Basic Math Questions and Answers

Write an equation of the line perpendicular to the given line that contains P. P(8, − 4); y = x/4+5

Garrett can order stickers from two companies. Company A charges a $30 design fee plus $0.80 per sticker. Company B charges a $14 design fee plus $1.20 per sticker. How many stickers would Garrett have to order for the cost at both companies to be the same?

Given the cubic function f(x)=3x³-5x²-34x + 24: a) Show that x=4 is a zero off. Use this zero to write down a factor of f b) Use polynomial long division to find the other zeros off. Show your algebraic work.

C(f)=16-5f a.) Find m b.) What is the C-intercept? c.) Find C(3)

Find the domain of the function y = 3 tan(2x/3).

Julia has $5.00 to spend on lemons. Lemons cost $0.59 each, and there is no tax on the purchase. Which of the following inequalities can be used to represent a, the number of lemons Julia can buy?

A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than 9? Write your answer as a fraction.

The supply and demand curves for a business dealing with wheat are Supply: p= 1.45 +0.00014x² Demand: p= (2.373 -0.007x)² where p is the price in dollars per bushel and x is the quantity in bushels per day. Use a graphing utility to graph the supply and demand equations and find the market equilibrium. (The market equilibrium is the point of intersection of the graphs for x > 0. Round your answers to two decimal places.)

A rectangular prism has a height of 3 inches and a volume of 27 cubic inches. The height of this prism is changed to 6 inches, and the other dimensions stay the same. What is the volume of the prism with this change?

For the following infinite series, find the first four terms of the sequence of partial sums. Then make a conjecture about the value of the infinite series. 3+0.8+0.08 +...

The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 180 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store. number of items - continuous; total time - continuous number of items - continuous; total time - discrete number of items - discrete; total time - discrete number of items - discrete; total time - continuous

In sailing, it is not possible to head straight into the wind. In order to get upwind, a sailboat simply sails at an angle to the wind and then turns to sail back toward where it wants to go. Assume that a boat needs to get directly upwind 6000 m. If it sails off at a 45 degree angle to the wind and then turns back 90 degrees towards the original goal, how far would it have to sail to get directly upwind 6000 meters? Round to the nearest tenth. Distance to get directly upwind 6000 meters: meters 8485.3 010392.3 4242.6 6000

A landfill has 60,000 tons of waste in it. Each month it accumulates an average of 360 more tons of waste. What is a function rule that represents the total amount of waste after m months? Let W represent the total amount of waste and m represent months. A. W = 360m + 60,000 B.W = 60,000m + 360 C.W = 360m - 60,000 D.W = 60,000m - 360

Determine whether the conclusion follows logically from the premises. If my jeans are tight, then I will go on a diet. My jeans are tight. Therefore, I will go on a diet. Valid argument Invalid argument If I win the lottery, then we can all go on a cruise. I won the lottery. Therefore, we can all go on a cruise. Valid argument Invalid argument

A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10 adults over 50, what is the probability that at least six wear sunglasses? 0.700 0.006 0.850 0.200

Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points. (-1,3) and (0,0) (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the parallel line is -3.(Type an integer or a simplified fraction.) B. The slope of the parallel line is undefined. (b) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the perpendicular line is undefined. B. The slope of the perpendicular line is .(Type an integer or a simplified fraction.)

Put the equation y = x² + 24x + 135 into the form y = (xh)² + k:

Use a graphing utility to find the x-intercepts of the graph of the function. y=x²-9x-10 Select the correct choice below and fill in any answer boxes within your choice. A. The x-intercept(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed.) B. There is no x-intercept.

Your current wage is $1,500 plus 3% commission per month. During your 6-month employee review, your boss suggests to change your base rate to $1,200 but is offering you a larger commission percentage. What commission rate would he need to offer to make up for the reduced base rate? Your past 6 month sales numbers are: $10,000, $12,450, $8,756, $10,354, $10,938, and $11,452.

A sprinkler rotates 360° to water a circular region. If the total area watered is approximately 2,200yd², determine the radius of the region (the radius is length of the stream of water). Round the answer to the nearest yard. Select one: a. 19 yd b. 350 yd c. 6 yd d. 26 yd

In order to pay for college, the parents of a child invest $15,000 in a bond that pays 10% interest compounded semiannually. How much money will there be in 17 years? Round your answer to the nearest cent.

