Math Questions

Find the difference quotient f(x+h)-f(x)/ h,where h0, for the function below. f(x) = -4x²-3x+1 Simplify your answer as much as possible.

Find the difference quotient f(x+h)-f(x)/h where h0, for the function below. f(x)=6x-7 Simplify your answer as much as possible.

Chris is super hungry and wants to eat an entire pizza. The radius of the pizza is 6 inches. If Chris eats the whole pizza, how many square inches did he consume?

For the polynomial below, 2 is a zero. h(x)=x³ + 4x²8x - 8 Express h (x) as a product of linear factors.

A laptop computer is purchased for $4900. Each year, its value is 80% of its value the year before. After how many years will the laptop computer be worth $1000 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

A car is purchased for $43,000. Each year it loses 30% of its value. After how many years will the car be worth $5400 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

Use the remainder theorem to find P (3) for P(x) = -x + 3x³-x+5. Specifically, give the quotient and the remainder for the associated division and the value of P (3).

Find the exact value of cos(arccos(√2/2)).

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (4, -3). What is the vertex of the function defined as g(x) = f(x) - 3?

Let 8 be an angle such that tanθ=2/3 and cscθ>0. Find the exact values of sin θ and secθ

There is a sales tax of $15 on an item that costs $153 before tax. A second item costs $81.60 before tax. What is the sales tax on the second item?

At a school dance, tickets are sold at the door and each ticket is the same price. The amount of money the school makes from the dance is equal to the total amount of money collected from ticket sales minus the total cost of the DJ and decorations. For this dance, the total cost is fixed and is not dependent on the number of tickets sold. If 75 tickets are sold, the school loses $150. If 100 tickets are sold, the school makes $100. What is the total cost of the DJ and decorations? $250 $300 $900 $1,000

Solve the equation for exact solutions over the interval [0°,360°). 2cos 2θ=-√3

A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x)=0.8x²-352x+49,032. How many cars must be made to minimize the unit cost? Do not round your answer.

Find the direction angle of the vector u = -3i+5j. That Is, find the angle between 0° and 360° that u makes with the positive x-axis (measured counterclockwise), when u is in standard position. Do not round any intermediate computations, and round your answer to the nearest whole number.

The number of milligrams D (h) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is given by the following function. D(h)=50e-0,25h When the number of milligrams reaches 33, the drug is to be injected again. How much time is needed between Injections? Round your answer to the nearest tenth, and do not round any Intermediate computations.

An art student wants to take a triangle with side lengths of 9, 9, and 15 and enlarge it so that the longest side of a new triangle is 22.5. What will be the length of the other two sides of the new triangle? 13.5 12 11.5 10

When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.

Nicole, Pablo, and Ravi sent a total of 117 text messages over their cell phones during the weekend. Ravi sent 9 more messages than Nicole. Pablo sent 4 times as many messages as Ravi. How many messages did they each send?

Find the surface area of a sphere that has a circumference of 20π cm,, in terms of square centimeters.

Two docks are located on an east-west line 2581 ft apart. From dock A, the bearing of a coral reef is 56°22'. From dock B, the bearing of the coral reef is 326°22'. Find the distance from dock A to the coral reef.

Find the volume of a pyramid with a square base, where the side length of the base is 18.5 in and the height of the pyramid is 10.9 in. Round your answer to the nearest tenth of a cubic inch.

You are building a rectangular flowerbed for your back yard. The flowerbed will surround the flowers and sit on the ground. The ground where you want to plant the flowers is 4 ft. by 7 ft. How many feet of boards will you need to build the flowerbed? Your answer should be a number only.

What is the volume of a hemisphere with a radius of 4.8 ft, rounded to the nearest tenth of a cubic foot?

You want to build a sandbox for your little brother. You know you need to buy wood to frame the outside of the box. If the dimensions of the box will be 6 ft. by 8 ft., how many feet of lumber will you have to buy? Your answer should be a number only.

Which of the following functions have an amplitude of 4 and a period of 2? Select all that apply. y = 4 cos 2x y=2 sin 4x y = 4 сos πx

What is the volume of a sphere with a diameter of 6.4 cm, rounded to the nearest tenth of a cubic centimeter?

