Algebra Questions

Problem 8 Let W be the subspace of M12 12 i e 12 x 12 matrices consisting of all matrices whose diagonal entries are zero Find the dimension of W Problem 8

Clint is making a 10 lb bag of trail mix for his upcoming backpacking trip The chocolates cost 4 00 per pound and mixed nuts cost 7 00 per pound Clint has a budget of 6 10 per pound of trail mix Use the variables c and n to represent the number of pounds of chocolate and the number of pounds of nuts he should use respectively Determine a system of equations that describes the situation Enter the equations below separated by a comma How many pounds of chocolate should Clint purchase C pounds How many pounds of mixed nuts should Clint purchase pounds

Find an orthogonal matrix A where the first row is a multiple of 0 1 0 A

Unit 3 Please answer all parts of the question Math 3 7 1 Key Features of Radical Functions e Consider the function f x 2 x 3 4 1 Record all of the transformations of f x from the parent function g x A a x n K h Q71 Stretch 02a21 Compress Zaz 2 k left or Right or down up Determine the domain and range moves right 3 up 4 f x has Reflection across stretches 2 look at the desmos look at beginning 3 4 table lues

A local theater sold 200 tickets to a matinee play with a total revenue of 2 104 00 Each adult ticket cost 15 00 and each child s ticket cost 8 00 Use the variables a and c to represent the number of adult tickets sold and the numbe of children s tickets sold respectively Determine a system of equations that describes the situation Enter the equations below separated by a comma How many adult tickets were sold a tickets How many children s tickets were sold tickets

4 3x 10x 3 2x 1

Solve the following system of equations There is a unique solution which should be entered as the ordered triplet x y z 2x 5y z 25 4x 4z 24 6x 15y3z 27

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 an d a 5b Problem 7 A 0 1 7 1 1 1 0 5 D 1 0 1 1 0 1 7 5 G 1 0 7 1 1 0 1 5 Select B 1 1 0 1 0 1 7 5 C 1 0 7 1 0 1 1 5 F 0 1 7 1 0 1 1 5 E 1 0 1 1 1 0 7 5 H 1 1 0 1 1 0 7 5

Solve the following system of equations If there is a unique solution enter it as an ordered pair in the form x y If there is no solution enter Inconsistent If there are infinitely many solutions enter your answer as a line in the form y mx b 2x 4y 24 5x 7y 54

X 49 0

Part 2 Solve by factoring 3 2x 9x 5 0

2 5 x 3 125 2

1 2x 28

roblem 1 Which of the following sets of vectors are independent i 1 2 1 3 2 0 2 4 1 ii 1 2 1 3 2 0 5 6 0 iii 1 2 1 3 2 0 7 10 2 Problem 1 A none of them B ii only C i only D i and iii only E ii and iii only F iii or G all of them H i and ii only F

Establish the identity 1 tan 0 cos 0 1 Rewrite the left side expression by expanding the product Do not simplify

f x 7 3 e 4 solve f x 8

12 5 points Prove identity sin x csc x cos x csc x

A wooden artifact from an ancient tomb contains 35 percent of the carbon 14 that is present in living trees How long ago to the nearest year was the artifact made The half life of carbon 14 is 5730 years years

The half life of Radium 226 is 1590 years If a sample contains 500 mg how many mg will remain after 1000 years Question Holni Dost to forum

Solve the given system of equations If the system has no solution say that it is inconsistent x 2y 3z 13 2x y z 1 3x 2y 2z 13 Select the correct choice below and fill in any answer boxes within your choice OA The solution is x y and z Type integers or simplified fractions OB There are infinitely many solutions Using ordered triplets they can be expressed as x y z x y z any real number Simplify your answers Type expressions using z as the variable as needed OC There are infinitely many solutions Using ordered triplets they can be expressed as ou

Solve the given system of equations If the system has no solution say that is it inconsistent y 2 4z 8 2y z 4 X 2x and z A The solution is x Type integers or simplified fractions O B There are infinitely many solutions Using ordered triplets they can be expressed as z any real number x y z x y Simplify your answers Type expressions using z as the variable as needed O C There are infinitely many solutions Using ordered triplets they can be expressed as

Solve the system of equations If the system has no solution say that it is inconsistent Graph the lines of the system 6x 48 x 4y 0 Click to enlarge graph 10 8 6 4 2 10 8 go 6 4 2 2 4 y

9 10 31x 24 A 5 2x 5X5x 3 B 10 x 3x 8 C 2x 3 5x 8 D 205x3x 4 10 101 60 162 108 A 612x 35m 6 B 62 315 6 C 2 5n 3 x 3 D 60 3X 6

7 3x 22x 35 A 3x 7 x 5 B 2x 7 x 7 C 3 x 7 x 5 D 3x 7 x 5 8 8 15x65x 70 A 5 3x 7Xx 2 B 5 3x 7 x 2 C x 7 3x 2 D al3x 7

