Basic Math Questions and Answers

A farmer wishes to fence off two identical adjoining rectangular pens, each with 1936 square feet of area, as shown in the figure. What are x and y so that the least amount of fence is required? x= ft (Type an exact answer.) y =

Solve the following system of equations using the Desmos calculator: 2x+8y = 6 -5x - 20y = -15 True or False: The system of equations has an infinite number of solutions. True False

Determine whether the following the slopes of the lines are parallel, perpendicular, or neither. (-2,13) and (2,1) (3,-4) and (-5,20) Neither Parallel Perpendicular

A map on Rodrigo's phone shows the distances from his apartment building to the nearest restaurants. Restaurant Distance Taco truck 0.3 mi north Café 0.4 mi east Korean bistro 0.7 mi south Sandwich shop 0.8 mi east a. How much farther is it from the taco truck to the Korean bistro than it is from the café to the sandwich shop? Show your work.

During a snowstorm, Connor tracked the amount of snow on the ground. When the storm began, there were 5 inches of snow on the ground. Snow fell at a constant rate of 3 inches per hour until another 9 inches had fallen. The storm then stopped for 7 hours and then started again at a constant rate of 1 inch per hour for the next 6 hours. Make a graph showing the inches of snow on the ground over time using the data that Connor collected.

Find the volume of the largest open box that can be made from a piece of cardboard 31 inches by 17 inches by cutting equal square's from the comers and turning up the sides. in ³. The maximum volume is

Reagan uses the context clue of contrast when talking about "script" in section 1 of "A Time for Choosing"? What does he contrast "script" with in this passage? A. "As a matter of fact" B. "permitted to choose my own words" C. "The sponsor has been identified." D. "the choice that we face in the next few weeks" 3

Does a rhombus fit with proptery #2? No Yes

Including a 8% sales tax, an inn charges $164.16 per night. Find the inn's nightly cost before tax is added.

The wheels on a car have a radius of 15 in. and make 1 revolution every 0.15 sec. What is the average linear speed of the tire? (Round to two significant digits) The average linear speed of the tire is about

Solve the equation by completing the square. x²-11x +30=0 Choose the appropriate process for rearranging the equation, if needed, before completing the square to obtain an equation of the form (x + k)² = d.

Marina had $24,500 to invest. She divided the money into three different accounts. At the end of the year, she had made $1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%. If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had she placed in each account?

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 165 grams of a radioactive isotope, how much will be left after 3 half-lives? Use the calculator provided and round your answer to the nearest gram.

Let f(x) = 5x + 4 and g(x) = 5x² + 4x. After simplifying, (fog)(x) =

Investing. How many years will it take $4,000 to grow to $7,100 if it is invested at 6% (A) compounded quarterly? (B) compounded continuously? (A) years (Round to two decimal places.) (B) years (Round to two decimal places.)

Solve the following systems of equations by elimination, if a solution exists. 7x+14y=28 6y-12=-3x Select the correct choice below and fill in any answer boxes in your choice. A. The solution to the system is x = y = 1. B. There are infinitely many solutions. C. There is no solution.

The function h(x) = (x + 6) can be expressed in the form f(g(x)), where f(x) = x^8, and g(x) is defined below: g(x) =

GDP is the sum of: a. personal consumption, investment, government purchases of goods and services, exports, and imports. b. personal consumption, investment, government purchases of goods and services, and net exports. c. personal consumption, investment, government purchases of goods and services, and net imports. d. value added, net imports, and government purchases of goods and services.

The three sides of a triangle are n, 3n - 1, and 2n + 1. If the perimeter of the triangle is 42 inches, what is the length of each side? Separate multiple entries with a comma.

Solve the equation. 2x-(7x+5)=5x-45 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is B. There is no solution.

The coordinate on a map for San Francisco are (57,13) and those for Sacramento are (127,72). Note the coordinate represent miles. Find the distance between the two cities to the nearest mile.

A certain forest covers an area of 2800 km². Suppose that each year this area decreases by 7.75%. What will the area be after 9 years? Use the calculator provided and round your answer to the nearest square kilometer.

A restaurant manager wants to purchase 200 sets of dishes. One design costs $15 per set, while another costs $45 per set. If she wants to use her entire budget of $6600, how many of each design should be ordered? Select the correct choice below and fill in any answer boxes in your choice A. She should buy of the $15 sets. She should buy of the $45 sets. (Type whole numbers.) B. There are infinitely many solutions. C. There is no solution.

Find a value for k such that the graph will have the specified number of - intercept y = x² + k If the graph were to have 2 - intercept(s),

A principal of $4200 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 15 years? Use the calculator provided and round your answer to the nearest dollar.

Given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.

