Basic Math Questions and Answers

Solve the equation by factoring. 2x(x - 2) = 6x² - 5x Rewrite the equation in factored form. =0 (Factor completely.) The solution set is

Dave will drive 42.3 miles from home to his doctor's office. Then he plans to drive 24.4 miles from the doctor's office to a department store. Finally, he will drive 48.5 miles from the department store to home. If Dave's car gets 22 miles per gallon of gasoline, then the total amount of gasoline his car will use during these three trips is a. Between 3 and 4 gallons b. Between 4 and 5 gallons c. Between 5 and 6 gallons d. Between 6 and 7 gallons e. Between 7 and 8 gallons

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of degree Celsius. II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I only B) II only C) III only D) I and II only

A driver averaged 42 miles per hour and took 7 hours to travel between two cities. What is the distance between the two cities? The distance between the two cities is

A shark can take in 600 cubic meters of water in a day when it is feeding. If a shark has taken in 3 x 10 cubic meters of water, how many days has it been feeding? Write your answer in standard notation.

Sketch the graph of y = 2(x - 2)² + 4. Then identify the vertex

The function below has at least one rational zero. Use this fact to find all zeros of the function. g(x)=7x + 29x²³ + 24x² - x - 3 If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.

The sales tax on an item is 5%. Express the total cost, C, in terms of the price of the item, P. Be sure to use the correct case of the variable when entering your expression.

Classify the polynomial by degree and number of terms: f(x) = 4x² - 2x¹ +1 Quadratic trinomial Quartic trinomial Quadratic polynomial Quartic polynomial

Perform the following sequence of transformations on ADEF. D(0, 4), E(2, 0), and F(-1, -3). Translate ADEF 5 units left and 1 unit down Reflect the image AD'E'F' across 3x + 3y = 6 b. Write the algebraic description for the translation. From preimage to image 1. c. Are triangles congruent? How do you know?

Solve the equation. X+5/3= X+2/4 = 5 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is B. There is no solution. (Simplify your answer.)

Which of the following is a false statement? A horizontal cross section of a cylinder and a cross section of a sphere are the same shape. The diagonal cross section of a pyramid is a rectangle. The cross section of a sphere is the same no matter where the cross section is cut. A perpendicular cross section of a cylinder and a horizontal cross section of a rectangular pyramid are the same shape.

A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a passenger train leaves the same station for Chicago traveling 60 mph. How long before the passenger train overtakes the freight train?

Which function has real zeros at x = -10 and x = -6? f(x) = x² + 16x + 60 f(x)=x²-16x + 60 f(x) = x² + 4x + 60 f(x) = x² - 4x + 60

Profit A cellular telephone company esti- mates that, if it has x thousand subscribers, its monthly profit is P(x) thousand dollars, where P(x) = 12x - 200. a. How many subscribers are needed for a monthly profit of 160 thousand dollars? b. How many new subscribers would be needed to raise the monthly profit from 160 to 166 thousand dollars?

Write each expression in radical form. Use "sqrt(x)" fo

To determine whether this possible extrema is a maximum or a minimum, we can use the Second Derivative Test. Again differentiate with respect to s. Therefore, the maximum profit occurs when s = 400 maximum We can therefore conclude that the amount of money the company should spend on advertising in order to yield a maximum profit is $86800

What is the perpendicular cross section from the apex to the base of a pyramid? Circle Square Triangle Rectangle

Tim is choosing between two cell phone plans that offer the same amount of free minutes. Cingular's plan charges $39.99 per month with additional minutes costing $0.45. Verizon's plan costs $44.99 with additional minutes at $0.40. How many additional minutes, a, will it take for the two plans to cost the same?

Graph the following system of equations. x+y = - 4 y=x-8 Use the graphing tool to graph the linear equations.

How much of a(n) 60% orange juice drink must be mixed with 3 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice? The amount of 60% orange juice drink is gallons.

On the first Tuesday of every month, Roth's gives seniors a 15% markdown on everything they purchase including sales merchandise. On the first Tuesday of this month, Jack Graham, a senior, purchased a three-piece suit marked down 40%. If he paid a total of $152.79, including a 7% sales tax, what was the suit's regular selling price?

A pharmacist wishes to mix a solution that is 8% Minoxidil. She has on hand 60 ml of a 3% solution and wishes to add some 10% solution to obtain the desired 8% solution. How much 10% solution should she add?

Select all the expressions that are equivalent (equal) to 2. Show your 8+ (-9) + 3 -4+15-7 -9+8+3 -9-(-12) + (-1) 13-6-3 8- (9+3)

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1800. What was the rate charged per hour by each mechanic if the sum of the two rates was $135 per hour? Note that the ALEKS graphing calculator can be used to make computations easier. First mechanic: $ per hour Second mechanic: $ per hour

Use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then use a graphing utility to graph the function and estimate your answer graphically. (Round your answers to five decimal places.)

Find the real solutions of the equation. 32x4-4x²-1=0 What is the solution set? Select the correct choice below and fill in any answer boxes in your choice. A. B. There are no real solutions.

Suppose two trains leave a station at the same time, traveling in opposite directions. Train B travels 20 mph faster than Train A. In 3.5 hours, the trains are 378 miles apart. Find the speed of each train. The speed of Train A is

In industry, the relationship be- tween wages and the quit ratio of employees is defined to be the percentage of employees that quit within 1 year of employment. The quit ratio of a large restaurant chain that paid its employees the minimum hourly wage ($7.25 per hour) was .2 or 20 employees per 100. When the company raised the hourly wage to $8, the quit ratio dropped to .18, or 18 employees per 100. a. Assuming a linear relationship be- tween the quit ratio Q(x) and the hourly wage x, find an expression for Q(x). b. What should the hourly wage be for the quit ratio to drop to 10 employees per 100?

