Basic Math Questions and Answers

Yesterday, Ivan went on a bike ride. His average speed was 9 miles per hour. Today, he went on another ride, this time averaging 12 miles per ho days, he biked for a combined total time of 11 hours. Let x be the number of hours he biked yesterday. Write an expression for the combined total number of miles he biked in the two days.

An electric board determines its monthly bills for residential customers by charging a base price of $14.00 plus an energy charge of 10.34 cents for each kilowatt-hour (kWh) used. Write an equation for the monthly charge y (in dollars) as a function of x, the number of kWh used.

Solve for v. v²-8v+16=0 If there more than one solution, separate them with commas. If there is no solution, click on "No solution."

Rick's lumberyard has 460 yd of fencing with which to enclose a rectangular area. If the enclosed area is x yards long, express its area as a function of its length.

A DVD-rental company has 10,500,000 subscribers, an increase of 140% from five years ago. Find the number of subscribers five years ago.

Water drips from a faucet at a rate of 41 drops/minute., Assuming there are 15,000 drops in a gallon, how many minutes would it take for the dripping faucet to fill a 1-gallon bucket? Round your answer to the nearest whole number.

Let f(x) = 9x³ - 12x² - 31 and let g(x) = 3x - 1. Find f(x)/g(x) 3x²-3x - 1 3x³ + x² + 2x + 22 3x²-3x-1-33²1 3x²-3x - 3²1

Consider the polynomial function: P(x) = 2x³ - 11x² + ax - 40 If x+4 is a factor of this polynomial, what is the value of a? a=40 a-4 a=86 a=76

1/Factor the following equation: y = x² - 4. Identify the x- intercepts, the y - intercept, and domain and range x- intercepts /y-intercept/domain / range / increasing/decreasing intervals. y = x² - 4.

A bank loaned out $18,000, part of it at the rate of 6% per year and the rest at 14% per year. If the interest received in one year totaled $2000, how much was loaned at 6% How much of the $18,000 did the bank loan out at 6%?

On a map, the endpoints of a straight fence are located at A(4,12) and B(8,22). Lisa plans to install a gate in the fence and wants the gate's hinges to be the same distance from both ends of the fence. At what point on the map will the gate hinges be placed? A (0,2) B. (2,5) C. (6,17) D. (12,34)

A manufacturing company that produces prerecorded DVDs finds that the total daily revenue R for selling z items at p dollars per item is given by R(x) = 10.5x 0.05x² Factor a from each term on the right side of the equation to find the formula that gives the price p in terms of x. Then, use it to find the price they should charge if they want to sell 100 DVDs per day.

Determine whether y is a function of x. x² + y² = 4 Yes, y is a function of x. No, y is not a function of x. It cannot be determined whether y is a function of x.

Find an equation of the line through the given pair of points. (-2,-9) and (-7,-6) The equation of the line is

Eliza went to the store and bought 3 lbs of apples at $1.99 per lb, two loaves of bread at $.89 per loaf, a box of cereal at $3.99 per box, and a gallon of milk at $3.19 per gallon. If Eliza paid with $20, how much change did she receive? $5.70 $14.93 $5.07 $14.39

Find a linear equation that expresses the relationship between the temperature in degrees Celsius C and degrees Fahrenheit F. Use the fact that water freezes at 0°C (32°F) and boils at 100°C (212°F).

Find the one-sided limit (if it exists). lim X→(1/2) + 13x² tan πx Step 1 The sign of the value of x² is always ---Select--- f(x) = 13x² tan лx at any point x is ---Select--- so the sign of the value of the function that of tan X.

When Ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams (mg) per kilogram (kg) of body weight when the fever is under 102.5 degrees Fahrenheit. How much medicine would be usual dose for a 18 month old weighing 19 pounds? milligrams Round your answer to the nearest milligram.

Lee Jenkins worked the following hours as a manager for a local Pizza Hut: 13 3/4,,3 1/4, ,8 1/4 and 3 1/2. How many total hours did Lee work?

