Basic Math Questions and Answers

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?

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