Basic Math Questions and Answers

Write the sentence as an equation. Let the variable x represent the number. 1 The quotient of 17 and a number is 6 ..... The given sentence written as an equation is (Type an equation using x as the variable. Use integers or fractions for any numbers in the equation.)

Trina's watering can is 10 inches tall. Felipe's watering can is 4 inches taller. How much taller than one foot is Felipe's watering can?

Grayson has 4 small photo albums and 6 large photo albums. Each small album can hold up to 112 photographs. Each large album can hold up to 184 photographs. How many photos can Grayson keep in the albums? Enter your answer in the box. photos

(1 point) If f(x) = sin(x4), find f'(x). Find ƒ'(2).

Simplify the complex rational expression and make sure to state the restrictions on the variable:

Solve the inequality -3 < 2x + 5 ≤ 13. -8 < x≤8 -4 < x < 4 -4 < x ≤ 4 0 1<x≤9

A pair of power functions having the same exponents but different coefficients is given. f(x) = (6x)² and g(x) = 62x² In the long run, which function in the pair dominates?

Repeat the following procedure for the four given numbers. Add 7. Double the result. Subtract 12. Divide by 2. Subtract the original selected number.

Solve for exact solutions over the interval [0,2π). cos 2x = 1/2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions f answers as needed.) B. The solution set is Ø.

Let f(x) =4x²/2x - 9 (a) Find the vertical asymptote(s) of the graph of f(x). (b) Find the horizontal asymptote(s) of the graph of f(x). (c) Find the slant asymptote(s) of the graph of f(x).

Suppose an and bn are series with positive terms and b, is known to be convergent. (a) If an> b, for all n, what can you say about an? Why? we cannot say anything about an an diverges by the Comparison Test. an converges if and only if a ≤ 4b. an converges if and only if an ≤ 2bn. an converges by the Comparison Test. (b) If an < b for all n, what can you say about an? Why? an converges if and only if an converges if and only if n ≤an bn. Σan converges by the Comparison Test. an diverges by the Comparison Test. We cannot say anything about an

Brianni decided to ride her bike from her home to visit her friend Gabe. Three miles away from home, her bike got a flat tire and she had to walk the remaining two miles to Gabe's home. She could not repair the tire and had to walk all the way back home. How many more miles did Brianni walk than she rode?

Mark needs to cut a board to use for a project. The board is 12 feet long. He first has to cut off 24 feet from one end of the board. He then cuts the remaining section of board into 4 equal pieces. Which equation can be used to determine the the length of each equal piece?

You are taking a casual bike ride around your neighborhood. You cover 4 miles over the course of 35 minutes. If the radius of your bike's tires is 21.5 in, determine the number of revolutions per minute your tires experienced, on average, during your ride. Round your final answer to two decimal places.

Solve the following equation for on the interval [0, 2π). 3 csc (θ) + 5 = 0 Select all correct answers. Select all that apply: 1.795 0.499 3.785 5.640 3.044 4.756

An object is launched directly in the air at a speed of 32 feet per second from a platform located 8 feet in the air. The motion of the object can be modeled using the function f(t) = −16t² +32t + 8, where t is the time in seconds and f(t) is the height of the object. How long, in seconds, will the object be in the air before hitting the ground? Round your answer to the nearest hundredth of a second. Do not include units in your answer.

Solve for d. (d - 9) (d - 8) = 0 Write your answers as integers or as proper or improper fractions in simplest form.

Determine all solutions for the following equations. sec(θ) = -2/√3

You invested $5000 between two accounts paying 5% and 6% annual interest, respectively. If the total interest earned for the year was $290, how much was invested at each rate? $ was invested at 5% and $ was invested at 6%. FERRE

P Find the center, foci, and vertices of the ellipse. Graph the equation. 42 (x-5)²/64+ (y+6)²/25=1 Type the coordinates of the center of the ellipse in the boxes below. (h,k) = (0)

A new candle 24 centimeters tall burns at the rate of 5 centimeters per hour. 11. Write a formula for its height, h, after it has been burning t hours. Find the height of the candle after it has burned 3 hours. 12.

Determine whether (1, 1) and (-1, 4) are solutions to 2x + 5y ≤ 7. Both (1, 1) and (-1, 4) are solutions. (1, 1) is a solution, but (-1, 4) is not. (-1, 4) is a solution, but (1, 1) is not. Neither (1, 1) nor (-1, 4) is a solution.

A rectangular lot whose perimeter is 290 ft is fenced along three sides. An expensive fencing along the lot's length cost $15 per foot. An inexpensive fencing along the two side widths costs only $3 per foot. The total cost of the fencing along the three sides comes to $1635. What are the lot's dimensions? *****

Use a linear approximation to estimate the number (27.07) 2/3. Make sure that your answer is correct to at least 9 decimal places. Answer:

- A connected graph G without multiple edges or loops has five vertices: A, B, C, D, and E. Vertices B, C, D have degrees of 3 and Vertex A has a degree of 1. What is the degree of the vertex E if the maximum possible numbers of paths in G from A to B is 5? 1 2 I need to learn this.

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours? $394 $440 $472.80 $512.20

Juliet is trying to increase her savings account and she decides that she is going save an additional $700 every month. If her monthly take home pay is $5,430, what proportion of her monthly take home pay is she saving?

