Algebra Questions

Slape 1 4 6 0 FIND THE SLOPE OF THE LINEAR FUNCTION IN EACH BOX YOU TRY SLOPE SLOPE 2 3 3 y y 8x 6 SLOPE SLOPE 20 14 8 1 y 268 196 124 40 20 96 12 60

Find the general solution of the system whose augmented matrix is given below 1 42 3 12 1 12 Select the correct choice below and if necessary fill in the answer box es to complete your choice O A O C X X is free X3 is free X 11 X 11 OB X X is free X3 OD The system has no solution

Choose h and k such that the system has a no solution b a unique solution and c many solutions X hx 5 2x 4x k OH The system has a unique solution only when h c Select the correct answer below and fill in the answer box es to complete your choice Type an integer or simplified fraction OA The system has many solutions only when h OB The system has many solutions only when k OC The system has many solutions only when h OD The system has many solutions only when h O E The system has many solutions only when h OF The system has many solutions only when h OG The system has many solutions only when k H The system has many solutions only when h and k and k COOP and h is any real number and k is any real number and k and k and k is any real number and h is any real number and k

Choose h and k such that the system has a no solution b a unique solution and c many solutions X hx 5 2x 4x k F The system has no solutions only when h 2 and k 10 OG The system has no solutions only when h OH The system has no solutions only when k and k is any real number and h is any real number b Select the correct answer below and fill in the answer box es to complete your choice Type an integer or simplified fraction OA The system has a unique solution only when h OB The system has a unique solution only when k OC The system has a unique solution only when k OD The system has a unique solution only when h O E The system has a unique solution only when h OF The system has a unique solution only when h OG The system has a unique solution only when h and k is any real number and h is any real number and h is any real number and k and k and k is any real number and k

Determine if b is a linear combination of a a2 and a3 5 HH a 0 12 D 3 15 Choose the correct answer below O A Vector b is a linear combination of a a2 and a3 The pivots in the corresponding echelon matrix are in the first entry in the first column the second entry second column and the third entry in the third column B Vector b is a linear combination of a a2 and a3 The pivots in the corresponding echelon matrix are in the first entry in the first column and the second em the second column OC Vector b is not a linear combination of a a2 and a OD Vector b is a linear combination of a a2 and a3 The pivots in the corresponding echelon matrix are in the first entry in the first column the second entry second column and the third entry in the fourth column

et u 11 1 Let b and v 11 Show that h is in Span u v for all h and y How can it be shown that a vector b is in Span u v A Determine if the system containing u v and b is consistent If the system is inconsistent then b is in Span u v OB Determine if the system containing u v and b is consistent If the system is consistent b might be in Span u v C Determine if the system containing u v and b is consistent If the system is consistent then b is in Span u v OD Determine if the system containing u v and b is consistent If the system is consistent then b is not in Span u v h Find the augmented matrix ix u v b y

Let u 11 1 Let b and v h 11 1 h y Show that is in Span u v for all h and y How can it be shown that a vector b is in Span u v O A Determine if the system containing u v and b is consistent If the system is inconsistent then b is in Span u v OB Determine if the system containing u v and b is consistent If the system is consistent b might be in Span u v C Determine if the system containing u v and b is consistent If the system is consistent then b is in Span u v Determine if the system containing u v and b is consistent If the system is consistent then b is not in Span u v OD Find the augmented matrix x u v b

Write a vector equation that is equivalent to the given system of equations x 3x3 0 5x 8X2 X3 0 X 3x 8x3 0 Choose the correct answer below O A 1 O C B 8 X3 O O O 04 0 1 O B 0 19 X X 0 1 3 8 X3 H 3 B BH 3 0

Choose the correct answer below OA There is a pivot position in each row of the coefficient matrix The augmented matrix will have nine columns and will not have a row of the form 000000001 so the system is consistent OB There is at least one row of the coefficient matrix that does not have a pivot position This means the augmented matrix which will have nine columns have a row of the form 000000001 so the system is inconsistent OC There is at least one row of the coefficient matrix that does not have a pivot position This means the augmented matrix which will have nine columns 00000001 so the system could be inconsistent have a row of the form i OD There is a pivot position in each row of the coefficient matrix The augmented matrix will have seven columns and will not have a row of the form 0000001 so the system is consistent

Find the general solution of the system whose augmented matrix is given below 1 7 0 1 0 4 0 10 0 8 1 0 00 1 8 3 0 00 0 0 0 Select the correct choice below and if necessary fill in the answer boxes to complete your answer O C X x 0 X3 is free OB X X is free X4 is free X5 is free x X3 is free X5 is free OD The system is inconsistent

system 2 5 H 6 O 11 that is equivalent to the given vector equation 5 Choose the correct answer below OA 2x 5x 5 4x1 5 7x 6x 9 OC 2x 5x 5 5 4x1 7x 6x 9 9 O B O D 2x 5x 5 4x x 5 7x 6x 9 2x 4x1 5X2 9 5 7x 6x 5