Which transformation rule below translates points 5 units to the left and 2 units up? A. (x,y) → (x + 5,y + 2) B. (x,y) → (x - 5,y - 2) C. (x,y) → (x + 5,y - 2) D. (x, y) → (x - 5, y + 2)

An online shopping club has 5,200 members when it charges $9 per month for membership. For each $1 monthly increase in membership fee, the club loses approximately 200 of its existing members. Write and simplify a function R to represent the monthly revenue received by the club when x represents the price increase. Hint: Monthly revenue = # members • monthly fee.

Find the difference quotient f(x+h)-f(x)/h where h#0, for the function below. f(x)=-3x²+6x-9 Simplify your answer as much as possible.

In a right triangle the two legs have measurements of 8 inches and 18 inches. Use the Pythagorean theorem to calculate the length of the hypotenuse. 144.00 inches 388.00 inches 12.00 inches 5.10 inches 19.70 inches

The bearing from City A to City B is N 42° E. The bearing from City B to City C is S 48° E. An automobile driven at 55 mph takes 1.6 hours to drive from City A to City B and takes 1.8 hours to drive from City B to City C. Find the distance from City A to City C. (Neglect the curvature of the earth.) The distance from City A to City C is approximately (Round to the nearest mile as needed.) miles.

A rectangular-shaped window is 200 centimeters long and 5 meters wide. What is the area of the window? A. 1,000 square centimeters B. 250 square centimeters C. 14 square meters D. 10 square meters

A thread is being pulled off a spool at the rate of 61.9 cm per sec. Find the radius of the spool if it makes 123 revolutions per min. r≈cm (Round to two decimal places as needed.)

The formula w=θ/t can be rewritten as =θ wt. Using wt for θ changes s = rθ to s = rwt. Use the formula s = rwt to find the value of the missing variable. s=4π cm, r = 3 cm, w =π/6 radian per sec

Present value. A promissory note will pay $45,000 at maturity 9 years from now. How much should you be willing to pay for the note now if money is worth 4.25% compounded continuously?

A principal of $3800 Is Invested at 7.75% interest, compounded annually. How many years will It take to accumulate $11,000 or more in the account? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

Find the direction angle of the vector w=6i-4j. That is, find the angle between 0° and 360° that w makes with the positive x-axis (measured counterclockwise), when w is in standard position. Do not round any intermediate computations, and round your answer to the nearest whole number.

Travis Thompson uses his credit card to obtain a cash advance of $600 to pay for his textbooks in medical school. The interest rate charged for the loan is 0.04921% per day. Travis repays the money plus the interest after 25 days. a) Determine the interest charged for the cash advance. b) When he repaid the loan, how much did he pay the credit card company?

Estimate the solution to the following system of equations by graphing. 3x + 5y = 14 6x - 4y = 9

A forest ranger in an observation tower sees a bear 15 miles to the north. The ranger also knows there are campers located 19 miles due west of her post. To the nearest mile, how far are the campers from the bear?

Write an explicit equation for the nth term of the geometric sequence 3584, 896, 224,.... Find the sixth term of this sequence.

Recently, a certain bank offered a 10-year CD that earns 2.52% compounded continuously. Use the given information to answer the questions. (a) If $20,000 is invested in this CD, how much will it be worth in 10 years? approximately $ (Round to the nearest cent.)

From the top of a building, the angle of depression to a car parked on the street below is 48°. If the building is 75 ft. tall, how far is the car parked from the base of the building? 112.1 ft. 83.3 ft. 100.9 ft. 67.5 ft.

A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. If n represents the number of nickels and d represents the number of dimes, which of the following systems of equations can be used to represent this situation. n+d=4.45 0.05n+ 0.10d = 60 0.05n+ 0.10d = 60 0.05n+ 0.10d = 4.45 n+d=60 5n+ 10 d = 4.45 n+d=60 0.05n+ 0.10d = 4.45

The area of a circle with a radius of 3.65 cm is cm² Round answer to nearest tenth.

Use the remainder theorem to find P (2) for P(x)=2x³-2x² - 2x+4. Specifically, give the quotient and the remainder for the associated division and the value of P (2).

Jayla bought a table and some chairs at a furniture store. The equation that models this situation is y= 35x + 30, where y is the amount of money she spent and x is the number of chairs she bought. What does the y-intercept mean in this situation? A. She paid $30 for the table. B. She paid $35 for each chair. C. She paid $30 for each chair. D. She paid $35 for the table.

A car is purchased for $27,000. Each year it loses 20% of Its value. After how many years will the car be worth $11,000 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

For the polynomial below, -3 is a zero. g(x)=x³ + 5x² + 16x + 30 Express g (x) as a product of linear factors. g(x) = 0