Algebra Questions

Multiply and simplify the rational expression x 25 x 3x 40 2 2 X 64 x 2x 35 x 25 x 3x 40 x 64 x 2x 35 Simplify your answer Type your answer in factored form

9x y 225 The endpoints of the minor axis are 5 0 5 0 Use a comma to separate answers as needed Type an ordered pair using integers or fractions OA CHICK CAR The foci of the ellipse are 0 10 2 0 10 2 Simplify your answer Use a comma to separate answers as needed Type an ordered pair Type exact answers for each coordinate using radicals as needed Graph the ellipse Choose the correct graph below B The domain of the ellipse is Type your answer in interval notation Type an exact answer using radicals as needed OC Ay Q

Find the graph of the following ellipse Identify the domain range center vertices x y 25 16 A 1 AY What are endpoints of the minor axes of the ellipse 0 4 0 4 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed Which graph is correct What are the foci of the ellipse hts of the minor axis OB www Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed OD O

a Find the intercepts of the graph of the following equation b Graph the equation 5x 8y 20 Il necessary I answer box to complete your choice O A The x intercept is Type an integer or a simplified fraction B There is no x intercept What is the y intercept Select the correct choice below and if necessary fill in the answer box to complete your choice O A The y intercept is 3 5 4 34 12 1 3 My 4

Solve the following equations for the unknown variable value clearly showing your work to both sides of the equation 2 8 4x 4 x 12 8 1 21 12 4 10 3 1 2 x 8 X 6 8 1 0 10 2 X 12 L 4 8 32 10 S 5 So X 9 2 x 10 d l X 8

Write an equation of the line Express the answer using either the general form or the slope intercept form of the equation of a line Q The equation of the line is Type an equation Use integers or fractions for any numbers in the expression

Graph the line that contains the point P 5 5 and has an undefined slope Find an equation of the line Use the graphing tool to graph the line Use the given point to graph the line Click to enlarge graph Write the equation of the line that contains the point P 5 5 and has undefined slope 10 10 8 6 4 2 di 2 4 6 84 ts 10

Find the graph of the following ellipse Identify the domain range center vertices endpoints of the minor axis and the foci x v 25 16 1 What is the center of the ellipse 0 0 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed What are the vertices of the ellipse 5 0 5 0 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed What are endpoints of the minor axes of the ellipse Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed

You have decided to plant a vegetable garden containing tomatoes peppers and cucumbers The garden will have 61 plants There will be twice as many tomato plants as pepper plants Tomato plants cost 2 00 each Pepper plants cost 5 00 each Cucumber plants cost 5 00 each You have 197 00 to spend on the plants Create a system of equations and the corresponding augmented matrix Then use technology to put that matrix in reduced row echelon form Then give the number of plants of each type that should be purchased Tomatoes Peppers

Solve the linear inequality Express the solution set using set builder and interval notation Graph the solution set 2 3 5x 24 4x The solution set expressed in set builder notation is x The solution set expressed in interval notation is Choose the correct graph of the inequality below O A 15 0 15 O B 15 0 15

Solve the inequality Write the solution in interval notation and graph it 6x 1 19 OA 3 00 OC 0 3 Choose the correct graph of the solution O A O B C OP OB 3 00 OD 0 3 1

Graph the given interval and then express the given interval as an inequality in terms of x 0 9 Choose the correct graph below O A O C 9 10 8 6 4 2 0 2 4 6 8 10 10 8 6 4 20 2 4 6 8 9 10 O B 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 6 6 8 9 9 10 8 10

17 10 12 x 18

Graph the given interval and then express the given interval as an inequality in terms of x 0 9 Choose the correct inequality OA x 9 B X 9 OC x 9

Question 1 10 points Which is the graph of y x 1 2 O 2 51 2 2 1 11 A 2 21

What is the equation of the following parabola in vertex form 5 4 3 2 1 31 2 11 21 31 4 2 3 4 5 y 5 x 2 4 y 5 x 2 4 y 5 x 2 4 y 5 x 4 2

Which of the below is the factored form of the polynomial showr m 6m 40 n 8 n 5 n 10 n 4 n 10 n 4 n 12 n 6

What would be the axis of symmetry in the graph below 54 2 1 Ox 1 O x 2 5 y 4 y 3 2

Given the standard form of a parabola y x 4x determine the vertex form of the graph y x 4 y x 2 4 y x 4 y x 2 4

The following parabola is in standard form y x 12x 5 What would need to be put in the space below to complete the square and covert to vertex form y x 12x 36 36 144 144 6 6 12 12 5

What is the vertex of the following parabola y 4x 24x 23 3 13 3 13 3 24 3 24

Find the graph of the following ellipse Identify the domain range center vertices endpoints of the minor axis and the foci x y 25 16 1 What is the center of the ellipse 0 0 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed What are the vertices of the ellipse Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed

A one way road passes under an overpass in the shape of half an ellipse 30 ft high at the center and 20 ft wide Assuming a truck is 12 ft wide what is the tallest truck that can pass under the overpass The tallest truck that can pass under the overpass is ft tall 30 f 20 ft