Solve for x, where x is a real number. √10x-21 = x If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Identify the slope and y-intercept, if they exist. 3x-y=2 Part 1 of 2 Select "Undefined" if applicable. Part 2 of 2 Write the intercept as an ordered pair. Select "None" if applicable. If there is more than one intercept, separate them with commas. y-intercept

Classify the following random variable according to whether it is discrete or continuous. the number of emails received on any given day discrete continuous

Forensic scientists use the following function to find the height of a woman if they are given the height of her femur bone, f, in centimeters. Find the height of a woman whose femur measures 59 centimeters. H(f) = 2.59f + 47.24

Given the polynomial f(x) = x² – 3x, what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 1 and a? Enter an integer as your answer. For example, if you found a = 8, you would enter 8.

Marta was pregnant 268 days, 258 days, and 270 days for her first three pregnancies. In order for Marta's average pregnancy to equal the worldwide average of 266 days, for how long must her fourth pregnancy last? In order to equal the worldwide average of 266 days, Marta's fourth pregnancy must last for days.

Graphing the solution region of a system of linear inequalities can get messy. Brainstorm ways of graphing the solution region that aren't so messy. Be creative. Select one of the systems below and work it out step by step using your method. Document each step either in a video or in an image. Provided systems: Three inequality system written in standard form: 4x+y> 8 2x-3y < 18 y<0 y>2x-5 y<-4x+2 X>0 Four Inequal 3y > x-24 4x + y<6 y<4x-1 y<0 v<x+6 y<x+3 X>0 Y>0 1. Give an overview of your favorite method(s). Explain why you like it and how it reduces the mess. Upload a video or series of images to explain your method step by step. Systems should have a minimum of three inequalities.

A population of rabbits oscillates 35 above and below an average of 129 during the year, hitting the lowest value in January (t = 0). Find an equation for the population, P, in terms of the months since January, t. P(t)= What if the lowest value of the rabbit population occurred in April instead?

A website got 4 x10⁹ views on Saturday and 8 x106 views on Sunday. How many times more views were on Saturday than Sunday?

Write the exponential equation x = 12^y in logarithmic form.

Michelle and Michael collect baseball cards. Michael has 5 more cards than Michelle. Together they have 27 cards. How many cards does each have?

When the sun is at a certain angle in the sky, a 100-foot building will cast a 25-foot shadow. How tall is a person if he casts a 1.5-foot shadow at the same time? Enter only the number.

Graph the equatiob y=-x² - 2x + 3 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Keith's school is due west of his house and due south of his friend Mary's house. The distance between the school and Mary's house is 15 kilometers and the straight-line distance between Keith's house and Mary's house is 17 kilometers. How far is Keith's house from school?

Plot the intercepts to graph the equation. x+4y=8 Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Diana has 360 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) = -w² +180w (b) The area is largest for W= (Simplify your ans

Alice loaned Juan $8080 at an interest rate of 15 % for 116 days. How much will Juan pay Alice at the end of 116 days? Round your answer to the nearest cent. Note: Assume 365 days in a year and 30 days in a month.

Which choice correctly compares the two decimal numbers to hundredths? A) 28.14> 29.11 B) 28.61 > 28.48 C) 29.13 < 28.37 D) 29.19 < 28.32

Graph the linear equation. y=-2/3x+1

Solve the equation 19t² + 4t =-12t³ State your answers as integers or reduced fractions, separated by commas.

At which points is the function continuous? y = 4√3x-2 The function is continuous on (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

There are 630 dishes that need to be rinsed. Omar can rinse them in 105 minutes by himself. It will take his friend Brian 70 minutes to rinse these dishes. How long will it take them if they rinse these 630 dishes together?

Solve for using the square root property. 2t²-12=-2

Graph the equation y = x² + 12x + 35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Click to plot points. Click points to delete them.

John is in a club that collects annual dues. In the first year that he was a member, he paid $20 in club dues. However, the club dues increase by $2 each year. Identify the function that describes the relationship between the number of years that John has been a member of the club and the dues he pays that year. f(n) = 20 + 2(n-1) f(n) = 20 + 2(n+1) f(n) = 20 + 2n f(n) = 20 + 2(n - 2)

Outside temperature over a day can be modelled sa sinusoidal function. Suppose you know the high temperature for the day is 95 degrees and the low temperature of 65 degrees occurs at 4 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Does the function f(x) = (0.85)x represent exponential growth, decay, or neither? A) Exponential decay B) Impossible to determine with the information given. C) Exponential growth D) Neither

Dominique is allowed to play up to 8 hours of video games this week. They want to play video games for at least 4 hours this weekend. Which of the following can be used to represent t, the number of hours they can play video games before the weekend?

The decay rate, k, for a particular radioactive element is 2.5%, where time is measured in years. Find the half-life of the element. The half-life is years. (Round to one decimal place as needed.)