Math Questions

f(x)=√x - 11. Find the inverse of f(x) and its domain. A. f¹(x) = x² +11; x2-11 B. ƒ ¹ (x) = (x + 11) ² ; x ≥ 0 C. ƒ ¹ (x) = x² + 11; x ≥ 0 D. f¹(x) = (x +11)²; x2-11

If P (5,4), find the image. of P under the following rotation. 270° counterclockwise about the origin

Find the value of Q in the following system so that the solution to the system is (4,2). 3x - 2y = 8 2x+3y = Q A. 14 B. 10 C. 12 D. 8

Answer the following questions for the function f(x)=x√x² + 25 defined on the interval -5 ≤ x ≤ 6. f(x) is concave down on the interval x = f(x) is concave up on the interval x = The inflection point for this function is at x = The minimum for this function occurs at x = The maximum for this function occurs at x =

Find an equation of the ellipse that has center (5, 2), a minor axis of length 4, and a vertex at (1,2).

Christopher looked at his quiz scores shown below for the first and second semester of his Algebra class. Semester 1: 78, 91, 88, 83, 94 Semester 2: 91, 96, 80, 77, 88, 85, 92 Which statement about Christopher's performance is correct? 1) The interquartile range 3) The mean score for for semester 1 is greater semester 2 is greater than the interquartile than the mean score for range for semester 2. semester 1. 2) The median score for semester 1 is greater than the median score for semester 2. 4) The third quartile for semester 2 is greater than the third quartile for semester 1.

Which pair of functions are inverses of each other? A. f(x) = 7/x - 2 and g(x) = x+2/7 B. f(x) = x/7 + 10 and g(x) = 7x - 10 C. f(x) = 9x - 6 and g(x) = x-6/9 D. f(x)= 3√11x and g(x) = (x/11)³

When Jose installs a new app on his phone, it creates a square icon on his home screen. The square starts with side lengths of 1 cm. The side lengths grow by 2.8 cm each second until the square reaches its maximum size. What is the perimeter of the square after 1.5 seconds? Recall that the perimeter of a shape is the sum of its side lengths. 16.8 centimeters 19.2 centimeters 20.8 centimeters 29.2 centimeters

Find the maximum and minimum values of the function g(θ) = 2θ - 8 sin(θ) on the interval [0, π]

Which of the following polynomials is in standard form? A. F(x) = 5x+2x³ - x² - 3 B. F(x) = -3-x²+2x³ +5x C. F(x) = 2x³ -x +5x-3 D. F(x) = -3 +5x-x²+2x³

There are 20 chocolate candies in a bag. What is the probability of reaching in the bag and pulling out a strawberry? A. 1, since all of the candies are chocolate, there is 100% chance of pulling out a strawberry B. 1/2, because half of the time you will get a strawberry C. 0, it would be impossible to pull out a strawberry because there are no strawberries in the bag

For the following exercises, find the quantities for the given equation. 1. Find dy/dt at x = 1 and y = x² + 3 if dx/dt = 4 2. Find dx/dt x = -2 and y = 2x² + 1 if dy/dt = -1. 3. Find dx/dt at (x, y) = (1, 3) and z² = x² + y² if dx/dt = 4 and dy/dt= 3.

Find the angle between the vectors (-9, -8) and (-8, 7). Carry your intermediate computations to at least 4 decimal places. Round your final answer to the nearest degree.

Suppose a point has polar coordinates (-4, -11π/6) with the angle measured in radians. Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in [-2π, 2π].

What is the first step when factoring the trinomial ax²+bx+c? A. Look for a common factor in each term. B. Factor the simplified trinomial. C. List the factors of the leading coefficient. D. List the factors of the constant term.

Line j passes through the points (0, 0) and (c, d). Line k passes through the points (0,0) and (-d, c). Lines j and k are perpendicular neither parallel

Consider the function f(x) = 8(x - 2)^2/3. For this function there are two important intervals: (-∞, A) and (A, ∞) where A is a critical number. A is For each of the following intervals, tell whether f(x) is increasing or decreasing. (-∞, A): (A, ∞): For each of the following intervals, tell whether f(x) is concave up or concave down. (-∞, A): (A, ∞):

Line m passes through the points (-4, 3) and (-4, 7). What is the slope of the line that is perpendicular to line m? -4 undefined zero

Rachel spent $24.15 on vegetables. She bought 2 lbs of onions, 3 lbs of carrots, and 1 1/2 lbs of mushrooms. If the onions cost $3.69 per lb, and the carrots cost $ 4.29 per lb, what is the price per lb of mushrooms? a. $2.60 b. $2.25 c. $2.80 d. $3.10

Solve the inequality. -3x - 5 ≥ 7 A. x ≤ 4 B. x ≥ 4 C. x ≤ -4 D. x ≥ -4

The function f(x) = 6x + (4/x) has: • a local minimum at x = with value f(x) = • a local maximum at x = with value f(x) =

Solve the quadratic equation using completing the square: x² - 12x + 23 = 0 x=-6+ √59 or x = -6-√√/59 x=6+ √13 or x = 6 - √13 x = 6 + √59 or x = 6 -√√59 x=-6+√13 or x = -6 -√13

Given that 26x⁹ + 5x³⁹ y + y^8 dy/dx Now find an equation of the line tangent to the graph of 26x9 + 5x³9 y + y = 32 at (1, 1):

A party room costs $50 plus $6 per person. To reserve a party room, you must spend at least $98. Which inequality could help you figure out how many people you should invite so that you spend at least $98? A. 56p < 98 B. B. 50+ 6p ≥ 98 C. 50+ 6p ≤ 98 D. 50-6p ≤ 98

The two sets of data below represent the number of runs scored by two different youth baseball teams over the course of a season. Team A: 4, 8, 5, 12, 3, 9, 5, 2 Team B: 5, 9, 11, 4, 6, 11, 2, 7 Which set of statements about the mean and standard deviation is true? 1) mean A< mean B standard deviation A > standard deviation B 2) mean A> mean B standard deviation A < standard deviation B 3) mean A < mean B standard deviation A < standard deviation B 4) mean A> mean B standard deviation A > standard deviation B

A car rental company offers two plans for renting a car. Plan A: 35 dollars per day and 10 cents per mile Plan B: 65 dollars per day with free unlimited mileage How many miles would you need to drive in one day for plan B to save you money? Enter the exact answer as an inequality using the variable m to represent the number of miles.

