Basic Math Questions and Answers

Solve the system of equations. Give your solution as an ordered pair. 16x - 2y = 18 2/9 x + 2/9 y = 2

At the ice cream shop, there are 14 shakes sold for every 6 malts. Record the ratios below. a. malts to shakes b. malts to total

Add the following polynomials: (15t³ - 11t^6) + (24t^6 - 27t³)

Find the sum of the polynomials: (-8x^5 + 10x^4 + 2x² - 5) + (3x^5 - 11x^4 - 3x² + 11x)

Solve this system of equations using the method of elimination (addition). Use the infinity symbol if infinitely many solutions exist, or enter DNE if there are no solutions. 3x - 2y = 3 - 1x + 2y = -1

Using the decimal standard form. Compare using >, <, or =. 51 tenths 5.1 < > =

A construction company is planning to bid on a building contract. The bid costs the company $1500. The probability that the bid is accepted is 1/4 . If the bid is accepted, the company will make $38,000 minus the cost of the bid. a. What is the expected value in this situation? (Round to the nearest dollar)

A culture of bacteria is growing at the rate of 20e^0.8t cells per day, where t is the number of days since the culture was started. Suppose that the culture began with 50 cells. (a) Find a formula for the total number of cells in the culture after t days. T(t) = (b) If the culture is to be stopped when the population reaches 500, when will this occur? (Round your answer to one decimal place.) days

Two cars leave towns 1000 kilometers apart at the same time and travel toward each other. One car's rate is 12 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.

Elsa, Rafael, and Dan sent a total of 119 text messages over their cell phones during the weekend. Dan sent 4 times as many messages as Rafael. Rafael sent 5 fewer messages than Elsa. How many messages did they each send? Number of text messages Elsa sent: Number of text messages Rafael sent: Number of text messages Dan sent:

Erica has $840 in her savings account and she has to pay $45 each month to her parents for her cell phone. Andres has $240 and he saves $30 each month from his job walking dogs for his neighbor. At this rate, when will Erica and Andres have the same amount of money? How much will they each have? In month(s) they will both have $

How long (in years) will it take a $300 investment to be worth $1000 if it is continuously compounded at 11% per year? (Give the answer to two decimal places.)

For services rendered, an attorney accepts a 120-day note for $5,200 at 7% simple interest from a client. (Both interest and principal are repaid at the end of 120 days.) Wishing to use her money sooner, the attorney sells the note to a third party for $5,270 after 60 days. What annual interest rate will the third party receive for the investment? The third party will receive an annual interest rate of %. (Type an integer or decimal rounded to two decimal places as needed.)

The sum of two numbers is 75. The difference of the two numbers is 29. 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 75." Write an equation that expresses the information in the sentence "The difference of the two numbers is 29." Solve the system you have written above. The larger number, x is The smaller number, y is

A loan of $1,020 was repaid at the end of 12 months with a check for $1,050. What annual rate of interest was charged? The annual rate of interest was charged at %. (Round to two decimal places as needed.)

The polynomial y = -0.77⁴ +2.9x² +25.6 describes the billions of flu virus particles in a person's body z days after being infected.Round answer to 2 decimal places. There are billion virus particles in a person's body 3 days after being infected.

A law office orders business stationery. The cost is $17.05 per box. (a) Write a function that represents the cost C (x) (in $) for x boxes of stationery. (b) There is a 6% sales tax on the cost of merchandise and $9.58 for shipping. Write a function that represents the total cost T (a) for a dollars spent in merchandise and shipping. (c) Find (T ℃) (x). (d) Find (T ℃) (5) and interpret its meaning in the context of this problem. C(x) =

Solve the following inequality. x/4 > -6 (Simplify your answer.)

The sum of three numbers is 72. The first number is 8 more than the second. The third number is 2 times the first. What are the numbers? First number: Second number: Third number:

Solve the system of equations: 4/3x-3/5y=-19/10 -1/4x+1/4y=9/16

An entry level civil engineer's annual pay is $63,648 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its civil engineers. If the firm cuts the work year to 50 weeks but keeps the same rate of pay, how much should the civil engineer expect his annual pay to decrease? Round your answer to the nearest dollar.

The label on a bottle of medicine reads "Each 5 mL teaspoonful contains glucose. 1.87 g: levulose, 1.87 g; and phosphoric acid, 21.4 mg." a. Find the amount of phosphoric acid in the recommended dosage of two teaspoons. b. If the bottle contains 5 ounces, find the quantity of phosphoric acid in the bottle. (1 oz 30 mL)

(a) The diameter of Pluto at its equator is approximately 2.39 × 10³ kilometers. Write this number in standard notation. (b) An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.000196 meters. Write this number in scientific notation.

The average of a list of numbers is their sum divided by the number of numbers in the list. A female lion had 4 cubs. They weighed 2 1/20, 3 3/20, 4 9/10, and 4 3/5 pounds. What is the average cub weight?

The equation 12x + 15y = 390 represents the total revenue during a one-day fundraiser. In the equation, x represents the number of youth T-shirts sold, and y represents the number of adult T-shirts sold. If there were 10 youth T-shirts sold, how many adult T-shirts were sold? 18 T-shirts 20 T-shirts 24 T-shirts 45 T-shirts

Subtract the polynomials: (4y² + y - 4) - (8y² + 2y - 5)

Given the solution to the following system of equations written as an ordered pair. 3.7y - 11.1x = - 33.3 3.3y + 13.2x = 62.7

MP Use Repeated Reasoning Jessie has 50 packages of sports cards. There are 10 sports cards in each package. How many sports cards does Jessie have?

Function Operations, Adding and Subtracting Given the function f(x) = 7x - 5 and the function g(x) = 2x² + 6 determine each of the following. a) Evaluate: f(7) + g(9) b) Evaluate: f(2) - g(8) c) Evaluate: f(1/4) + f(4) d) Evaluate: f(1/3) - f(4/5)

Melissa wants to put a fence around the garden in her back yard in San Antonio. Since one side is adjacent to the house, she will only need to fence three sides. There are two long sides and one shorter side parallel to the house, and she needs 165 feet of fencing to enclose the garden. The length of the long side is 5 feet less than two times the length of the short side. Write an equation for L, the length of the long side, in terms of S, the length of the short side. L = Find the dimensions of the sides of the fence.

Jennifer has $0.50 in nickels and dimes. The number of dimes is 5 less than twice the number of nickels. Find the number of nickels.

The Elimination (Addition) Method Solve the following system of equations with the ELIMINATION METHOD. Write your answer as an Ordered Pair. If infinitely many solutions exist, enter ∞ "00". If no solution exists, enter DNE System of Equations 5x + 4y = 42 10x + 8y = 84

Use the order of operations to evaluate this expression: (-2 + 1)² + 5(12 ÷ 3) - 9. Type the correct answer in the box. Use numerals instead of words. The value of the expression is

A pancake recipe that serves 30 people calls for 12 eggs. Marti wants to make enough to serve only 10 people. What is the ratio of eggs to servings for the reduced recipe? A. 2 to 5 B. 1 to 3 C. 5 to 2 D. 5 to 6

Add the following polynomials: (13s³-7s) + (38s-9s³)

Find the x-coordinate(s) of the point(s) on the graph of f where the tangent line is horizontal. (Round your answer(s) to two decimal places. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = (x² + 16x + 6) (8 - x) X =

Emily and her twin sister Erica were each given $500 for their birthday. Emily deposits her money in an account, that pays 4.75% interest compounded annually. Erica deposits her money in a 5% simple annual interest account. After 10 years how much more money will Emily have her account? F $22.41 G $45.26 H $250.00 J $295.26

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?