13. Randy and Mico work in a car station. The time that Randy takes in washing a car alone is 10 minutes less than the time that Mico takes in washing the same car. Which of the equations represent the time randy takes in washing the car. A. x-10 B. x(x- 10) X-10 D.

19) Avia Company sells a product for $120 per unit. Variable costs are $80 per unit, and fixed costs are $1200 per month. The company expects to sell 670 units in September. The unit contribution margin is A) $40 per unit B) $80 per unit C) $200 per unit D) $120 per unit Answer:

Diana has 520 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) = 260w-w² (b) The area is largest for W = 130 yards. (Simplify your answer.) (c) The maximum area is 16900 square yards. (Simplify your answer.)

Solve the following equation for on the interval [0, 2π). csc (θ) + 3.35 = 0 Select all correct answers. Select all that apply: 0.272 2.191 5.980 3.137 3.445 0.973

A bag contains 12 yellow and 8 purple marbles. Joe pays $2 for the opportunity to pick a marble from the bag. If he picks a yellow marble, he does not get anything. If he picks a purple marble, he gets $k. The game is fair. Find the value of k. Give an exact answer. Do not include the dollar sign in your answer.

A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month. If M represents the number of movies that the user rents, and C represents the user's total charge for the month, find the relationship between M and C. Select the correct answer below: M= 6C + 12 C= 12M + 6 M 12C+6 C=6M + 12

A commuter plane provides transportation from an international airport to surrounding cities. One commuter plane averaged 280 mph flying to a city and 140 mph returning to the international airport. The total flying time was 3 h. Find the distance between the two airports.

Use the long division method to find the result when 8x³ + 18x² + 11x + 2 is divided by 2x + 1.

After descending for 8 minutes, an airplane is at an altitude of 24800 feet. After descending for 20 minutes, the plane's altitude is 12800 feet. Assuming a linear function, write an equation in the form a(t) = mt+b that shows the altitude, a, after t minutes of descent. Provide your answer below: a(t) =

Ernie deposited $4000 between two savings accounts. One account paid 4% simple interest and the other paid 2%. At the end of one year, Ernie had earned $140 in interest for both accounts. How much money did Ernie deposit in the account that paid 4% interest?

Given that the degree of the polynomial f(x) is 5, which of the following most accurately describes the number of x- intercepts that f(x) has? Select the correct answer below: f(x) has at most 4 x-intercepts. f(x) has at least 4 x-intercepts. f(x) has at least 5 x-intercepts. f(x) has at least 6 x-intercepts. f(x) has at most 5 x-intercepts. f(x) has at most 6 x-intercepts.

A woman decides to invest $4000 in an IRA CD at the end of each year for 10 years. If she makes these payments and the certificates all pay 6%, compounded annually, how much will she have at the end of the 10 years?

Given that the degree of the polynomial f(x) is 4, which of the following most accurately describes the number of x- intercepts that f(x) has? Select the correct answer below: f(x) has at least 4 x-intercepts. f(x) has at most 3 x-intercepts. f(x) has at least 5 x-intercepts. f(x) has at most 4 x-intercepts. f(x) has at least 3 x-intercepts. f(x) has at most 5 x-intercepts.

I can break apart unknown facts into known facts and solve multiplication problems. Madison broke up a large array into a 3 x 4 array and a 5 x 4 array. What was the large array that Madison started with? Use evidence to justify your thinking.

The number x of printer cartridges that a store will sell per week and their price p (in dollars) are related by the equation x² = 7000 - 5p². If the price is falling at the rate of $1 per week, find how the sales will change if the current price is $30.

Each day a small business owner sells 200 pizza slices at $3.00 per slice and 85 sandwiches at $3.00 each. Business expenses come to $70 per day. What is the owner's profit for a ten-day period?

A toy shop sells baby rattles in green and yellow. For every two green rattles the toy shop sells, it sells 7 yellow rattles. If the company sells 108 rattles, how many yellow rattles did they sell?

Allistair throws a biased six-sided dice. The probability of getting a 6 with this dice is 0.4. The other numbers are equally probable. If he throws the dice 3 times, what is the probability that he gets 5, 3 and 2 in this order?

Let a and b be positive constants. If a > b, then which of the following is true? It is not possible to tell anything about the relationship between a³ and b³. a³ > b³ a³ = b³ b³ > a³

g(x)=3x²-18x+22 (a) Write the equation in the form g (x)= a (x-h)²+k. Then give the vertex of its graph. (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 verte of the vertex. Then click on the graph-a-function button.

The graph to the right shows that the three components of love, namely passion, intimacy, and commitment, progress differently over time. Passion peaks early in a relationship and then declines. By contrast, intimacy and commitment build gradually. What is the maximum level of intensity for passion? After how many years in a relationship does this occur?

Which description lists Earth's layers from most superficial to deepest? a Lithosphere, lower mantle, asthenosphere, outer core, inner core b Asthenosphere, Lithosphere, lower mantle, inner core, outer core c Inner core, outer core, lower mantle, ästhenosphere, lithospherea d Lithosphere, asthenosphere, lower mantle, outer core, inner core

5. A French toast recipe uses 2 eggs to make 14 slices of French toast, Brenda wants to make 98 slices of French toast to feed her family and friends. How many eggs will Brenda need to make 98 slices?