Math Questions

Indicate the equation of the given line in standard form, writing the answer in the equation box below. The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5,-5).

What is the vertex of the quadratic function below? y = x² - 8x+1 A. (8, 1) B. (-4, 15) C. (4, -15) D. (-8, 129)

Use the sum of cubes formula to factor. Be sure to factor out any common factors. x³+27

Choose the kind(s) of symmetry. (Select all that apply.) H point line none plane

First factor out the greatest common factor from each term. Then factor the remaining polynomial. 4x² + 16x+12 4x² + 16x + 12 =

Harold moves no more than 43 of his sheep and goats into another field. Fewer than 22 of the animals are goats. Let s represent the number of sheep and g represent the number of goats. Which two inequalities represent this situation? A. s> 22 B. g <22 C. s+ g≤ 43 D. s-gs 43

If P = (5,4), find the image of P under the following rotation. 180° counterclockwise about the origin ([?], [ ]) Enter the number that belongs in the green box. Enter

What are the domain and range of the function represented by the set of ordered pairs? {(-13, 9), (-7,-5), (5, 14), (11, -10)} A. Domain: {-13, -7, 5, 11} Range: (-10,-5, 9, 14) B. Domain: {-10, -5, 9, 14) Range: (-13, -7, 5, 11) C. Domain: -13 ≤x≤ 11 Range: -10y≤ 14 D. Domain: -10 ≤ x ≤ 14 Range: -13 sys11

Grace bought a television for $329 and some DVDs for $5.75 each. Write an equation to find out how many DVDs Grace bought if she spent a total of $363.50. 329 +5.75m = 363.50

Stacy is building a candy house. She worked on it 3 hours before lunch and 6 hours after lunch. How many total hours did Stacy spend working on the candy house? Give your answer as a mixed number in simplest form. Enter the number that belongs in the green box.

There is a spinner with 11 equal areas, numbered 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 2 or a multiple of 5?

Use the quadratic formula to solve the equation: x² + 3x - 5 = 0 x = -5 + √13/2 or x = -5-√13/2 x = -3+√29/2 or x = -3-√29/2 x = 5+√13/2 or x = 5-√13/2 x = 3+√29/2 or x = 3-√29/2

Indicate the equation of the given line in standard form, in the equation box below. The line through point (-3, 4) and perpendicular to a line that has slope 2/5

Solve 5ax + 6ax = 7ax+8 for x. Assume a‡0. O A. x = 2/a O B. x = 1/a O C. x = 2a O D. x = a

An airplane ascends at an angle of elevation of 22" for a ground distance of 7850 feet. What height does the plane gain during this ascent? Draw a picture on paper to support your answer, and round your answer to the nearest whole foot.

The circumference of a sphere was measured to be 86 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.

After making twenty-sixth payment of $480.00 on your car loan, you wanted to find out how much is left of your original 5 years loan at 4.1% compounded monthly of $26,000.00. What is the amount of the remaining balance of your car loan? The remaining balance of your car loan would be $ (Round to 2 decimal places.)

Mandy flipped a coin 50 times. The coin landed on tails 20 times. What was the experimental probability for landing on tails? A 3/5 B 2/5 C 4/5

Answer the statistical measures and create a box and whiskers plot for the following set of data. Min: 1, 2, 2, 4, 5, 9, 10, 12, 14, 14 Q1: Med: Q3: Max: Create the box plot by dragging the lines:

The following is the student's incorrect work in solving a quadratic using the zero product property. Explain the student's mistake. Step 1: x²-3x - 4 = 8 Step 2: (x-4) (x + 1) = 8 Step 3: x 4 = 8 or x + 1 = 8 Step 4: x= 12 or x = 7 -

Which of the following options is a 3rd degree polynomial with exactly 1 real root? A. F(x)= x+3x²-9x-27 B. F(x)= x +9x² +27x+27 C. F(x)=x²-9x² +27x-27 D. F(x)= x+3x² +9x+27

Name the kind or kinds of symmetry the following figure has: point, line, plane, or none. (Select all that apply.) 2 line point plane none

Given that f(x) = x² - 13x + 36 and g(x) = x-9, find (f+g)(x) and express the result in standard form.

Find the angle between the vectors (7, 2) and (9, -3). Carry your intermediate computations to at least 4 decimal places. Round your final answer to the nearest degree.

Suppose a point has polar coordinates (3, π/2) 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].

Consider the function f(x)=√2-x+7 for the domain (-∞, 2]. Find f(x), where is the inverse of f. 1 Also state the domain off in interval notation.

When using the rational root theorem, which of the following is a possible root of the polynomial function below? F(x) = 3x³x² + 4x +5 A. -5/3 B. -7 O C. 4/3 D. 6

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):