The augmented matrix of a linear system has been reduced by row operations to the form shown Continue the appropriate row operations and describe the solution set of the original system GILER Select the correct choice below and if necessary fill in the answer boxes to complete your choice A The solution set has exactly one element 0 Type integers or simplified fractions OB The solution set has infintely many elements C The solution set is empty 18 00 00 01

Determine whether the statement below is true or false Justify the answer Every elementary row operation is reversible Choose the correct answer below OA The statement is true Interchanging can be reversed by scaling and scaling can be reversed by replaceme OB The statement is true Replacement interchanging and scaling are all reversible OC The statement is false The only reversible row operation is interchanging two rows OD The statement is false The only reversible row operations are scaling a row and interchanging two rows

Find an equation involving g h and k that makes this augmented matrix correspond to a consistent system 1 3 79 0 5 12 h 3 4 9 k What equation must be satisfied for the augmented matrix to correspond to a consistent system Select the correct choice below and fill in the answer box to comp your choice Simplify your answer OA 3g h k OB 3g h k O c 3g h k OD 3g h k

the statement below is true or false Justify the answer Two matrices are row equivalent if they have the same number of rows Choose the correct answer below ACCEN OA The statement is false Two matrices are row equivalent if the equation corresponding to the first row of the first matrix is equivalent to the equation corresponding to the first row of the second matrix the equation corresponding to the second row of the first matrix is equivalent to the equation correspon to the second row of the second matrix and so forth OB The statement is false Two matrices are row equivalent there exists a sequence of elementary row operations that transforms one matrix into the other C The statement is true It is the definition of row equivalence OD The statement is true Two matrices are row equivalent if there exists can only occur if the matrices have the same number of rows sequence of elementary row operations that transforms one matrix into the other T

The augmented matrix of a linear system has been reduced by row operations to the form shown Continue the appropriate row operations and describe the solution set of the original system Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The solution set is empty B The solution has infinitely many elements C The solution set contains one solution 0 Type integers or simplified fractions 1 1 0 0 1 3 0 0 0 0 1 0

ide 4x 4x 2 3 X 2 4x 4x 3 x 2 Simplify your ansv

Perform the division 4m 10m 6m 3 2m 4 4m 10m 6m 3 2m 4 Simplify your answer Use integers or fractions fa

A landscaper is planting a tree that is now 61 cm tall The tree will grow 3 cm per month for x months The tree will grow to be at most y cm tall Write an inequality showing this relationship

3 L y 3 3 3

In a survey of 251 professional athletes it was found that 118 of them owned a convertible 116 of them owned a giant screen TV and 108 owned a sporting goods store 15 owned a convertible and a store 43 owned a TV and a store and 59 owned a covertible and a TV 6 owned all three items 1 How many athletes did not own any of the three items 2 How many owned a covertible and a TV but not a store 3 How many athletes owned a convertible or a TV 4 How marty athletes owned exactly one type of item in the survey 5 How many athletes owned at least one type of item in the survey 6 How many owned a TV or a store but not a convertible

FIND THE SLOPE OF THE LINEAR FUNCTION IN EACH BUL SLOPE 987 59 6 327 9 8 7 6 5 4 3 2 1 123456789 2 WN V 6799 in 6 7 8 SLOPE x

58 69 3 3 2 1 y 414 1 23 g x x 3

8 y 2x 5 654 3 2 1

19 X 5 y 3x 3 6 54 3 2 LLC A 11 I 6 y x 3 6543

it 8 y 2x 5 I x 9 19 1 9 7 y x 2

A Igebra 1 2 9 6 y x 3

3 y x 3 54 3 2 1 I 4 y

4 y 2x 4

HW 1 7 due Tuesday 1 8 N 02019 Kuta Software L L C All rights reserve Graph the equations shown below clearly labe 1 y 3x 4 2 y 5 5 1 3 2 1 N 6 x I 6 5

Name Oyinkansola Alaran rights reserved w clearly labeling at least two points 2 y 3x 1 6 5 4 3 2 1 2 Aft

13 14 15 13 23 42 A B 9 D 6 3 2 20 5 16 3 3 2 16 4 10 3 71 Write each expression in radical form 14 68 w 6 Write each expression in exponential form 15 A 7m C 24 B 68 D 36 Simplify B 7 D 2m

