Basic Math Questions and Answers

Mark wants to borrow $1,000 to purchase a nice bicycle. The local bank provides him with a loan with an annual interest rate of 10 percent. How much interest should Mark pay after one year?

For the function, supply a valid technology formula. f(x) = e-4x Use technology to compute the missing values in the following table accurate to four decimal places.

Suppose f(x) is a rational function with leading term -1, has three roots: a root at z = -2 of degree 1, a root at r = 0 of degree 1, and a root at r= 1 of degree 1, f(x) also has a vertical asymptote at r= -1 of degree 3. 1) leading term: -1 2) roots : √ 2 (deg. 4), 0 (deg. 1), 1 ( deg.1) (a) Determine the sign decomposition of f(x):

A new measurement system is emerging. This system uses the following conversions: 3 gallons = 6 liquettes and 4 liquettes = 9 miniliquettes In this new new system, 85 gallons would be how many miniliquettes?

Write the definition as a biconditional statement. 13. A scalene triangle is a triangle with three sides with different lengths. 14. A square is a rectangle with four sides that are the same length. 15. Perpendicular lines are lines that intersect at a 90° angle.

Solve the system of equations by substitution. x = 5y + 12 3x + 7y= -8 The solution of the system is x = and y=

Using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation 10.0y 4.55x = 581 where x is the number of years after 2000. (a) What is the projected population in 2022? y = (b) In what year is the population predicted to be 67.2 million?

A wholesale store advertises that for $20 you can buy one pound each of peanuts, cashews, and almonds. Cashews cost as much as peanuts and almonds combined. You purchase 2 pounds of peanuts, 1 pound of cashews, and 3 pounds of almonds for $36. What is the price per pound of each type of nut? (See Example 4.)

A promoter needs to make $50,700 from the sale of 1100 tickets. She charges $43 for some tickets and $60 for the others. (a) If there are x of the $43 tickets sold and y of the $60 tickets sold, write an equation that states that the sum of the tickets sold is 1100. (b) How much money is received for the sale of x tickets for $43 each? (c) How much money is received for the sale of y tickets for $60 each? (d) Write an equation that states that the total amount received from the sale is $50,700. (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $50,700.

x² + Bx + 1/4 Find the value of "B" that will make the expression a perfect square trinomial Write the trinomial as a product of two factors

In a right triangle, the measure of one leg is 11 inches and the other leg is 15 inches. Rounded to three decimal places, what is the length of the hypotenuse?

For a right triangle, the Pythagorean Theorem is a² + b² = c². In a right triangle, the measure of one leg is 8 inches and the hypotenuse is 24 inches. Rounded to three decimal places, what is the length of the other leg?

A waterfall has a height of 1500 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 20 feet per second. The height, h, of the pebble after t seconds is given by the equation h=-16t²+20t+1500. How long after the pebble is thrown will it hit the ground? seconds after it is thrown. The pebble will hit the ground about

Jackson is working two summer jobs, landscaping and clearing tables. He must work no less than 14 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours landscaping, I, and the number of hours clearing tables, c, that Jackson can work in a given week.

A ball is thrown upward with an initial velocity (v) of 11 meters per second. Suppose that the initial height (h) above the ground is 9 meters. At what time t will the ball hit the ground? The ball is on the ground when S = 0. Use the equation S = -5t² + vt + h. The ball will hit the ground in seconds.

Which of the following are solutions to the inequality below? Select all that apply. -9 ≤1+p P=-6 p=-2 P=-7 P=-8

The length of one leg of a right triangle is 7 cm less than the length of the other leg. The length of the hypotenuse is 13 cm. Find the lengths of the legs.

A rectangular piece of plywood 3.00 ft by 7.00 ft is cut from one corner to an opposite corner. What are the angles between the edges of the resulting pieces? Include all resulting angles. The angle(s) is/are degrees.

Suppose g(t) = t² − 5t + 6. (a) Find, simplifying your answer as possible: g(0) (numbers) (b) Solve g(t) = 0, simplifying your answer as possible: t =

The combination of cold temperatures and wind speed determine what is called wind chill. The wind chill is a temperature that is the still-air equivalent of the combination of cold and wind. When the wind speed is 25 mph, the wind chill WC depends on the temperature t (in degrees Fahrenheit) according to the equation below. WC = 1.337t - 24.094 For what temperatures does it feel at least 41°F colder than the air temperature? That is, find t such that WC ≤ t - 41. (Round your answer to two decimal places).

Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and six. What is the algebraic expression?

Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = 3|x+4| What transformations are needed in order to obtain the graph of h(x) from the graph of f(x)? Select all that apply. A. Horizontal stretch/shrink B. Reflection about the x-axis C. Horizontal shift D. Vertical stretch/shrink E. Vertical shift F. Reflection about the y-axis

Using the Addition Method, find the value of y in the system of equations 2x = 3y - 5 and 5x+6y= 28

Use transformations of the graph of f(x) = x³ to determine the graph of the given function. g(x) = (x+3)³

A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.72°. The camera is 154.0 cm above the surface. How far is the camera from the rock?

Which of the lines in the picture is parallel to line ? Explain how you know. b. Explain how to translate, rotate or reflect line to obtain line k. c. Explain how to translate, rotate or reflect line to obtain line p.