11 11 12m 2m 30 A 2 3m 5X2n 3 B 12 n 5 n 3 C 2 3m 5 2n 3 D 3 2m 5Xx 1 12 12 9 33r 10 A 6r 3r 4 B 10 4 3 c 2 2 9r 10 D 3r 1X3r 10

5 2n 24m 54 A n 6Xx 10 B 4 n 3 2 C 2 n 3 9 D 2 n 3X 9 6 6 7m 29m 24 A 7m 8Xm 1 B 8 7 3 C Not factorable D 7m 8 m 3

3 r 4 60 A r 6Xr 10 B 10 4 C Not factorable D 6 r 8X 1 4 4 x 11x 28 A x 4 x 7 B x 4x 2 C x 4 x 7 D x 8 x 6

2022 KWIN oftware LL C Factoring Quadratics Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3 3 4r 60 A r 6 r 10 B r 10 4 C Not factorable D 6 r 8 1 All rights reserved 2 4 2 k 3k A k k 3 B k 4 k 10 C Not factorable D 2 k 9 k 7 4 x 11x 28 A x 4 x 7 B x 4 x 7 C x 4 x 7 D x 8 x 6

els that are the same 6x 2 2 6x 1 a Show that when x 3 Arun s answer is incorrect Explain why his method is incorrect f Discuss your answers to parts a to e with other learners in How will you convince them about your findings if your ans Simplify these expressions Make sure you factorise the numerator before you cancel with the denominator 6x 3 b 5x 10 3 5 Show that 6x 4 20x 25 simplifies to 7x 3 C 6x 9 3 d 8x 20 4

13 How does the graph of y y m x x compare with the graph of y y m x x Include examples in your explanation

12 Which equation matches each graph Describe each graph in terms of its slope and y intercept b y 3 x 2 d y 3 x 2 a y 3 2 x 1 c y 3 2 x 1 Graph A Graph B y 4 2 b Graph C 0 2 4 14 Match each graph with its equation Justify your choice a 2 2 0 0 2 0 y f x 6 ly 2 13 How does the graph of y y m x x compare with the graph of y y m x x Include examples in your explanation 0 2 Graph D 2 X 0 2 y 1 2 x 2 y 2 2 x 1 y2 2 x 1 y 1 2 x 2 X y g x y 1 x 2 1 y 2 x 1 y 1 3 x 2 2 c a y 4 b y h x 2 0 7 10 b y 3 c y 1 4 d y y 2 3 2 35 2 x 8 15 Use a graphing calculator or a computer with graphing software Graph each equation Sketch or print the graph Write instructions that another student could follow to get the same display x 5 x y 1 x 2 3 y 1 y 1 Volume of Liquid mL 10 20 2 y 2 x x 11 x 2 x 2 0 375 x 4 0 5 x 6 3 16 Chlo conducted a science experiment where she poured liquid into a graduated cylinder then measured the mass of the cylinder and liquid Here are Chlo s data Mass of Cylinder and Liquid g 38 9 51 5 a When these data are graphed what is the slope of the line and what does it represent b Choose variables to represent the volume of the liquid and the mass of the cylinder and liquid Write an equation that relates these variables c Use your equation to determine the mass of the cylinder and liquid when the volume of liquid is 30 mL d Chlo forgot to record the mass of the empty graduated cylinder Determine this mass Explain your strategy

Graph each line a The line passes through T 4 1 and ha slope 3 b The line passes through U 3 4 and ha slope 2 c The line passes through V 2 3 and has 1 slope 2 3 d The line has x intercept 5 and slope

ern city finds its residents moving to the suburbs Its population is declining 0 04t where t is time measured in years since according to the function P t 1 526 000e 2015 a What is the estimated population of the city in 2020 2 pts b In what year will the population decline to 1 000 000 3 pts 0 0001216t 10 The function P t Pe can be used for carbon 14 dating a Using the formula above what is the half life for carbon 14 Please show all work or how you determined the half life 2 pts

8 Solve each equation below 4 pts each a 0 05 1 15 5 c log 2x 4 2 b log x log x d 4ln 6x 5 15 2

9 a For each line write an equation in slope point form i P 2 4 4 4 2 0 2 4 4 20 P 4 2 y f x N X y y h x 2 ii iv y g x 2 6 0 2 y 2 0 y y k x N X P 1 2 b Write each equation in part a in slope intercept form then determine the P 3 3 X

12 Which equation matches each graph Describe each graph in terms of its slope and y intercept a y 3 2 x 1 b y 3 x 2 d y 3 x 2 c y 3 2 x 1 Graph A Graph B 4 5 6 2 2 0 2 0 Graph C N 2 20 NO 2 X Graph D 2 0 2 6 y x

11 Write an equation for the line that passes through each pair of points Write each equation in slope point form and in slope intercept form a B 2 5 and C 1 1 b Q 4 7 and R 5 2 c U 3 7 and V 2 8 d H 7 1 and J 5 5

