Basic Math Questions and Answers

Write a function g(x) that represents the exponential function f(x) = 2x after a vertical stretch by a factor of 2 and a reflection across the x-axis. Graph both functions. Find the equation for g(x).

For what value of k will the function y = 3x²+4r-7/x²-5x+k have asymptotes at x = 6, x= -1, and y = 3? (A) k=6 (B) k=-6 (C) No such value of k exists because regardless of the horizontal asymptote is y = 0 (D) No such value of k exists because there will be a hole, not a vertical asymptote, at x= -1

Suppose Solid A and Solid B are similar. Solid A has an edge length of 18 cm, and the corresponding edge in Solid B is 12 cm. If the volume of Solid A is 229.5 cm³, what is the volume of Solid B in cubic centimeters?

What number must you add to complete the square? x^2+8x=50

Consider the function f(x) = 4 - 4x², -5 ≤ x ≤ 2. The absolute maximum value is and this occurs at x = The absolute minimum value is and this occurs at x =

Question Help ▼ In a survey of 1000 drivers from Region A, 864 wear a seat belt. In a survey of 1000 drivers from Region B, 915 wear a seat belt. At a=0.05, is there evidence to support the claim that the proportion of drivers who wear seat belts in Region A is less than the proportion of drivers who wear seat belts in Region B? Assume that the samples are random and independent. Complete parts (a) through (e) below. (a) Identify the claim and state Ho and Ha- Identify the claim. Let population 1 be drivers from Region A and let population 2 be drivers from Region B. Choose the correct answer below. A. The claim is that the proportions of drivers who wear seat belts in both regions add up to 1. B. The claim is that the proportions of drivers who wear seat belts in both regions are equal. C. The claim is that the proportion of drivers who wear seat belts in Region A is less than the proportion of drivers who wear seat belts in Region B. D. The claim is that the proportion of drivers who wear seat belts in Region A is greater than the proportion of drivers who wear seat belts in Region B.

The volume of a cone is 800 cubic feet. If the radius of the base is doubled and the height remains the same, what will be the volume of the new cone? . 6,400 ft³ 1,200 ft 1,600 ft³ 3,200 ft³

Solve the following system of equations. 2x² + 4y² =68 3x² - 5y² = 3

Find the difference and enter it in the box below. Enter exponents using the caret (^). For example, write 4x² as 4x^2. (2x + 4x4-2x+3) - (4x4-2x³+3)

After being rearranged and simplified, which of the following equations could be solved using the quadratic formula? Check all that apply. A. 2x²-6x-7 = 2x² B. 5x³-3x+10= 2x² C. 2x²-3x+ 10 = 2x+ 21 D. 5x²+2x-4 = 2x²

At a time t seconds after it is thrown up in the air, a tomato is at a height (in meters) of f(t) = -4.9t² + 65t +1 m. A. What is the average velocity of the tomato during the first 5 seconds? (Include units.) B. Find (exactly) the instantaneous velocity of the tomato at t = 5. (Include units.) C. What is the acceleration at t = 5? (Include units.) D. How high does the tomato go? (Include units.) E. How long is the tomato in the air? (Include units.)

Identify the variable expression that is not a polynomial. A. x+12 B. x^-9 + y^3 C. 33 D. y^9+ 27

A directed line segment begins at F(-10, -2), ends at H(4, 4), and is divided in the ratio 4 to 2 by G. What are the coordinates of G? (-0.87, 2) (-1.6, 2) (3.3, 5) None of the other answers are correct (-0.67, 2)

Solve the following system of equations. 3x² + 3y² = 123 5x² - 4y² = -20 Solution(s): • Enter your answers as points: (x, y) • Because these systems are non-linear, you may have more than one solution. • If you have more than one solution, enter your answers as a list of points: (co, y0), (1.1) • Use 'sqrt(...)' to enter radical answers, do not use decimal approximations.