One number exceeds another by 13. The sum of the numbers is 57. What are the numbers?

Julie borrows the same $1,000 for her furniture. However, the bank she went to charges a compound interest of 10 percent. If Julie's loan will be paid off in two years, how much will Julie pay the bank in total?

What are the coordinates of the point of intersection of y = 5x-3 and y = 13-3x? The coordinates of the point of intersection are

In a regular hexagon, one of the sides measures 3.0 centimeters. What is the distance, in centimeters, between the flats of the regular hexagon? (Round to three decimal places, if necessary) Your Answer:

A cylinder of water was holding a volume of 2 mL of water. An irregularly shaped stone was put into the cylinder and the volume rose to 8 mL. If the mass of the stone was 21 g, what was its density? 2.63 g/mL 2.1 g/ml 10.5 g/mL 3.5 g/mL

What is the accuracy of the measurement 1.320 inches? 2 significant digits oneth of an inch tenth of an inch hundredth of an inch 3 significant digits 1 significant digit 4 significant digits thousandth of an inch

After a busy day of orders, a florist has 6 roses, 7 lilies, 3 carnations, 35 chrysanthemums, 27 sunflowers, 18 violets, and 9 tulips left in her inventory. Part A: Write a ratio that compares the number of roses to the number of violets. Part B: Describe what three other comparisons have the same ratio. Part C: Provide reasoning why more than one comparison can be made with the same ratio.

Solve the polynomial inequality. (x+2) (x-1) (x+4) <0 (-∞, -4) U (-2,1) (-2, 1) (-∞, -4) U[-2, 1] (-4,-2) U (1, ∞)

Consider a curve satisfying the equation y = ar²+bx+c. Suppose that • The curve passes through the point (3,66) and the tangent to the curve at this point is given by y = 23x - 3. • The curve intersects the y-axis at the point (0, 15). Find the values of a, b and c.

A group of mountain climbers begih an expedition with 250 pounds of food. They plan to eat a total of 12 pounds of food per day. Write and solve a linear equation to find the number of days their food will last.

Write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). Then graph the circle. r = 3; (h,k)=(-2,-1) The standard form of the equation of this circle is (x + 2)2 + (y + 1)² = 9. The general form of the equation of this circle is

A circle has the equation x² + y²-3x-6y +9=0. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is (Type an ordered pair, using integers or fractions.)

A statistics student takes a pop quiz that consists of three true-false questions. Let's consider the experiment to be the answering of three questions where each can be either answered correctly or incorrectly. Let "C" represent the answering of any given question correctly, and "I" as answering the question incorrectly. Assume that the student has a 50% of correctly answering each question. What is the probability that the student gets all three questions wrong? Show your work in the space provided below, and present your answer in DECIMAL form (eg., 0.999).

Ms. Nickel has a jar of candy on her desk. Jessica thinks there are 3,498 piece of candy in the jar. There are actually 4,182 pieces. What is the difference between Jessica's guess and the actual number of pieces of candy?

Burnem Inc. manufactures thumb drives and sells them to a distributor. Burnem's total cost and total revenue (in dollars) for x thumb drives are given by the following equations. Total cost = 5x + 4430 and Total revenue = 15x How many thumb drives must Burnem sell to break even?

Find an equation for f^-1(x), the inverse function. f-¹(x) = 0

A waterfall has a height of 1000 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet per second. The height, h, of the pebble after t seconds is given by the equation h = - 16t² +24t+1000. How long after the pebble is thrown will it hit the ground? The pebble will hit the ground about seconds after it is thrown.

You plant 300 grass seeds in your circular garden. If your garden has a diameter of 6 feet, how many grass seeds are there per square foot? 10.6 grass seeds per square foot 2.65 grass seeds per square foot 15.92 grass seeds per square foot 50 grass seeds per square foot

If the density of New York City is 26,403 people per square mile, and the city is 302 square miles, how many people are living in New York City? 6,723, 874 people 7,973,706 people 1,346,395 people 880,000 people

Solve the system of equations by elimination, if a solution exists. 8x- 11y=2 |2x -2.75y = - 13 Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice. A. The solution of the system is x = and y = (Type integers or simplified fractions.) B. There are infinitely many solutions. C. There is no solution.

In which way is the word document used in this sentence? I will need your legal identification documents in order for you to be eligible for a driver's license. A. noun - a written or printed paper B. verb to record or make note C. verb - to support with citations or references

Write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). Then graph the circle. r=2; (h,k)=(3,4) ..... The standard form of the equation of this circle is (x-3)² + (y-4)² = 2². (Type your answer in standard form.) 2 2 The general form of the equation of this circle is x² + y² - 8x+6y=0 (Simplify your answer. Type an equation.)

Set Topic: Completing the square. Find the last term to make the trinomial into a perfect square trinomial: x² + 18x + Write the perfect square trinomial as a product of two factors:

A company finds it can produce 25 heaters for $6650, while producing 30 heaters costs $7900. Express the cost, y, as a linear function of the number of heaters, x. Determine the cost to produce 40 heaters Express the cost, y, as a linear function of the number of heaters, x.