Math Questions

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.

Let θ be an angle such that csc0= 7/4 and tanθ <0. Find the exact values of cotθ and cosθ.

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

Consider the following quadratic function. f(x)= 3x² +6x-1 (a) Write the equation in the form f(x)= a (x-h)²+ k. Then give the vertex of its graph. Writing in the form specified: f(x) = Vertex: (b) Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

You have a circular mirror in your house that desperately needs cleaning. The diameter of the mirror is 3 feet. How many square feet of the mirror will need cleaning?

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.)

Using interval notation, identify the domain for the function: f(x)=2x+1/ x-4 (-∞,∞) (-∞,4)U(4,∞) (-∞,-4)U(4,∞) (-∞,2)U(2,∞)

Find the exact value of arctan (tan5π/6) Write your answer in radians in terms of π.

Given Z1 = 3+0i and 22 = -1- 2i, calculate the product z1z2 and express all three complex numbers in polar form, rounding all angles to the nearest degree in the interval 0° 0 < 360°. Express all moduli in simplest radical form.

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 circular spinner is divided into 4 regions and the regions are colored blue, red, yellow, and green. Each region occupies a fourth of the circle. Suppose you decide to play a "game" with your friend. If he spins and it lands on green, you will give him $5. If he spins and it lands on any other color, he has to give you $3. What is the mathematical expectation for this game? Should your friend play with you? Your friend should play because on average he will win $1 each time he plays. Your friend should NOT play because on average he will lose $4 each time he plays. Your friend should NOT play because on average he will lose $1 each time he plays. I have no idea. When did we ever learn this?

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.

Find the difference quotient f(x+h)-f(x)/h where h≠0, for the function below. f(x)=5x²-6x-7 Simplify your answer as much as possible.

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.

The goals scored per game by a soccer team represent the first quartile for all teams in a league. What can you conclude about the team's goals scored per game? Choose the correct answer below. A. The team scored fewer goals per game than 75% of the teams in the league. B. The team scored fewer goals per game than 25% of the teams in the league. C. The team scored fewer goals per game than 50% of the teams in the league. D. The team scored fewer goals per game than 100% of the teams in the league.

In triangle ABC, AC = 6, AB = 7, and BC = 5. Which is true? The measure of ∠C is the least of the three angles. The measure of ∠B is the greatest of the three angles. The measure of ∠B is the least of the three angles. The measure of ∠C is the greatest of the three angles.

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

Ms. Pullara and Ms. Chng are both looking at the top of the school in the distance in the same line of sight, although Ms. Chng is 100 m ahead of Ms. Pullara. Ms. Pullara observes the school at an angle of 18 with the ground. If the top of the tower is 400 m from Ms. Chng, what is Ms. Chng's angle of sight with the ground? First make a sketch and then solve the problem to the nearest degree. /5

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?