The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.

For - 11 ≤ x ≤ 13 the function f is defined by f(x) = x³ (x + 1)² On which two intervals is the function increasing (enter intervals in ascending order)? Find the interval on which the function is positive: Where does the function achieve its minimum?

f(x) = √3x g(x) = √48x Find (f g)(x). Assume x ≥ 0. A. (f.g)(x) = 12√x B. (f g)(x) = √51x C. (f.g)(x) = 12x D. (f.g)(x) = 72x

Given a continuous function f(x) with f(-5) = - 1 and f(9) = - 8: There must be a number c with − 5 < c < 9 and f(c) = - 4.6. There might be a number c with - 5 < c < 9 and f(c) = - 4.6. There cannot be a number c with -5 < c < 9 and f(c) = - 4.6.

John lives in Vermont and Julie lives in Florida. One January day, it was 52°F in Florida and -9°F in Vermont. What was the difference in temperatures?

Find an equation of the ellipse that has center (3, 2), a minor axis of length 2, and a vertex at (3,-9).

Solve 3x + 3 = 21. A. x = 6 and x = -8 B. x= -6 and x = -8 C. x= 6 and x = -6 D. x=-6 and x = 8

An equation for the line L is: y = 3 + 3/2 (x - 17) The angle L makes with the x-axis is:

Solve the triangle BQK where b=3.43, q = 6.51, and Q = 90°. Which of the following statements are true about BQK? There is at least one correct response. Choose all correct responses. Rounded to the nearest degree, the measure of angle K = 53° The perimeter of BQK is approximately 17.3 The perimeter of BQK is approximately 15.47 Rounded to the nearest degree, the measure of angle B = 32° None of these statements are true about AABQK

Use the graph of the function f shown to estimate the following limits and the function value. Complete parts (A) through (D). (C) Find the limit lim x⇒1 f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x⇒1 f(x) B. The limit does not exist. (D) Find the function value f(1). A. f(1) = B. The function does not have a value.

Which of the following is a validation of congruency between two polygons? if by applying only rotation you can make them coincide if by applying only translation you can make them coincide if by applying rigid motions you can make them coincide if by applying dilation you can make them equal

Define the sets A, B and C as: A = {-7, 4, 0, 3} B = {-7, 0, 4, 6} C = {-5, 4, 0, 2, 4, 6} List all values of a that satisfy each statement. - x is in A and x is in B: x is in A or x is in C: x is not in B and is in C:

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1400 bacteria selected from this population reached the size of 1849 bacteria in six hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

A school board wants to implement a new lunch program, but wants to know how the students feel about it. Which sample is the best predictor of how the students feel? A. Select 7th graders at random. B. Select the first 10 students that show up to lunch. C. Ask the other members of the school board. D. Select random students from every grade.

You know that the following information about f(x): f(3) = 14 f(14) = 2 f'(14) = 2 f'(3) = 13 If F(x) = f(f(x)) and G(x) = (F(x))² then: F'(3) = G'(3) =

a. When 50.19 and 50.67 are multiplied, the answer should have Enter the answer, using the correct number of significant figures: 50.19 x 50.67 = b. When 50.19 and 50.67 are summed, the answer should have Enter the answer, using the correct number of decimal places: 50.19 +50.67: =

The critical numbers of the function f(x) = (8x - 8) e^4x are:

In slides 2-4, use the side lengths to determine if the triangle is acute, obtuse, right, or not a triangle. 19, 6, 12

Rosario and Enrique are in the same mathematics class. On the first five tests, Rosario received scores of 78, 77, 64, 86, and 70. Enrique received scores of 90, 61, 79, 73, and 87. How much higher was Enrique's average than Rosario's average? 15 points 2 points 3 points 4 points

a. When 28.40 and 27.6 are divided, the answer should have ____ Enter the answer, using the correct number of significant figures: 28.40/27.6 = b. When 27.6 is subtracted from 28.40, the answer should have ___ Enter the answer, using the correct number of decimal places: 28.40 27.6 =

The number 1.464163 rounded to 4 significant figures is: The number 418.308 rounded to 3 significant figures is: The number 43.94754 rounded to 5 significant figures is:

f(x) = 3x + 8. Find the inverse of f(x). A. f ¹ (x) = 3x - 8 B. ƒ ¹ (x) = x - 3 / 8 c. f ¹ (x) = x - 3 / 3 D. f¹(x)= 8 - 3x

You want to solve the following system of equations by addition. What should you do first, so that one variable is eliminated when you add the equations? -2x+4y=10 3x-2y=-7 A. Multiply the top equation by -3. B. Multiply the top equation by 3 and the bottom equation by -2. C. Multiply the top equation by 2 and the bottom equation by 3. D. Multiply the bottom equation by 2.

Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. -1 (multiplicity 2), 3+2i