5 Write an equation for the graph of a linear function that a has slope 5 and passes through P 4 2 b has slope 7 and passes through Q 6 8 c has slope and passes through R 7 5 d has slope 0 and passes through S 3 8

5 An einem Berufskolleg sind 60 der Sch ler weiblich und 40 m nnlich Von den Sch lerinnen rauchen 30 unter den m nnlichen Sch lern liegt die Quote bei 25 Wahrscheinlichkeit dass jemand der raucht weiblich ist a Wie gro ist die b Wie gro ist die Wahrscheinlichkeit dass jemand der nicht raucht weiblich ist C Wie viel Prozent aller Sch lerinnen und Sch ler rauchen 6 In einem Industrieunternehmen sind 95 der Produktion fehlerfrei In der Endkon trolle werden 90 der defekten Produkte aussortiert jedoch auch 5 der funktions f higen Teile a Formulieren Sie den Sachverhalt unter Benutzung von bedingten Wahrscheinlich keiten b Stellen Sie den Sachverhalt mit einer Vierfeldertafel dar c Wie hoch ist die Wahrscheinlichkeit dass ein verkauftes Produkt fehlerhaft d Wie hoch ist die Wahrscheinlichkeit dass ein aussortiertes Produkt fehlerfrei ist

1 Given the following examples determine if the function graphed is one to one If the function is one to one graph its inverse If the function is not one to one explain why n 2 points each Function 0 5 5 5 One to One no Graph of Inverse OR Explanation of why Inverse does not exist It is infinite FOR D

3 A line passes through D 3 5 and has slope 4 a Why is y 5 4 x 3 an equation of this line b Why is y 4x 7 an equation of this line

4 For each equation identify the slope of the line it represents and the coordinates of a point on the line a y 5 4 x 1 b y 7 3 x 8 c y 11 x 15 d y 5 x 2 4 e y 6 x 3 8 f y 21 x 16

quation 2 pts each log 1 243 x 7 Graph f x log4 x 2 5 pts a What is the y intercept s b What is the x intercept s c What is the domain of f x d What is the range of f x log 49 1 log 0 log 2 0 x

4 Graph the function f x 2x2 1 5 pts What is the y intercept s b What is the x intercept s c What is the domain of f x d What is the range of f x 10 10 10 5 Solve the following three equations without using logarithms 3 pts each 2x 2 82x 5 4 3 27 e4x 1 e

f x x 1 Domain of f Range of f Pomain of fl ange of f g x 2x5 Domain of g Range of g Domain of g Range of g 3 Alex is considering some options for making a deposit a What amount deposited today at 3 1 interest compounded monthly will grow to 12 000 in 5 years 3 pts b If Alex only has 10 000 to deposit now what annual interest rate compounded monthly is necessary for tho

What point represents the vertex height above ground 10 8 0 0 2 2 14 2 3 4 16 0 distance from launc

7 3x 22x 35 A 3x 7 x 5 B 2x 7 x 7 C 3 x 7 x 5 D 3x 7 x 5 9 10x 31x 24 A 5 2x 5 5x 3 B 10 x 3 x 8 C 2x 3 5x 8 D 2 5x 3 x 4 11 12n 2n 30 A 2 3n 5 2n 3 B 12 n 5 n 3 C 2 3n 5 2n 3 D 3 2n 5 n 1 8 10 12 8 15x 65x 70 A 5 3x 7 x 2 B 5 3x 7 x 2 C x 7 3x 2 D x 3x 7 10 60n 162n 108 A 6 2n 3 5n 6 B 6 2n 3 5n 6 C 2 5n 3 n 3 D 60 n 3 n 6 12 9 33r 10 A 6r 3r 4 B r 10 4r 3 C 2 r 2 9r 10 D 3r 1 3r 10

1 oftwa Factoring Quadratic Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3 3 r 4r 60 A r 6 r 10 B r 10 4 C Not factorable

2022 Kuta Software LLC All rights reserved Factoring Quadratics Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3 3 r 4r 60 A r 6 r 10 B r 10 4 C Not factorable D 6 r 8 r 1 5 2n 24n 54 A n 6 n 10 B 4 n 3 n 2 C 2 n 3 n 9 D 2 n 3 n 9 2 4 6 2 k 3k A k k 3 B k 4 k 10 C Not factorable D 2 k 9 k 7 4 x 11x 28 A x 4 x 7 B x 4 x 7 C x 4 x 7 D x 8 x 6 6 7m 29m 24 A 7m 8 m 1 B m 8 7m 3 C Not factorable D 7m 8 m 3

a 3 3 3 3 11 5 7 1 27 13 15 x 8 15 17 19 1 n 11 21 12 b 2 5 x 10 7 x 15 3 k 5 V 5 2 3 2 3 2 x 2 14 9 4 8 10 12 6 2 21 1 14 16 m 12 5 18 x 2 2 3 11 v 4 n 5 6 3 m 14 4 b 8 8 1 P 6 n 3 3 2 2 1 7