Basic Math Questions and Answers

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].

For a certain product, the revenue is given by R = 30x and the cost is given by C(x) = 10x + 1700. To obtain a profit, the revenue must be greater than the cost. For what values of x will there be a profit?

A rectangular sandbox is surrounded on all sides by a strip of grass that is 5 feet wide on all sides. The length of the sandbox is 4 feet more than the width, and the total area for the sandbox and the grass is 189 square feet. Find the dimensions of the sandbox. The length of the sandbox is feet and the width is feet.

A city has a population of 250,000 people. Suppose that each year the population grows by 8%. What will the population be after 8 years? Use the calculator provided and round your answer to the nearest whole number.

Kendra and her horse completed the barrel racing course in 15.839 seconds. What is this number rounded to the nearest tenth? Explain how you decided.

Soybean meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240-lb mixture that is 8% protein? How many pounds of cornmeal should be in the mixture? pounds

Use a calculator to solve the equation. Round your answer to three decimal places. 3.251x 8.632= -3.1(8.628x + 4.915) X =

Consider the following function. 4x + 2, x ≤ -1 x² - 3, x>-1 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)

Of all the numbers whose difference is 40, find the two that have the minimum product. The two numbers whose difference is 40 and that have the minimum product are

Junior is saving money in his piggy bank. He starts with 10 cents and adds two pennies each day. Create a table. draw a complete graph, and write an equation to model this situation, where x represents the number of days and y represents the amount of money.

A retired woman has $200,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another riskier fund that has a 13% annual yield. How much should she invest in each fund if she would like to earn $20,000 per year from her investments? 9% fund $ 13% fund $

Find the x-intercept and y-intercept of the graph of - 2x + 4y = - 8. Then graph. x-intercept = ( ,0) y-intercept = (0, )

Norio is running to raise money for charity. He finds 2 people who have pledged to donate money based on the distance he runs. His neighbor says he will donate $0.25 fe every 40 feet Desmond runs. His aunt also says that she will donate $20 for every mile runs. If Desmond runs a total of 4 miles during the cancer awareness run, how much money will he have raised based on these two donations? (1 mile = 5,280 feet)

Solve the system of equations below using the Desmos calculator: -14-20y-7x 10y + 4 = 2x The solution to the system of equations is

The percent P of the U.S. population with Internet access is given by 25P - 34t = 1378 where t is the number of years past 1990.+ (a) What percent of the U.S. population had Internet access in 2005? (Round your answer to one decimal place.) P = % (b) In what year will 90% have Internet access?

Carolyn walked 3 miles from her house to the library and then 2 1/2 miles farther to the grocery store. Returning home by the same route, she walked 1 2/3 miles before stopping at a friend's house. How many miles did Carolyn have left to walk home?

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. 1/ x-4 - 3/x+2 = 6/x²-2x-8 ***** a. What is/are the value or values of the variable that make(s) the denominators zero? X= (Simplify your answer. Use a comma to separate answers as needed.)

Find the average rate of change of g(x) = - 4x³ + 2 from x= -1 to x = 3.

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).