Use the quadratic formula to solve x 3x 1 0 3 5 3 5 2 2 O O 3 13 3 13 2 2 3 5 3 5 2 2 3 13 3 13 3 13 2 2

How is the graph of g x x 1 related to the graph of f x x

91 x9

Graph the ellipse Identify the center vertices endpoints of the minor axis and foci 20x 560 7y The center is 0 0 Simplify your answer Type an ordered pair The vertices are Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as nee

Solve the following equation by COMPLETING THE SQUAR X 10 7 2 x 5 2 6 x 10 98 x 5 24 O 2x 20x 2 0

d 2x 6 8 6 9 2x 3

Use the interactive figure to find your answer Use the left and right arrow keys to move along a slider as needed Click here to launch the interactive figure P Conics Rectangular Form Google Chrome The length of the major axis is Simplify your answer 4 media pearsoncmg com cmg pmmg mml shared precalc ifigs HTML5 1Fig2 20Precalc2 conics Conic Ellipse x h a Parameters a b o y k 6 4 5 1 Conics Rectangular Form 9 8 7 9 8 7 6 5 4 3 2 6 15 4 3 2 4 2 1 ty 1 2 3 4 5 6 7 8

1 A 11 1 a Find a basis for the column space of A b Find a basis for the nullspace of A A 0 11 0 B 1 0 0 0 0 1 0 0 C 1 11 1 0 11 0 D 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 E 1 11 1 0 11 0 1 10 0 F 1 11 1 0 11 0 1 10 0 1 1 1 G 1 1 1 H 1 11 1 Problem 9 a C Problem 9 b 0 1 1 11 14 1 0 1 1 A 1 1 0 1 0 1 B 1 1 0 1 1 0 1 C 1 0 1 D 1 0 E 1 1 0 1 F 1 1 0 1 G 1 1 0 1 1 0 1 H 1 1 0 1 0 Select

Find the graph of the following ellipse Identify the domain range center vertices endpoints of the minor axis and the foci x v 1 25 9 What is the center of the ellipse Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed

Exercise Show that the Hademaard gate H below is a unitary operator Describe what it does to 10 and 1 H 4 2

Sketch the graph of the solution set of the system of inequalities Label the vertices of the region 6y 2 4x 2x 3y 5

13 Simplify cos 2x 5y cos 2x 5y

0 An elm tree that is 6 meters tall casts a shadow 8 meters long If a nearby redwood tree is 12 meters tall how long will the redwood tree s shadow be Write your answer as a whole number or a decimal Do not round meters

4 Graph the image of rectangle STUV after a dilation with a scale factor of 1 centered at the origin V 104 8 9 6 2 U T

Solve for n 9n 19n 17 13

Solve for q 16q 2q 139 13q 15

Write the coordinates of the vertices after a dilation with a scale factor of centered at the origin 10 8 6 4 2 104 8 6 4 H IN 2 2 6 E 2 4 6 00 8 G 10 F

Problem 9 a A Problem 9 b 11 1 A 0 11 0 B 1 0 0 0 0 1 0 0 C 1 11 1 0 11 0 D 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 E 1 11 1 0 11 0 1 10 0 F 1 11 1 0 11 0 1 10 0 1 1 1 G 1 1 1 H 1 11 1 Select 0 1 11 14 0 1 a Find a basis for the column space of A b Find a basis for the nullspace of A 1 1 1 Select A 1 2 1 0 1 7 0 1 B 1 1 0 1 0 1 C 1 0 1 D 1 E 1 0 1 F 1 0 1 G 1 1 0 1 0 1 1 1 0 1 0 1 0 1

Paired or not paired Decide whether each situation involves paired or not paired data Then select the correct program for constructing a CI to estimate the difference a The wait times for Caucasian Walmart customers ages 56 34 45 23 18 and 41 were recorded Then the wait times for non Caucasian Walmart customers ages 56 34 45 23 18 and 41 were recorded The data is Select an answer so we should use the program Select an answer b We take a random sample of 50 days and record Microsoft stock and Apple stock on those same days The data is Select on opow chou

14 Given f x 3 2x and g x 2x 1 a 5 Find f g b 2 What is the domain off g c 2 Find

2 We can already study our first gate at this point Consider the NOT gate 0 G 1 N 2 1 Note that this matrix is unitary in that N NT N where the symbol means take the transpose the complex coniugate

Problem 7 Find a basis for the subspace of R4 consisting of all vectors of the form a b c d where c a 7b and d a 5b A 0 1 7 1 1 1 0 5 B 1 1 0 1 0 1 7 5 C 1 0 7 1 0 1 1 5 D 1 0 1 1 0 1 7 5 E 1 0 1 1 1 0 7 5 F 0 1 7 1 0 1 1 5 G 1 0 7 1 1 0 1 5 H 1 1 0 1 1 0 7 5

11 2x6 10 13 2 4x 10 15 5 3x 10 12 12 5x 2 14 4 10x 6 16 12 2x 8

7 8 6 17 5x 33 8 17 2 3x

Find the angle in degrees between vectors u 8 7 and v 8 3 0

9 3 5 2x 10 1 5

1 5x 24 59 3 1 x 1 2 C Show your work to solve each of the equations below 2 12x 22 26