Which polynomial represents the sum below? 9x² + x + 2 + 3x^4+2x+2 A. 12x^6 + 9x+4 B. 3x^6 + 9x² + 3x+4 C. 3x^4 + 9x² + 3x+4 D. 3x^4 + 9x+4

Each letter of the alphabet is written on separate cards in red ink. The cards are placed in a container. Each letter of the alphabet is also written on separate cards in black ink. The cards are placed in the same container. What is the probability that a card randomly selected from the container has a letter written in black ink or the letter A or Z? 8/13 15/26 1/2 7/13

If a plane intersects a right cylinder, the cross-section is a circle. Which of the following describes a counterexample to this statement? A. If the plane is parallel to the bases, the cross-section is a circle. B. If the plane is perpendicular to the bases, the cross-section is a rectangle. C. If the plane is tangent to the bases, the cross-section is a line. D. None of these, the original statement is always true. (4 pts.)

This question does not have an attempt limit. This problem is worth 1 point. Your recorded score for this problem is 0.0%. Your submissions on this problem will be graded. Let f(x) = (3x - 2) (x²-2). Find all the values of x for which f'(x) = 0. Present your answer as a comma-separated list:

Enter the degree of the polynomial below: 6x6 +9x³+3x²-4x10-9x5-5x6

What is the coefficient of the term of degree 1 in the polynomial? 2x8-5x²+3x+4

Which of the following is a polynomial? A. (x6-2)/(x4 + 3) B. + x4 + 16 C. xy + 2 D. x²-1

Sodium chlorate crystals are easy to grow in the shape of a cube by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length z, calculate dV/dz when x = 5 mm. dV/dz =

The mean age of the people in room 5 is 29 years. The mean age of the people in room 6 is 35 years. If there are 27 people in room 5 and 22 people in room 6, then what is the mean age of all the people in room 5 and room 6 put together? (nearest tenth). 30.7 31.7 29.6 32

In 2000, the population of St. Louis was 346,904, and it decreased to 319,257 in 2010. If this population decrease were modeled by an exponential decay function, what value would represent the y-intercept? Explain your reasoning.

Subtract the polynomials: (6x³ - 4x + 5)-(3x3-5x² + 6x-2). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write 4x2 as 4x^2.

Select all of the transformations that always maintain a shape's congruency? * A reflection A dilation A reflection then a dilation A rotation then a translation A translation then a reflection

Dylan bought 3 identical shirts online for a total cost of $71.83 including a flat rate of $7.99 for shipping. Drag numbers to complete an equation to find the cost of each shirt, s. Each number may be used only once.

Which description represents this equation? 7x-2=33 Two times the quantity of seven less than a number equals thirty-three. Seven less than two times a number equals thirty-three. Two less than seven times a number equals thirty-three.

Change 749,921,154 to Roman numeral (Assume the Roman Numerals in blue have double bar over them and Roman Numerals in red have one bar over them) CDCXLVIII MXXI CCXXXIX DCCXLIX CMXXXI CCLIV DCXLVIII MCXXI CLIV DCCXLIX CMXXI CLIV

Nick and Miguel are the partners in a local health food store. They need $85,000 to start the business. They invested in the ratio 3:7, Nick and Miguel respectively. How much money did Nick invest? Just input the numbers in your answer. Do not insert a dollar sign.

If you flipped the graph of y=x²+2x-2 vertically, you would get the graph of y = -(x²+2x-2). A. True B. False

The senior class is planning to take two separate trips to Disneyland. On the first trip, the seniors had to rent 12 vans and 10 buses with 690 students. On the second trip, they only needed 7 vans and 10 buses as they only took 615 students. There was no difference in the size of the vans and no difference in the size of the buses. How many students went in each van? How many students went in each bus? Let x = Let y = Equation 1: Equation 2:

If a town with a population of 82000 people increases by 12% annually, what will the population be after 5 years? Round your answer to the nearest whole number.