Ryan and Maria are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and packages of crocus bulbs. Ryan sold 12 bags of windflower bulbs and 5 packages of crocus bulbs for a total of $217. Maria sold 5 bags of windflower bulbs and 10 packages of crocus bulbs for a total of $225. Find the cost each of one bag of windflower bulbs and one package of crocus bulbs.

The school that Paul goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 9 adult tickets and 10 child tickets for a total of $255. The school took in $135 on the second day by selling 5 adult tickets and 5 child tickets. What is the price each of one adult ticket and one child ticket?

Veronica's Violin Village sold 1,500 violins in the month of July. In the month of August they decreased their sales by 165 violins. By what percent did they decrease their monthly sales of violíns from July to August? Their monthly sales decrease by

A nurse mixes 60 cc of a 70% saline solution with a 30% saline solution to produce a 36% saline solution. How much of the 30% solution should he use?

Jessie enjoys running every day for exercise. On Monday, he ran 3.30 miles. On Tuesday, he ran 3.09 miles and on Wednesday he ran 2.98 miles. On what day did Jessie run the farthest?

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint (Hint. Let (x,y) be the unknown endpoint Apply the midpoint formula, and solve the two equations for x and y.) midpoint (-21,4), endpoint (-19,8) The other endpoint is

Let v(t) represent an object's velocity, in feet per minute, at time t minutes. Which of the following is the best interpretation of v'(1) = 6? The velocity of the object after 1 minute is 6 feet per minute. The displacement of the object during the first minute is 6 feet. The total distance traveled by the object during the first minute is 6 feet. The acceleration of the object after 1 minute is 6 feet per minute squared.

A veterinarian has the following pricing policy for grooming pets: $25 for pets 15lbs and under, $35 for pets over 15lbs and 50lbs or less and then $35 plus $2 for each additional pound over 50lbs. How much do you pay total if you have a 12lb cat, 44lb dog and 59lb dog?

Determine whether the graph of the function has a vertical asymptote or a removable discontinuity at x = -1. Graph the function using a graphing utility to confirm your answer. f(x) =x² 1/X + 1 vertical asymptote removable discontinuity

In June, the Wright family started saving for a trip to Florida. The Wrights expect their vacation to cost $6500. They deposit $1200 in June and their deposit grows by 15% each month. How many months will it take the Wright family to save for their trip? 15 months 11 months 10 months 13 months

Given the polynomial functions j(x) and k(x), find j(x) - k(x). j(x)=x²- x k(x) = 2x³ + x² - 1 2x³ + x + 1 2x³ + 2x²-x-1 -r³+x-1 -2x³-x+1

Estimate the total number of hours Americans spend stuck in traffic each year. If you are unfamiliar with estimation techniques, you may find it difficult to know how to begin solving this problem. This tutorial is designed to introduce you to the art of estimation. Learning to calculate rough estimates has many applications both in the sciences and in other fields. The ability to estimate the order of magnitude of unknown quantities can produce invaluable guides for measurements and planning. When estimating, you are looking for a number that is within an order of magnitude (i.e., a power of ten) of the actual value_ This is a broad range, so it is neither necessary nor desirable to work with precise numbers. You want numbers that are both reasonable and easy to use in calculations. For example, there are 365 days in a year. For the purposes of estimation, 365 is unnecessarily precise; 3 x 10² or 4 x 10² are both reasonable approximations and are more convenient for calculation. There is no definite rule concerning the precision of approximations. How coarse you make your approximations depends on how you plan to use the numbers and how precise you want your estimate to be. When beginning any approximation problem, ask yourself, "What do I need to know in order to solve this?" This particular problem asks about Americans, so the total number A of Americans is a good place to start. In actuality, there are a little over 325 million. Choose a convenient approximation for this value, express it using scientific notation, and enter it below. Do not check your answer yet.

