Math Questions

x+2y-2z = 10 -3x+4y+z=-5 -5x+y+3z=-21 Find the unique solution to this system of equations. Give your answer as a point.

Josie and Red are two dogs standing next to each other at the dog park. Josie starts running straight west and Red starts running straight east. After 22 seconds, the two dogs are 1,100 feet apart. Suppose Red runs 4 feet per second faster than Josie. How fast were each of the dogs running?

A gardener has 880 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. shorter side: What dimensions would guarantee that the garden has the greatest possible area? ft (feet) longer side:

Find the x-intercept(s) algebraically. f(x)=2x²-9x+9 X= (Type an exact answer, using radicals needed. Use integers or fractions for any numbers in the expression. Type each solution only once. Use a comma to separate

Solve the system by elimination or by any convenient method. (If the system is dependent, enter DEPENDENT. If there is no solution, enter NO SOLUTION.) x + 2y = 3 3x+6y= 12 (x, y) =

If a car travels 37 miles per gallon of fuel (in other words, the car does 37 mpg), how many kilometers does it travel per liter of fuel? Use the conversion factors on page 55 (that is, use 1 mile 8/5 km and 1 gallon = 8 pints and 1 liter ≈ 2 pints). The car trav's about km on one liter of fuel

Graph the following quadratic function. f(x) = x² + 4x Find the vertex of the function.

Suppose you wish to take out a loan for $15,000 at an annual interest rate of 5.25%, compounded monthly. If you want each payment to be as close as possible to $200.00, how long should the period of the loan be? Choose the correct answer below. 10 years 9 years 8 years 7 years

(a) Approximate the probability that 71 or more have hypertension. The probability that 71 or more have hypertension is approximately.

Tomas needs exactly 6 potatoes to make 12 potato pancakes. Which of the following statements are true? Tomas needs exactly 12 potatoes to make 24 potato pancakes. Tomas needs exactly 18 potatoes to make 36 potato pancakes. Tomas needs exactly 24 potatoes to make 44 potato pancakes. Tomas needs exactly 30 potatoes to make 60 potato pancakes. Tomas needs exactly 36 potatoes to make 78 potato pancakes.

Fourteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is defective?

In ΔCDE, M∠C = (x − 4)°, m∠D = (11x – 11)°, and m∠E = (x + 13)°. Find m∠C.

Find the LCM of the set of algebraic expressions. 20y², 12yz, 15z

Consider the following equation of a circle. (x + 3/7)² +y ² = 25/9 Find the center, (h. k).

The last time Brea played softball, she hit the ball 35% of the times she was at bat. Based on this information, how many times will Brea hit the ball the next time she plays softball if she is at bat 20 times? F 4 G 7 H 15 J 6

The owner of Kensington Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 15 small arrangements and 15 large arrangements, which took her a total of 195 minutes. After lunch, she arranged 12 small arrangements and 7 large arrangements, which took 121 minutes. How long does it take to assemble each type?

Your teacher will give you a set of four function machines. Your team's job is to get a specific output by putting those machines in a particular order so that one machine's output becomes the next machine's input. As you work, discuss what you know about the kind of output each function produces to help you arrange the machines in an appropriate order. The four functions are reprinted below. f(x)=√x h(x) = 2x - 7 g(x) = -(x - 2)² k(x) = - x/2 -1 a. In what order should you stack the machines so that when 6 is dropped into the first machine, and all four machines have had their effect, the last machine's output is 11? b. What order will result in a final output of 131, 065 when the first input is 64?

According to a survey, 10% of Americans are afraid to fly. Suppose 1,100 Americans are sampled. a. What is the probability percentage that 121 or more Americans in the survey are afraid to fly? b. What is the probability percentage that 165 or more Americans in the survey are afraid to fly? c. What is the probability percentage that 8% or less of the Americans surveyed answered they were afraid to fly?

A sales team estimates that the number of new phones it will sell is a function of the price that it sets. It estimates that if it sets the price at a dollars, it will sell f(x) = 6,818 - 7x phones. Therefore, the company's revenue is x(6,818 - 7x). Find the price that will maximize the company's revenue. Select the correct answer below: 511 487 489 491 507

The function g is defined as follows. g(x)=4x²+3 If the graph of g is translated vertically downward by 8 units, it becomes the graph of a function f. Find the expression for f(x). Note that the ALEKS graphing calculator may be helpful in checking your answer.

Four joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.

Standard form: Expanded form: 9 * 1,000,000 + 8 * 1,000 + 7 * 100 + 6 * 10 Word form:

Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour? 0.8 of an inspection in 1 hour 4 inspections in 5 hours 1.25 inspections in 1 hour 5 inspections in 4 hours

Greg deposited $4000 into an account with 4.3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years? Do not round any intermediate computations, and round your answer to the nearest cent.

Write the equation of the line passing through (-2,-4) that is parallel to 3x + 5y = 11.

A projection made in January of 2005 determined that x years later, the average property tax on a three-bedroom home in a certain community will be T(x) = 48x 3/2 + 40x + 1300 dollars. Estimate the percentage change by which the property tax will increase during the first half of the year 2012.

Find the zeros of the following polynomial. f(x) = x³ + 12x4 +36x³ List the zeros separated by commas. For example, if you found that the zeros were x = 1, x = 2, enter 1, 2, 3. Provide your answer below:

A fence is to have 3 1/2 wide boards between two posts that are 94 1/4 apart so that the space between each board is the same. Calculate the number of boards and the spacing so that the spacing between the boards is as small as possible. Round your answer for the spacing to the nearest 16th of an inch.

