the run). 2 OC. From this point, move 4 units up (the rise) and units to the right (the run). 3 OD. From this point, move 3 units up (the rise) and 2 units to the right (the run).

Solve for u, where u is a real number. 3=√√2u+15 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

A rental truck costs $45.45 for a day plus 74¢ per mile. (a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day. C = X (b) Find the.total.cost of the rental if it was driven 194 miles. C = $ * Enter a number.

Give the slope and y-intercept of the line whose equation is given. Then graph the linear function. 3 f(x) = 5x-7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The slope is ***** (Simplify your answer. Type an integer or a fraction.) OB. The slope is undefined.

A silver dollar is dropped from the top of a building that is 1346 feet tall. Use the position function below for free-falling objects. s(t) = -16t² + vt + so (a) Determine the position and velocity functions for the coin. s(t) = -161² 1346 v(t) = -32t (b) Determine the average velocity on the interval [1, 2]. -48 ft/s (c) Find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = -32 ft/s V(2) = ft/s -64 (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t = 9.17 S (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) 9.147 ft/s

Solve (w+7)²-36 = 0, where w is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click "No solution."

Translate the sentence into an inequality. The difference of twice a number and 10 is greater than or equal to -29. Use the variable b for the unknown number.

The length of a rectangle is 9 yd more than twice the width x. The area is 396 yd². Part 1 of 3 (a) Write an equation in terms of x that represents the given relationship. The equation is xx + 9x (yd) = 396(yd) Part: 1/3 Part 2 of 3 ☐=0 The width is X (b) Solve the equation to find the dimensions of the given shape. yd.

Select the answer that best completes the given statement. The graph of the equation x= 1 is a/an line. standard horizontal undefined vertical regression

Solve your equation in the previous step for y. y = 20- 60-x 3 X P(x) = 3 Step 3 The product P of the two numbers is xy. Use your result from the previous step to write the product as a function of x only. 60x-x² 3 (60-x)x Step 4 Rewrite P(x) by completing the square. P(x) = -1/3 ✔ -1/3 (x-30 30 X )² + 300✔✔ 300) Step 5 Use your result from the previous step to complete the following statements. The maximum value of the product, occurring at the vertex of the graph of P(x), is X. This maximum occurs when x = 30 , and y = Therefore, what are the two numbers? (Enter your answers as a comma-separated list.) 4 X.

Solve for x, where x is a real number. -3 = √2x+6-1 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval. (If an answer c not exist, enter DNE.) f(x) = minimum maximum 5 x - 2 (x, y) = (x, y) = (2,7]

Translate the sentence into an inequality. Two times the sum of a number and 16 is at least -21. Use the variable w for the unknown number.

The growth of a company can be described by the equation N = 700(0.06)0.st where t is the number of years the company has been in existence and N is the number of employees. (a) What is the number of employees when t = 0? (This is the number of employees the company has when it starts.) N = employees (b) What is the number of employees when t = 8? (Round your answer to the nearest whole number.) N = employees

You need a 85% alcohol solution. On hand, you have a 65 mL of a 30% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?

A company reimburses its sales representatives $150 per day for lodging and meals plus 37¢ per mile driven. Write a linear equation giving the daily cost C to the company in terms of x, the number of miles driven. How much does it cost the company if a sales representative drives 221 miles on a given day? $ 231.77

2 Solvex -50, where x is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click "No solution." -5√2 x = 5 0.0.... X 08 0/6 Ś No solution ?

Solve for u, where u is a real number. √√u=2 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

What operation on both sides of the equation isolates the variable on one side? Give the solution of the equation. 3x = 2x - 10 Enter the exact answer.

Solve for w, where w is a real number. w = -3

2 Solve x =96, where x is a real number.

If x= -5 and y = -9, evaluate the expression. 6x²-5y² Select the correct choice below and fill in any answer boxes within your choice. A. The answer is (Type an integer or a simplified fraction.) B. The expression is undefined.

Solve for y, where y is a real number. √√/y=-4

The length of a rectangle is 6 yd longer than its width. If the perimeter of the rectangle is 44 yd, find its area. 8 08 2 0yd²

Answer the following questions using the information given. The length of a small ant is 3-10-3 meter and the length of a large ant is 3.5-10-² meter. a.) Find the difference in length, in millimeters, of the two ants. Write your answer in scientific notation. millimeters. b.) If there is a trail of 2 small ants and 1 large ant in a straight line, find the total length of the line. Write your answer in scientific notation. meters.

Use the quadratic formula to solve for x. 2x²+x-9=0 (If there is more than one solution, separate them with commas.) x = -1+√2-1-√2 VE 0/6 09 00 X S ?