Given the polynomial functions f(a) and g(x), find h(x) = f(x) = g(x). f(x)= 4¹-a³ +3m² +6 g(x)=5a-2a² + 3m - 2 h() = -4¹+4+²+3x+4 h(x) = 4r¹ - 6x³ +5²-32-8 h(a)-4a¹-62³5² +38 h(x) 42-62³ ²3x4

Which of the following is the best version of the underlined portion of sentence 2 (reproduced below)? Elk have been observed, cavorting over patches of snow, jumping and twisting their bodies, even when abundant bare ground is available nearby. (as it is now) observed cavorting over patches of snow, jumping and twisting their bodies, observed, cavorting over patches of snow, jumping, and twisting their bodies observed cavorting, over patches of snow, jumping and twisting their bodies,

The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). What is the fee per stop?

A square power-takeoff shaft with 2 1/4-inch sides needs to be covered with a round guard. The guard should have at least 2/5-inch clearance at all points. What should be the inside diameter of the guard? Round to the nearest hundredths place.

Helen purchased 3 books from an online bookstore and received a 20% discount on her total order. Each book cost the same amount. The shipping cost was $10 and was not discounted. Write an expression that can be used to represent the total amount Helen paid for 3 books plus the shipping cost. Simplify the expression, and then identify each term, the constant term, and the factors and coefficients of the terms that contain a variable.

A local Target store bought 98 pizzas at Pizza Hut for its holiday party. Each guest ate 1/9 of a pizza and there was no pizza left over. How many guests did Target have for the party?

Quilters Newsletter Magazine gave instructions on making a quilt. The quilt required 6 yards of white-on-white print, 5 yards blue check, yard blue-and-white stripe, yards blue scraps, yard yellow scraps, and 5 yards lining. How many total yards are needed? 6125 fitin Total yards

A company finds it can produce 30 heaters for $8800, while producing 35 heaters costs $10,150. Express the cost, y, as a linear function of the number of heaters, x.

Which of the following is a characteristic of the authoritarian parenting style? Placing high value on conformity and obedience Giving reasonable demands Expressing warmth and affection Listening to the child's point of view

Michael Wittry has been investing in his Roth IRA retirement account for 24 years. Five years ago, his account was worth $215,670. After losing of its original value, it then gained of its new value back. What is the current value of his Roth IRA? (Do not round intermediate calculations.) Current value

A student earned grades of 92, 83, 77, 84, and 82 on her five regular tests. She earned a grade of 95 on her class project, and her homework grade was 77. The five regular tests count for 60% total of the final grade, and the project counts for 15%, and the homework grade also counts for 15%. If the final exam counts for 10% of the final grade, what minimum grade on the final will ensure that she gets a weighted average of at least 80 (B-) for her final weighted mean grade?

Joy Wigens, who works at Putnam Investments, received a check for $5,935. She deposited 1/5 of the check in her Citibank account. How much money does Joy have left after the deposit?

A police officer uses a radar gun to determine the speed of five vehicles traveling on the highway. The speed of those vehicles are as follows. 65, 63, 67, 57, 68 (a) Calculate the average speed of the five vehicles. (b) Calculate the standard deviation of the speeds given in the data set. (Round your answer to three decimal places.)

As a science experiment, Mo and Jo want to send their model rocket into space. They need 1/6 cup of H₂O (water) and 1/8 cup of a secret component. How much is there of these two components together? There is cup of these components together. (Type a whole number or a simplified fraction.)

Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.) f(x) = 8 / x^2 + 4x - 5

Some friends who were playing darts decided to impose a 5-point penalty for each dart that missed the dart board completely. During the evening, a boy had 2 darts in the 20-point section, 3 darts in the triple-15-point section, and 6 darts in the double-10-point section. He missed the dart board completely 5 times. How many points did the boy score?

James invested $20,000 into two accounts. One account pays 6% simple interest, while the other account pays 5% simple interest. If his interest earnings total $1120 after one year, how much did he invest at each rate?

Total replacement insurance coverage against breakage or loss of a new laptop computer is $19.00 per month increasing by 5% per year. What is the cost per month for two years? A- $18.33 B- $19.95 C-$20.95 D- $22.25

The Jetsons are taking a family vacation. Their car gets 30 miles per gallon in gas mileage. They are traveling for seven hours at a rate of 55 miles per hour. Assuming no stops, how much gas will they need to complete their seven hour trip? 20 gallons 12 gallons 13 gallons 4 gallons There is not enough information to answer the question