We determined R = 0.0825 and T = 9/15 The amount of the loan, the principal, was $70,000, giving P = Substitute these values into the formula to find the amount of interest earned (in $) at 8 1/4 % for 9 months. I = PRT

A particle moves according to the law of motion s = t³ - 8t2 + 3t, t ≥ 0, where t is measured in seconds and s in feet. (a) Find the average velocity over the interval [1,2] (b) Find the velocity at time t. (c) What is the velocity after 3 seconds? (d) What is the acceleration after 7 seconds? (e) Fort > 0, when is the particle moving in the positive direction?

Consider the parabola given by the equation: f(x) = 4x² + 14x -15 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two a -intercepts of the parabola and write them as a list, separated by

Google it: According to a report of the Nielsen Company, 82% of internet searches used the Google search engine. A sample of 100 searches is studied. Use the Cumulative Normal Distribution Table or technology. Round your answer to four decimal places. (a) Approximate the probability that more than 76 of the searches used Google. The probability that more than 76 of the searches used Google was approximately

After a baby was born, he began to gain weight at a rate of 1.5 pounds per month. The weight of the baby at birth was 10 pounds. Write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby t months after birth.

Find the equation of the line through (3, 1) with slope 7. Enter your solution in the form y = mx + b. y =

If a single pane of glass obliterates 2% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function below. p(n)= 100(0.98)n (a) What percent of light will pass through 20 panes? (b) What percent of light will pass through 30 panes? (c) Explain the meaning of the base 0.98 in this problem.

A gray crayon is made with 5 mL of black wax for every 6 mL of white wax. Which of the following wax mixtures will create the same shade of gray? Choose 2 answers: 10 mL of black wax mixed with 24 mL of white wax 15 mL of black wax mixed with 18 mL of white wax 35 mL of black wax mixed with 42 mL of white wax 20 mL of black wax mixed with 26 mL of white wax 45 mL of black wax mixed with 48 mL of white wax

Sketch the graph of a function f that satisfies all of the following properties. Indicate all asymptotes. (a) f(x) is defined for all real numbers except x = 1. (b) f(x) is discontinuous at x = -2 and x = 1, but is continuous for all other z. (c) f(x) is not differentiable at x = -2, x = 1, and x = 4 but it is differentiable for all other . (d) lim f(x) = 3, (e) lim f(x) = -2, (f) lim f(x) = -0.

Fill in the blanks Enter intercepts as ordered pairs, aka points. Then Graph the parabola given in vertex form. Vertex Form: y = (x + 4)² - 1 1. Does the parabola open up or down? Up Down 2. Vertex (x, y) = 3. Equation of the Axis of Symmetry:

Below, one description, one graph, and one equation are equivalent. Choose the proper set. You start with 2 Xbox360 games and each month you buy 2 new games. You start with 3 Xbox360 games and each month you buy 3 new games.

A rectangular parking lot has a length that is 6 yards greater than the width. The area of the parking lot is 160 square yards. Find the length and the width The parking lot has a width of The parking lot has a length of yards. yards.

7. A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people. a. Find a combination of small and large tables that seats exactly 150 people. b. Let x represent the number of small tables and y represent the number of large tables. Write an equation to represent the relationship between x and y. c. Explain what the point (20, 5) means in this situation. d. Is the point (20, 5) a solution to the equation you wrote? Explain your reasoning.

A lunar module weighs 12 tons on the surface of the Earth. How much work is done in propelling the module from the surface of the moon to a height of 55 miles? Consider the radius of the moon to be 1100 miles (from the center of the moon) and its force of gravity to be one-sixth that of Earth.

Henry made a shirt using 1/3 yards of red fabric and 3/4 yards of blue fabric. How many more yards of blue fabric did Henry use? Write your answer as a fraction in simplest form.

A school counts the number of students taking AMDM and find 205 students taking AMDM. They also count the number of students taking Physics and find 217 students taking the Physics. When they compare the two lists they find 86 student taking AMDM and Physics. What is the probability of a student taking AMDM given they are taking Physics. (Answer in decimal form rounded to the thousandth)

{(-9, 3), (5, -6), (3, -9), (-6, 5), ?} Which ordered pair can replace the missing value and create a function? (5,3) (9,3) (-6,-9) (-9,-6)

Graph the following quadratic function. f(x)=x²-9 Find the vertex of the function. The vertex is (Simplify your answer. Type an ordered pair.)

The coordinates of the endpoints of RT are R(-6,-5) and T(4,0), and point S is on RT. The coordinates of S are (-2,-3). Which of the following represents the ratio RS: ST? 1:2 2:3 3:2 3:4

You are playing a card game. If you pull an Ace you win $26, if you pull the King of hearts you win $204, if you pull a jack or a queen you win $13, all other pulls you lose. What price should you be charged to make this a fair game? $8 $7 $6 $5

The local bakery requires that Josh must spend at least $7 to be able to pay using a credit card. Cookies cost $2.10 each. A bottle of water costs $1.10. If c represents the number of cookies Josh would need to buy to pay for one bottle of water and the A cookies using a credit card, which of the following inequalities best models the situation described above?

A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while. a. How many miles has the car traveled if it has the following amounts of gas left in the tank? i. 15 gallons ii. 10 gallons iii. 2.5 gallons