Basic Math Questions and Answers

Find the average rate of change of the function f(x) = x² + 6x from x₁ = 4 to x₂ = 7. The average rate of change is (Simplify your answer.)

A tank holds 5075 gallons of water. How many containers of water can be filled from the tank if each container holds 6 1/4 gallons? (1) 813 (2) 812 (3) 811 (4) 810 (5) Not enough information is given.

The sum of two numbers is 79. The difference of the two numbers is 67. What are the two numbers? Let x be the larger number and y be the smaller number. Write an equation that expresses the information in the sentence "The sum of two numbers is 79." Write an equation that expresses the information in the sentence "The difference of the two numbers is 67." Solve the system you have written above. The larger number, x is The smaller number, y is

My investment in OHaganBooks.com stocks is losing half its value every 3 years. Find and interpret the associated decay rate. (Round your answer to one decimal place.) %

Find the minimum payment on an unpaid balance of $800.76. Assume that the minimum payment on a credit card is the greater of $27 or 2% of the unpaid balance. The minimum payment is $. (Round to the nearest cent as needed.)

Prompt: Mrs. Caddell was going to solve the equation 3x +7=2x-10, but she could not remember how!! Please explain how to solve this equation and help Mrs. Caddell! Be sure to use vocabulary! You can use an example but be sure to explain in words how to solve the equation! (Be sure to include at least 4-5 sentences.)

You and four friends go to Johnny Rockets. You all split the bill equally. Each person's share was $6.50. How much was the original bill? Let a represent the amount of the original bill.

A fifteen (15) year $8000 CD through Bank X pays 4.96% interest compounded weekly. A fifteen (15) year CD that pays 5% interest compounded annually is available at Bank Y. Explain which bank maximizes your investment.

Wade goes to a fast food restaurant and orders some tacos and burritos. He sees on the nutrition menu that tacos are 250 calories and burritos are 520 calories. If he ordered 7 items and consumed a total of 2830 calories, how many tacos and how many burritos did Wade order and eat? Tacos eaten: Burritos eaten:

Solve the system using any method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options. x - 2y = 10 -3x +7y = -34 No solution Infinite number of solutions

USING STRUCTURE Describe the transformation of the graph of the parent quadratic function to the graph of f(x)=1/2 (x-1)^2. Then identify the vertex. The graph of f is a function by a factor of 1/2 followed by a translation 1 unit of the graph of the parent quadratic function. The vertex is

Brother Isiah stopped at rest area A along the side of the highway. His map, shown below has a scale of 1 inches to 30 miles. If Isaiah's car suddenly stopped exactly halfway between rest area A and rest area B, what is the actual distance, in miles, between his location and rest area B?

The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of -0.3. See the figure below. Suppose that the height of the candle after 15 hours is 20.5 centimeters. What was the height of the candle after 6 hours?

What is the image of the point (2, -3) after a rotation of 180° counterclockwise about the origin?

What is the image of the point (3, -4) after a rotation of 180° counterclockwise about the origin?

At constant acceleration from rest, the distance traveled by a racecar is (directly) proportional to the square of the time elapsed. The highest recorded road-tested acceleration is 0 to 60 miles per hour in 3.07 seconds, which means that in 2 seconds the car would have traveled 57.32 feet. Suppose the racecar was tested on a 1-mile drag strip and continued to accelerate at the same rate for the entire mile. a. Find the constant of proportionality. b. How long would it take for the racecar to reach the finish line? c. What would be the racecar's average speed? d. What would the graph of the distance traveled as a function of time look like?

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 3x² +10x<25 Use the inequality in the form f(x) <0, to write the intervals determined by the boundary points as they appear from left to right on a number line. Interval Sign (Simplify your answers. Type your answers in interval notation. Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions.)

Which statement best describes the decimal equivalent of 7/8? It is a decimal that terminates after 2 decimal places. It is a decimal that terminates after 3 decimal places. It is a decimal with a repeating digit of 5. It is a decimal with repeating digits of 75.

Find the perimeter of the triangle whose vertices are (-2,-4), (3, 4), and (3, 8). Write the exact answer. Do not round.

Convert the given exponential function to the form indicated. Round all coefficients to four significant digits. f(t) = 2.3(1.007)^t; f(t) = Q₀e^kt f(t) =

The measure of one side of a square is (s+3) inches long. Which pair of expressions both represent the perimeter of this square? 2s+3and (s+3)(s+3) 2(s+3)and (s+3)(s+3) 4s+3and s+3+s+3+s+3+(s+3) 4s+3and s+3+s+3+s+3+(s+3)

Prove the Composition Theorem by ordering the statements of the paragraph proof. Given Figure A is transformed to figure A' by a rigid motion. Figure A' is transformed to figure A' by a rigid motion. Prove The composition of transformations from figure A to figure A" is a rigid motion. = every part of figure A' is congruent to the corresponding part of figure A" by the definition of rigid motion. = So, by the Transitive Property of Congruence, every part of figure A is congruent to the corresponding part of figure A". = Given that figure A' is transformed to figure A" by a rigid motion, = Given that figure A is transformed to figure A' by a rigid motion, = every part of figure A is congruent to the corresponding part of figure A' by the definition of rigid motion. = So, by the definition of rigid motion, the composition of rigid motions from figure A to figure A" is a rigid motion.

