Basic Math Questions and Answers

Find the difference quotient f(x+h)-f(x)/h, where h≠0, for the function below. f(x) = 3x² - 4

Complete the statement: If two polygons are similar, then their corresponding (1)__ are congruent and their corresponding__(2)____ are proportional. 1) Sides; 2) Areas 1) Angles; 2) Areas 1) Angles; 2) Sides 1) Sides; 2) Angles

Given that sinθ= 35/37 and cosθ <0, determine the values of the sine and cosine functions for 2θ sin2θ = (Type an integer or a simplified fraction.)

The Eiffel Tower, shown to the right, has a width of 328 feet and a height of 984 feet. Maria is designing a T- shirt for her trip to France and she wants to put a picture of the Eiffel tower on the front of the shirt. The maximum space she can use on the shirt is a rectangle with a width of .75 feet and a height of 1.5 feet. Maria uses a sclale factor of 1/k where k is an integer, to shrink the Eiffel Tower and fit it on the t-shirt. What is smallest possible value for k?

Let (-4,-3) be a point on the terminal side of θ. Find the exact values of cos θ, sec θ, and cot θ.

A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?

Kuro has a stack of 15 coins on a table with a volume of 8 cubic centimeters. He has stacked them perfectly straight creating a cylindrical shape. He accidentally bumps the table, causing the coins to shift to a leaning position; but are still stacked. What would be the best estimate of the volume of the stack once it has been bumped/shifted? The volume cannot be calculated 8 cubic centimeters 9 cubic centimeters 7 cubic centimeters

The average cost per DVD, in dollars, for a company to produce x DVDs on exercising is given by the formula A = 8x + 300/x, where A is the average cost per DVD and x is the number of DVDs produced. Complete parts a through c. a. Find the cost for producing 1 DVD. The average cost for producing 1 DVD is $ 308 (Simplify your answer.) b. Find the average cost per DVD for producing The average cost for producing 100 DVDs is $ 100 DVDs. (Simplify your answer.)

If a right triangle has two legs which have measurements of 12 inches and 14 inches, the length of the hypotenuse is inches. Use the Pythagorean theorem to calculate the length of the hypotenuse. Round answer to the nearest one hundredth.

A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 119 pounds requires 136 milligrams of medicine. What is the weight of a patient who requires 200 milligrams of medicine?

A company makes steel rods shaped like cylinders. Each rod has a diameter of 6 centimeters and a height of 20 centimeters. If the company used 45,781.2 cm of steel, how many rods did it make? Use 3.14 for π, and do not round your answer.

Find the exact value of sin (sin(-π/6) Write your answer in radians in terms of π.

California's growth rate in 2013 was 0.9%. There were roughly 38 million people living in California that year. Assuming the growth rate is stable, which equation models the population P, in millions, t years after 2013?

A tepee in the shape of a right cone has a slant height of 18.5 feet and a diameter of 20 feet. Approximately how much canvas would be needed to cover the tepee? 116 sq ft 58 sq ft 89 sq ft 58 sq ft

Find the difference quotient f(x+h)-f(x)/h f(x)=1/x+6 Simplify your answer as much as possible.

Use a calculator and evaluate A to the nearest cent. A=$15,000 e 0.04t for t=2, 7, and 10 Ift=2, A-$

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 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.

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?

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

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.

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.

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

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.

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.

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

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.

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?

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.

Directions: Complete the following statements. 1. The standard form of a quadratic equation is 2. The curve formed by a quadratic equation is called a 3. The formula for the axis of symmetry is 4. If the vertex is the highest point on the graph, it is called a 5. If a vertex is the lowest point on a graph, it is called a