The Riley and Brown families decided to go to a concert together. The Riley's live 6 miles west and 3 miles north of the concert. The Browns live 2 miles east and 4 miles south. How far apart do they live?

A car is purchased for $29,500. After each year, the resale value decreases by 25%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

In Exercises 7 and 8, write a rule for g and then graph each function. Describe the graph of g as a transformation of the graph of f. 7. f(x) = x³ + 2, g(x) = f(x - 1) 8. f(x)= x - 3x + 1, g(x) = 2f(x)

At a math contest, 12 problems were given. Five points were awarded for each correct answer, and two points were deducted for each incorrect answer. Matt's score was 39. How many correct answers did he have?

Problem number one. You are rolling a fair nine sided dice. The sample space is {1,2,3,4,5,6,7,8,9). We define E to be the event that the number rolled is even and T to be that the number rolled is a multiple of three. A) Find P(E) B) Find P(TIE).

In Chapter 1, we modeled the world population from 1900 to 2010 with the exponential function P(t) = (1436.53) - (1.01395)* where t = 0 corresponds to the year 1900 and P(t) is measured in millions. Use this model, to find the rate of change of world population (in million/yr) in 1920, 1959, and 2000. (Round your answers to two decimal places.)

Assume the point (2,7) is on the graph of y=f(x). Determine the value of n in the following situations: 1. (2,n) is on the graph of y=3f(x) with respect to x 2. (2,n) is on the graph of y=-2-5f(x) with respect to x 3. (2,n) is on the graph of y=f(x)+3 with respect to x.

What is the precision of the measurement 4.006 inches? 1 significant digit hundredth of an inch oneth of an inch thousandth of an inch tenth of an inch 3 significant digits

The range R of a projectile is shown below, where v0 is the initial velocity in feet per second and is the angle of elevation. R = V02/32 (sin 2θ) Use differentials to approximate the change in the range when v0= 2500 feet per second and is changed from 10° to 9º. (Round your answer to the nearest whole number.) ft

Identify the constant term b and coefficient m in the expression b + mt for the linear function q(t) = 3x + 17/4 Enter the exact answers.

The distance, d, in meters from the shore, of a surfer riding a wave is given by d = 150 - 7t, where t is the number of seconds since she caught the wave. Identify the initial value and the rate of change, and explain their meanings in practical terms using units. The initial value is The rate of change is

A circle has the equation x² + y² + 4x-6y - 23=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 city has a population of 240,000 people. Suppose that each year the population grows by 5.25%. What will the population be after 14 years? Use the calculator provided and round your answer to the nearest whole number.

When Sebastian left his house in the morning, his cell phone battery was partially charged. Let B represent the charge remaining in Sebastian's battery, as a percentage, t hours since Sebastian left his house. The table below has select values showing the linear relationship between t and B. Determine how much battery life Sebastian's phone would have 4 hours after leaving his house.

11. The numbers below follow a pattern. 0.006 0.06 0.6 6 A. What are the next two numbers in the pattern? B. What is the relationship between the terms in the pattern?

Write the conditional statement, the converse, the inverse, and the contrapositive of the statement. 10. 2t+3= 13 when t = 5. 11. The dog gets a treat when it performs the trick. 12. An isosceles triangle has two sides with the same length.

Evaluate the polynomial function for the given values of the variable. P(c)=4c²-17c+5; find P(4) and P(0).

Which sentence contains transitional words or phrases? A. As you can see, I am a better writer than a speaker. B. I am a better writer than a speaker. C. I am a good speaker. I am a better writer. D. I am a good speaker; I am a better writer.

Find the average rate of change of f(x) = 4x² - 6 on the interval [2, b]. Your answer will be an expression involving b.

Given the polynomial functions j(x) and k(x), find j(x)+k(x). j(x)=x²-x k(x) = 2x³ + x² – 1 2x³ + 2x²+x+1 -x³ +x-1 -2x³+2x² − x + 1 2x³+2x²-x-1

Find the average rate of change of g(x) = 2x³ + 6/x4 on the interval [-1, 1].

A bucket is the shape of a frustum of a cone. One base has a radius of 6 in., the top has a radius that is 8 in., and the bucket is 12 in. high. Using = 3.14, what is the area of the 6 in base? A₁ = sq in Using = 3.14, what is the area of the 8 in base? V = sq in Rounded to three decimal places, what is the volume of the bucket in cubic inches? A₂ = cu in Using 1 gal = 231 cu in, to the nearest whole gallon, how many gallons will the bucket hold?

The following rational equation has denominators that contain variables. For this equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 2x / x+2 =4- 4/x+2 X= ***** a. What are the value or values of the variable that makes the denominators zero?

Find the average rate of change of g(x) = 4x³ + 5/x2 on the interval [-1, 2].