Graph: y<1/4 x

The function h is defined below. h(x) =x+7/x^2-5x+4 Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas. x=

An amount of $38,000 is borrowed for 15 years at 6.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

A group of 2000 people signed up for a study that measured the effects of a new weight loss medication. The study noted that the medication might work differently in men than in women. The study planned to use an established weight loss medication, the new medication, and a fake treatment that contained no medication. Identify the response and explanatory variables in this experiment. Explanatory: how much weight is lost; Response: weight loss medication Explanatory: Gender; Response: how much weight is lost Explanatory: how much weight is lost; response: gender Explanatory: weight loss medication; Response: how much weight is lost

A grocery store advertises that 15 cups of granola cost $6.75. Which are equivalent prices? 2 cups for $0.90 5 cups for $2.45 8 cups for $3.60 10 cups for $4.05 19 cups for $8.55 25 cups for $11.75

Out of 9,700 college students surveyed, 776 responded that they do not eat breakfast. What percent of the students do not eat breakfast? Percent of the students %

Mai, Joe, and Dan sent a total of 104 text messages during the weekend. Joe sent 9 more messages than Mai. Dan sent 3 times as many messages as Mai. How many messages did they each send? Number of text messages Mal sent: Number of text messages Joe sent: Number of text messages Dan sent:

Rosa brought d drawings to an art show. After selling 15 of them, she had 38 left. Identify the equation that represents this situation and the correct solution. A. d-15-38; d = 23 B. d+15=38; d = 53 C. d+15=38;d = 23 D. d-15=38; d = 53

One number is 2 more than another. The difference between their squares is 28. What are the numbers? Answer How to enter your answer (opens in new window) smaller number = larger number =

An airplane flew from Chicago to San Francisco in 3.9 hours. If the cities are 1,950 miles apart, what was the average speed of the plane? mph

Suppose potato chips cost 36.5 cents per ounce. If a bag costs $4.67, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.

Find three consecutive even integers such that the square of the third is 52 more than the square of the second. The smallest integer is The middle integer is The largest integer is .

Factor completely. 3a^4-147 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 3a^4 - 147 = B. The polynomial is prime.

Raina's cow gives 1 1/2 gallons milk each day. How much is this in quarts? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.

The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. (If an answer does not exist, enter DNE.) x -2 -1 0 1 2 f(x) 1.125 2.25 4.5 9 18 g(x) 12 6 3 1.5 0.75 f(x)= g(x)=

Use synthetic division to find the result when 3x⁴ - 3x³ + 16x² - 11x - 31 is divided by x + 4. Provide your answer below: Write your answer in the form q(x) + r(x)/d(x) , where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor. Do not include a comma in any numbers in your answer.

Solve the compound inequality and give your answer in interval notation. 5x + 2<-23 AND-7x -8 ≤34

By weight, the ratio of chlorine to sodium in a salt is 56.72 to 21.00. How much sodium is contained in 56.00 kg of salt? There is kg of sodium. (Simplify your answer. Round to two decimal places as needed.)

- At Mr. Russa's garage sale, all books were one price, and all magazines were another price. Robert bought four books and three magazines for $1.45, and Jennifer bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?

Factor the following expression completely. m5n-625mn5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. m5n-625mn5 = B. The polynomial is prime.

For the following equation, find three ordered pair solutions by completing the table. Then use the ordered pairs to graph the equation. y=-3x+7 Find three ordered pair solutions of the given equation.

The percent error in a measurement is the ratio of the error in the measurement to the measurement itself, expressed as a percent. When writing a computer program, the memory remaining is determined as 2640 bytes and then it is correctly found to be 2720bytes. What is the percent error in the first reading? The percent error is %. (Round to one decimal place as needed.)

A Field Poll Survey reported that 59% of registered voters in a state approved of allowing two people of the same gender to marry and have regular marriage laws apply to them. Among 18 to 39 year olds (registered voters in this state), the approval rating was 77%. Six in ten registered voters in this state said that the upcoming Supreme Court's ruling about the constitutionality of a proposition was either very or somewhat important to them. Out of those registered voters who support same-sex marriage, 75% say the ruling is important to them. In this problem, let the following apply. • C = registered voters who support same-sex marriage • B = registered voters who say the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them • A = registered voters who are 18 to 39 years old. Part (a) Part (b) Find P(B). (Enter your answer to two decimal places.) P(B) = Part (c) Part (d) Part (e) Part (f)

At a local Dunkin' Donuts, a survey showed that out of 1,240 customers eating lunch, 496 ordered coffee with their meal. What percent of customers ordered coffee?

Write an equation of the line that passes through (5,-4) and is perpendicular to the line defined by x-3y=4. Write the answer in slope-intercept form (if possible) and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable. The equation of the line in slope-intercept form: y = −3x + 11 The equation of the line in standard form:

Graph the following inequality. Note: To graph the inequality: 1. Select the type of line below (solid or dashed). 2. Plot two points on the line. 3. Click on the side that should be shaded. x≥3

For the function f(x) = -5x² + x + 4, evaluate and fully simplify each of the following f(x + h) = f(x+h)-f(x)/h =

The population P (in millions) of Italy from 2003 through 2015 can be approximated by the model P = 57.59e0.0051t, where t represents the year, with t = 3 corresponding to 2003. (a) According to the model, is the population of Italy increasing or decreasing? Explain. Because the coefficient of the model is --Select-- the population is --Select--- (b) Find the populations of the country in 2003 and 2015. (Round your answers to three decimal places.) 2003 million 2015 million (c) Use the model to predict the populations of the country in 2025 and 2034. (Round your answers to three decimal places.) 2025 million. 2034