Basic Math Questions and Answers

Find the equations of both of the tangent lines to the ellipse ² + 4y² = 36 that pass through the point (12,3) List the line with the smaller slope first.

What is the correct step for substitution given the following system of equations? * y = 5x - 7 -3x - 2y = -12

Find all critical points of the function f(x) = x² − 2x + 4

If h is an explanatory variable and k is the corresponding response variable, which of these would be represented by the horizontal axis on a scatterplot? A. Both hand k B. h C. Neither h nor k D. k

The interior angle of a regular polygon is 144 degrees Name the figure. Regular heptagon Regular nonagon Regular octogan Regular hexagon Regular decagon regular pentagon regular 11-gon regular dodecagon

An ice cream shop's goal is to sell a mean of 45 ice cream cones per day. In one week, it sold the following numbers of ice cream cones each day. 54, 45, 33, 39, 48, 40, 21 How many more ice cream cones would it have had to sell during the week to meet its goal? A. 5 B. 35 C. 25 D. 15

A spotlight on the ground is shining on a wall 24m away If a woman 2m tall walks from the spotlight toward the building at a speed of 0.8m/s, how fast is the length of her shadow on the building decreasing when she is 4m from the building? Answer (in meters per second)

2. (a) Use bubble sort to sort 4, 2, 6, 5, 3, 1, showing the list obtained after each pass. (b) Use insertion sort to sort 4, 2, 6, 5, 3, 1, showing the list obtained after each pass. (c)] Use the greedy algorithm to make change using quarters, dimes and pennies for 40 cents.

Which of these pieces of data about a package delivered by the post office is considered categorical data? A. Surface area B. Weight C. Volume D. Drop-off location

Multiply the expressions. x²-11x+30/x²-2x-24 * x²-16/X²-25

10/11. A plane flying at 37,000 feet starts its descent when it is 150 miles away from the airport. At what constant angle of descent does the plane approach? To the nearest 10th of a degree. Helpful hint: 5280 feet = 1 mile

Select ALL of the following that are Pythagorean Triples. (There may be more than one so please select all triples.) 7, 24, 25 12, 15, 19 3,4,5 6, 8, 14 11, 13, 17 4, 5, 6

If there are 8 values in a data set, in order from smallest to largest, what is the median of the data set? A. The mean of the 4th and 5th values B. The 4th value C. The mean of the 5th and 6th values D. The 5th value

(x²+x)(x²-1)/(x²-4) ( x² +8x+12) (x²+x)(x²-1)/(x²-4) ( x² +8x+12)= where x≠

Complete the steps to solve the equation 6x +1.6 = 58. Write the original equation. 6x= Apply the Subtraction Property of Equality. x= Apply the Division Property of Equality. (Simplify your answer.)

The expression below is a sum of cubes. 125x³ +144 A. True B. False

Which polynomial represents the difference below? 8x³ + 5x + 6-(2x^7 + 3x) A. -2x^7 +8x³+8x+6 B. 6x^10+2x+6 C. -2x^7 + 8x³ + 2x+6 D. 10x^10 + 8x² +6

Which of these pieces of data about an animal at the zoo is considered numerical data? A. Gender B. Species C. Color D. Height

Which of the following correctly completes the square for the equation below? x+18x=0 A. (x+9)² = 81 B. (x+3/2)^2 = 9 C. (x+3)² = 9 D. (x+18)² = 81

Which of the following shows the polynomial below written in descending order? 3x³ +9x7-x+ 4x12 A. -x+3x³ +9x7 + 4x¹2 B. 4x12 + 9x + 3x³ - x C. 9x7 + 4x¹2 + 3x³ - x D. 3x³ + 4x¹2 + 9x²-x

The solution to a two-variable system is the point on a graph at which the lines cross. A. True B. False

Shopping While shopping for clothes, Tracy spent $34 less than 3 times what Jaclyn spent. Tracy spent $11. Write and solve an equation to find how much Jaclyn spent. Let x represent how much Jaclyn spent. The equation that can be used to determine how much Jaclyn has spent is Jaclyn spent $

The top and bottom margins of a poster are 2 cm and the side margins are each 2 cm. If the area of printed material on the poster is fixed at 388 square centimeters, find the dimensions of the poster with the smallest area Width= Height=

Solve the system of equations below by graphing them with a pencil and paper. Choose the correct ordered pair (b, u). u=-b+21 u=-2b+30 A. (5, 15) B. (9,12) C. (15,5) D. (12,9)

A restaurant serves dessert in a cone-shaped dish with a diameter of 7 cm. If the dish is 10 cm deep, how many cubic centimeters of dessert can the dish hold? Use 3.14 to approximate the answer to two decimal places if necessary. 512.87 cm3 128.22 cm³ 384.65 cm³ 73.27 cm³

For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange. Ages of teachers in the mathematics department of a certain high school: 25, 53, 36, 59, 25, 53, 25, 47, 47, 43 a. 41.3 b. 45 c. 47 d. 42 a. 31 b. 45 c. 25 d. 42 a. 41.3 b. 45 c. 25 d. 42 a. 26.3 b. 45 C. 25 d. 42

Which polynomial represents the sum below? (x^8+2x+1)+ (2x^4 + x² + 1) A. x^8 + 4x^4 + x² + 2 B. x^16 +16x^8 + x² + 2 C. 2x^8 + 8x^4 + 2x² +2 D. 16x^8 + x² + 2

Open-Ended Write an equation to represent the following description. Use pencil and paper. Describe a real-world situation the equation could represent. Eighteen less than four times a number is - 13. Choose the correct answer below. A. 18x-4 = -13 B. 4x 18 = -13 C. 18x + 4 = −13 D. 4x+18 = -13 E. 4(x-18) = 13

Select all of the sequences of transformations on the isosceles trapezoid below that would result in a congruent figure. A horizontal reflection, followed by a 3 unit translation down. A 5 unit translation to the left, followed by dilation by a scale factor of 1/2. A vertical reflection, followed by a rotation of 90 degrees clockwise. A vertical reflection, followed by a rotation 270 degrees counterclockwise. A rotation 180 degrees clockwise, followed by dilation by a scale factor of 3.

If the value of "y" varies directly with "x" and y=-51 when x = 3, find "y" if x = 2. Enter the number that belongs in the green box. y = [?]

Find the sum of the polynomials below: (8x9 + 6x6 - 2x+6) + (9x⁹ + 4x6 + 9x+7) A. 17x9 + 10x6-7x+13 B. 10x⁹ + 17x6 + 7x+ 13 C. 72x9 +24x6-18x² + 13 D. 17x + 10x + 7x+13

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