Use deductive reasoning to arrive at a conclusion based on the assumptions given. (a) ASSUMPTIONS (b) ASSUMPTIONS 1. All Martians have green eyes. 2. Henry is a Martian. 1. The sum of the measures of the angles of a triangle is 180. 2. In a particular triangle, the sum of the measures of two angles is 100. A prime number is any whole number that is divisible only by itself and 1. For example, 7, 11, and 13 are prime numbers. Evaluate the formula n² +n + 17 using all integer values of n from 0 to 9, inclusive. Do you notice a pattern? (a) Using inductive reasoning, draw a conclusion. (b) Is your conclusion true for all values of n? Test n = 16.

Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system. 3x - y = 4 2x + 3y = 21 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is x= 3 and y = 5. B. There are infinitely many solutions. Using ordered pairs, they can be expressed as {(x,y) | x= C. The system is inconsistent.

Evaluate the following polynomial using synthetic substitution! You need to know how to do this question with this method for future quizzes and tests so please don't solve another way. f(x) = x² + 3x - 20; x = 4

A 15 foot ladder is sliding down a building at a constant rate of 2 feet per minute. How fast is the base of the ladder moving away from the building when the base of the ladder is 9 feet from the building?

On a spring day the temperature, T in degrees Fahrenheit, is T = f(h) = 55+1.6h, where h is the number of hours since 8 AM. a) Identify the initial amount and the rate of change of T = f(h). Include units with your answer. b) What do they tell you? c) What is the temperature on a spring day at 4 PM? d) How long did it take for the temperature to reach 63 degrees Fahrenheit?

Solve the system by the addition method. x + 2y = -5 3x + 5y = - 10 Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is. (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Seth plots point B by reflecting point A(3.5, 4) across the x-axis and then reflecting the result across the y-axis. Seth says that point B has coordinates (-4,-3.5). Use words and a graph to show why Seth is incorrect.

Write down everything you know about the equation y = mx + b. You should include what this general equation represents, as well as what each of the different letters represents. Be as thorough as possible.

You are seeking to be emancipated from your parents. You are looking for an apartment. There are two final choices. Apartment A has a $1000 security deposit and costs $1200 each month. Apartment B has a $1500 and costs $1175 each month. How many months, m, will it take for the costs to be the same?

A balloon is rising straight up at a rate of 9 ft/sec. An observer is on the ground 120 feet from the point of lift-off. How fast is the angle of elevation changing at the moment the balloon is 50 feet in the air?

Jill plots point G with coordinates (a, b) in the coordinate plane. She reflects that point across the y-axis. In which quadrant is the reflection of point G in the coordinate plane? A Quadrant l B Quadrant II C Quadrant III D Quadrant IV

Claire is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof (point A) is 20°, and the angle of elevation from her eyes to the top of the antenna (point B) is 39°. If her eyes are 1.62 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.

Rewrite log (5x³ - 5x²) as a sum of terms. log (5) + log (x²) + log(x − 1) log (5) + log(x) + log(x) + log(x - 1) log (5) + log(x) + log(x) + log(x) - log (1) log (5) + log(x) + log(x) - log(x - 1)

Which sentence below uses a colon correctly? A. It is important to: eat well, sleep enough, drink water, and exercise. B. It is important to keep healthy habits: eat well, sleep enough, drink water, and exercise. C. It is: important to keep healthy habits, eat well, sleep enough, drink water, and exercise.

What must you do here before using long division on this polynomial problem? Put both polynomials in descending order. Find the least common multiple of both the divisor and the dividend. Use a place holder. Determine the prime factorization of the dividend.

Evaluate without using a calculator. Write "undefined" or "imaginary" if your result is not a real number.4√1/16 Write "undefined" or "imaginary" if your result is not a real number. Give your answer as a reduced fraction. No decimals.

The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars) on advertising is shown below. Find the amount of money the company should spend on advertising in order to yield a maximum profit.

Jacob invests $3,500 in an account that has an annual interest rate of 4.8% compoundec monthly. Addison invests $4,200 in an account that has an annual interest rate of 3.2% compounded continuously. Which of the following statements is true when comparing the amount of money in the two accounts after 10 years? After 10 years Addison has about $700 more than Jacob. After 10 years Jacob has about $74 more than Addison. After 10 years Addison has about $133 more than Jacob. After 10 years Addison and Jacob have the same amount of money in their accounts.

According to Sampling techniques, identify the type of sample obtained on each situation given below: 1) A pollster uses a computer to generate 500 random numbers, then interviews the voters corresponding to those numbers. [Select]

Given the parent function f(x) = x5, write an equation for the function g(x), in which f(x) is shifted down by 3, left by 1, and vertically stretched by a factor of 2. g(x) = 2(x + 1)5 - 3 g(x) = (x + 1)5 - 3 g(x) = 2(x + 1)5 +3 g(x) = 2(x - 1)5 - 3

Consumer Reports compared the effectiveness of an antiwrinkle cream with that of a plain moisturizer in reducing the appearance of wrinkles. The researchers enrolled 79 subjects with moderate to marked wrinkles, and instructed them to use both products, one on each side of the face, every morning for 12 weeks. The subjects didn't know which products they were using. At the end of the study, panelists examined before and after photos of the subjects to assess wrinkle appearance. The panelists did not know which product the subjects had used. Which of the statements is true? This study was a double-blind experiment, but not a randomized experiment. This study was a randomized, double-blind experiment. This study is just anecdotal. This study was an experiment, but not a double-blind experiment.