Basic Math Questions and Answers

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.)

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 15 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own? Do not do any rounding.

A voltage V across a resistance R generates a current I=V/R. If a constant voltage of 6 volts is put across a resistance that is increasing at a rate of 0.2 ohms per second when the resistance is 4 ohms, at what rate is the current changing? (Give units.) rate =

Find two points on the graph of this function, other than the origin, that fit within the given [-10, 10] by [-10, 10] grid. Express each coordinate as an integer or simplified fraction, or round to four decimal places as necessary.

Write in factored form by factoring out the greatest common factor. 6y³ - 3y

A population numbers 18,000 organisms initially and grows by 15.2% each year. Suppose Prepresents population, and t the number of years of growth. An exponential model for the population can be written in the form P = abt where P=

Richard mows 5 lawns for $25 each. He spends $15 on gas, then gives his dad half of what is left to cover his car insurance. He then spends $20 for himself and puts the remaining amount in his savings account. How many dollars did he put in his savings account? 20 2 55 42 35

If a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d = 3.57√h. Suppose the person's eye level is 8.41 meters above sea level. How far can she see to the horizon? Round your answer to the nearest tenth.

Simplify the following expressions completely: A) √49 = B)√144=

The police department in your city was asked by the mayor's office to estimate the cost of crime. The police began their study with burglary records, taking a random sample of 500 files since there were too many crime records to calculate statistics for all of the crimes committed. If the average dollar loss in a burglary, for this sample size 500 is $678, with a standard deviation of $560, construct the 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount. We can be 95% confident that the upper limit of our interval of dollar loss in crimes committed is

If 7000 dollars is invested in a bank account at an interest rate of 7 per cent per year, Find the amount in the bank after 5 years if interest is compounded annually: Find the amount in the bank after 5 years if interest is compounded quarterly: Find the amount in the bank after 5 years if interest is compounded monthly. Finally, find the amount in the bank after 5 years if interest is compounded continuously.

Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years. A) A = 100 + te² B) A = 100+ e²t C) A = 100e²t D) A = 100+ 2et

Approximate the number using a calculator. Round your answer to three decimal places. 3.2π 10.053 38.635 38.983 36.462

Decide whether a line with the given slope slants upward or downward or is horizontal or vertical m=3/2 Choose the correct answer below A horizontal B. upward C. downward D. vertical

A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 23 feet long, 17 feet wide, and 9 inches deep. a) Determine the volume, in cubic feet, of mulch the contractor will need. When appropriate, use the key on your calculator. b) If mulch costs $9 per cubic foot, what will the cost of mulch be? a) The volume is ft³. (Type an integer or decimal.)

Let f (x) = log2 (x) + 2 and g(x) = log2 (x³) - 4. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)