Evaluate the expression u²+² (u-v)² given that u = - - 5 and v = 4. u² + v² - (u - v)² = Jua I

The solution to the equation depends on the constant a. Assuming a is positive, what is the effect of increasing a on the value of the solution? Does it increase, decrease, or remain unchanged? O The value of the solution increases. O The value of the solution decreases. O The value of the solution remains unchanged. x-a=0

Assume that movie tickets cost p dollars for adults and q dollars for children. Write expressions for the total cost of tickets for: (a) 4 adults and 6 kids total cost (b) No adults and 7 kids total cost = (c) No kids and 8 adults total cost = (d) A adults and C kids total cost =

The length of a rectangle is three times its width. If the area of the rectangle is 147 yd², find its perimeter.

A standard queen bed hotel room at the Posh Inn is currently priced at $135 a day, after a 17% markup to offset inflation costs. What was the daily charge for the room before the increase? Choose one 5 points $157.95 $118.00 $115.38 $100.75

1 The lower the price for purchasing a song from an online music store, the more times the song is downloaded. Let d r(p) give the average number of daily downloads of a song as a function of the price of the song (in cents). Let Po be the price currently being charged for the song (in cents). What does the statement r(60) tell you about the number of downloads from the store? Or(60) gives the price, in cents, of the song if the average number of daily downloads is 60. Or(60) gives the price of the song if it has been downloaded a total of 60 times. Or(60) gives the average number of songs downloaded daily at a price of 60 cents per song. O r(60) gives the average daily revenue of the music store if the song costs 60 cents. Or(60) gives the total number of times the song is downloaded if it costs 60 cents.

Kira has scored 74, 61, 65, and 72 on her previous four tests. What score does she need on her next test so that her average (mean) is 72? X Ś ?

You are traveling on a zip-line between two towers. A bird's eye view of the zip-line is drawn below. Each box on the grid represents a 12 ft x 12 ft square. Consider tower A to be located at the origin (0,0). It takes you 48 seconds to travel from one tower to the other. Assume you travel at the same speed the entire time. A) Find the exact coordinates in feet of your location 15 seconds after you leave tower A traveling towards tower B. B) Calculate the distance that you traveled in that 15 seconds. Round your answer to the nearest tenth of a foot.

Before we start multiplying, we notice that (6x9)(6x - 9) = expression. (6x - 9)2 (6x9)(6x - 9) + 4 = (6x - 9)² - ³² +4 Substitute this into the

Danielle is creating a scale drawing of her room. The rectangular room measures 20 feet by 24 feet. If her drawing uses a scale where 1 inch represents 2 feet of the actual room, will her drawing fit on a 8.5 inch by 11 inch piece of paper?

Solve for v, where v is a real number. √2v+7-√4v+13 = 0 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". = 0 V = No solution 8 X 0/0 2:16 0.0.... Ś ?

Solve for y. 2y²=-11y-5 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $8,000, how much will be invested in each type of investment? The amount invested in CDs is $ The amount invested in bonds is $

Order the integers from least to greatest. a. 5.-7. 6.-2.0 b. -3. 5. 9.-8. 1 d. -42. -75. 69, 28, 64 e. 35.-117, 69, -171.-99 Order the integers from greches) to least. -T 7. 14.-28, 35 N 44 -25. 63. -32. 41 1 20. -40. 0. -40. 00 Orde the temperclures ton wames" to colded. |________12°F__PAYE__REVF- SF €21C. 1BC 4C7C

The lower the price for purchasing a song from an online music store, the more times the song is downloaded. Let d average number of daily downloads of a song as a function of the price of the song (in cents). Let po be the price currently being = r(p) give the charged for the song (in cents). What does the statement po r(Po) tell you about the number of downloads from the store? O The average revenue earned per download at the current price. O The total revenue of the music store when po songs are downloaded in a day. O The average daily revenue of the music store if the current price is doubled. O The total numbe of times the song is downloaded at the current price. O The average daily revenue of the music store from selling the song at the current price.

Animals often play an important role in the transportation of plant seeds. A 2014 study by Baldwin and Whitehead investigated the role played by fruit bats in seed transportation. The data provided give the weight in grams and length in inches of the fruit bats from this study. Click to download the data in your preferred format. CrunchIt! CSV Excel JMP Mac-Text Minitab PC-Text R SPSS TI-Calc Suppose Baldwin and Whitehead want to construct a linear model to predict the length of the wingspan of a fruit bat (in inches) from the bat's weight (in pounds). Calculate the y-intercept and slope of the least-squares regression line using weight to predict length. Give your answers precise to three decimal places. y-intercept: in slope:

Every Sunday, Sarah makes trail mix for the week. She always makes more than 3½ cups of the mix. Then she divides it equally into 7 bags. Write an inequality for the number of cups of trail mix, x, in each bag. Show your work.

Solve for y. 5y²-4=-y If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

Several months ago, a patient weighed 95 kg. When he comes in for his next appointment, he tells you he has lost 11 lb. If he is correct, how many kilograms should he weigh? kg

Perform the following conversion using either the proportion method or dimensional analysis. 180 mL = fl oz