The distance, d, in kilometres, a spaceship travels in t hours is given by the formula d = 40 000t. How long will it take the spaceship to travel 120 000 km? 3h 30 h 0.3 h 300 h

Which values are solutions to the inequality below? Check all that apply. x2≤36 A. 6 B. 7 C. 3 D. 36 E. 39 F. no solutions

The current student population of the Brentwood Student Center is 2,000. The enrollment at the center increases at a rate of 4% each year. To the nearest whole number, what will the student population be closest to in 3 years'? 1) 2,240 2) 2,250 3) 5,488 4) 6,240

What is the coefficient of the term of degree 7 in the polynomial? 4+ 6x^7 +10x-5x^6-2x^5

Which polynomial represents the difference below? (5x^7 +9x^4+3)-(x^4-3x) A. 5x^7 + 8x^4+3x+3 B. 4x^7 + 8x^4 -3x+3 C. 4x^11 +8x³ +3 D. 8x+6

Which of the following is the correct factorization of the polynomial below? 8x3 +64y3 A. (4x+4y)(2x+8y) B.(2x+4y)(4x²-8xy+16y²) C. (4x+2y)(4x²-2xy + 16y²) D. The polynomial is irreducible.

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds. A) .9893 B) .0107 C) .5107 D) .4893

Part C: Write and solve a system of inequalities to model the following situation: An acting company is holding a performance in an arena. They are selling student tickets for $2 and adult tickets for $4. The arena can hold at most 200 people (students and adults). No more than 25% of the people should be adults. The company is hoping to make at least $400 in ticket sales. How many student tickets and how many adult tickets should be sold to maximize the amount of money earned?

The population of a certain city was 4,192 in 2002. It is expected to decrease by about 0.38% per year. Write an exponential decay function, and use it to approximate the population in 2022. The exponential decay function where f(x) is the population of the city x years after 2002 is f(x) = The approximate population of the city in 2022 will be (Round to the nearest whole number as needed.)

Describe and correct the error a student made in identifying the growth or decay factor for the function y = 2.55(0.7)^x Choose the correct answer below and fill in the answer boxes to complete your choice. (Type integers or decimals.) A. The student incorrectly identified the decay factor. The rate of decay is so the decay factor is B. The student incorrectly identified the base. The base is decay factor is , so the C. The student incorrectly identified the function as exponential decay. It represents exponential growth. The rate of growth is so the growth factor is D. The student incorrectly identified the base and incorrectly identified the function as exponential decay. The base is____ So, the rate of growth is___and the growth factor is

Which of the following statements is true? The sum of the exterior angles of a triangle is 360°. The exterior angle at each vertex of a triangle is equal to the sum of the interior angles at the other two vertices. The sum of the interior and exterior angles at any one vertex of a triangle is 180°. All of these.

The area of a rug is represented by the following expression, x² + 4x-12, which of the following expressions represents the width of the rug if the length is x+6. (A ) x-6 (B) x+2 (C) x -2 (D) x+6

Write the contrapositive and negation of the statement. If it is not raining then I will drive. contrapositive: If it is raining then I will not dive. negation: It is raining and I will drive. contrapositive: If I will drive then it is not raining. negation: If it is not raining then I will not drive. contrapositive: If I will not drive then it is raining. negation: It is not raining and I will not drive. contrapositive: If I will not drive then it is not raining. negation: If it is not raining then I will not drive.

Find the sum and enter it in the box below. Enter your answer as a polynomial in descending order, and use the caret (^) for exponents. For example, you would write 4x² as 4x^2. x^5+2x³ +2x² +6x+3 + -3x -3x4 +2x³ +6x

The equation below specifies a function. Determine whether the function is linear, constant, or neither. 2x+3y=7 Choose the correct answer below. A. A constant function is specified by the equation. B. Neither a constant function nor a linear function is specified by the equation. C. A linear function is specified by the equation.

A person places $1380 in an investment account earning an annual rate of = 8.6%, compounded continuously. Using the formula V Pert, where Vis the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 10 years.

One hundred students out of 1200 at a school have been surveyed. Predict the number of students in the population that would answer similarly. Fourteen said they had an after-school job. 114 students 168 students 8571 students 147 students