A C 2x Write each expression in radical form 5 106 3 A 26 C 106 Simplify B 7x D 10x 6 6 81x A 729x C x B 10b D 106 B 7776x D 729x LLC All

1 3 4 Algebra Prep C2024 Kuta Software LLC All rights reserve PRACTICE TEST Simplify 1 64u y6 A 2u 2u v C 2v 2u v 3 x 7 2 2 A 4x 1 9 B 2uv 3u D 2u 3u v B 216x D 1 3125x Write each expression in exponential form 4 10x A 2 C 2x 6 2 B 7x D 10x 2 2 343x A x C 240

Which equation has a graph that is a parabola with a vertex at 5 3 y x 3 5 y x 5 3 Oy x 5 3 O y x 3 5

Which phrase best describes the translation from the graph y 6x2 to the graph of y 6 x 1 6 unit left 1 unit right 1 unit left 6 unit right

Which phrase best describes the translation from the graph y 2 x 15 2 3 to the graph of y 2 x 11 2 3 4 units to the right 8 units to the left 4 units to the left 8 units to the right

Which equation is y 3x 12x 2 rewritten in vertex for O y 3 x 2 14 y 3 x 2 10 y 3 x 2 10 y 3 x 2 2

Write the first 6 terms of each pattern Start at 10 each time a Multiply by 2 then subtract 5 each time b Multiply by 5 then subtract 2 each time c Subtract 5 then multiply by 2 each time d Subtract 2 then multiply by 5 each time

5 How many different re Irsive pattern can you find with 4 and 7 as the first 2 term Write the first 5 terms of each pattern then write the pattern rule

Solve each system by elimination 1 x 5y 5z 2 4x 5y 4z 19 x 5y z 20 3 x 5y z 17 5x 5y 5z 5 2x 5y 3z 10 5 4r4s 4t 4 4r s 2t 5 3r3s 4t 16 7 x y 2z 6 3x 2y 25 4x y z 12 2 4x 5y z 18 2x 5y 2z 12 2x 5y 2z 4 4 4x 4y z 24 2x 4y z 0 5x 4y 5z 12 6 x 6y 4z 12 x y 4z 12 2x 2y 5z 15 8 5a 5b 5c 20 4a 3b 3c 6 4a 3b 3c 9

8 9 1 7 4p A p C p Solve each equation Remember to check for extraneous solutions ANSWER SHOULD BE AN INTEGEROR A FRACTION 8 NO POINTS IF YOU ANSWER AS A DECIMAL 1 3n Simplify 9 63r A 93 C 3 210 Z C 1 6n 2 B 4p D 6p 3 n 4 2 n 30r B D B 3r 210 D 1890 10 12 10 15p 4 10 8 A 54p p 36p 2p B 20 6p 8 15p C 70 9 D 14p 3p 9 2p 12 4 3 5 4 4 3 5 A 2 8 3 2 5 43 B 8 4 2 4 3 20 D

Simplify 11 64u v 3 3 2 2 A 4x 4 A 2u 2u v C 2v 2u v 5 A x 1 C 2x 6 Write each expression in exponential form 4 10x 5 106 A 26 C 106 B 2uv 3u D 2u 3u v Simplify B 216x 1 D 3125x Write each expression in radical form 3 6 6 81x A 729x C x B 7x 7 D 10x 6 B 10b D 106 2 B 7776x D 729x 4 2 343x A x4 C 2401x 2 B 256x 2 D 7x

6 13 2 3 2 A B D 6 3 2 2 20 5 16 3 77 3 2 10 4 4 10 3 71 Write each expression in radical form 3 14 6b A 6b C 6b Write each expression in exponential form 15 7n A 7n C 2n Simplify B 6b D b 16 64m A 100m C 1024m 5 B 7n 5 D 2n 4 B 8m D 10000m4

Using the graph of f shown find three intervals on which f is one to one making each interval as arge as possible Ay 6 3 3 6 The intervals on which f is one to one are Simplify your answers Use a comma to separate answers as needed Type yo answers in interval notation

9 Which point is on the line 6y 3x 0 A 2 1 B 2 1 C 1 2 D 1 2 Bizi sedy Hind

4n 8n 8n 4n

Exercises 49 64 Complete the following a Find f x for the indicated values of x if possible b Find the domain of f Use words or inequalities to describe the domain 49 f x x for x 2 5 50 f x 2x 1 for x 8 1 51 f x x 3x for x 3 2 52 f x 5 x 2x for x 1 53 f x 12 3x for x 1 4

Which expression represents the area of the rectangle shown a 4x 5 units b 4x 5 units c 3x 7x 4 units d 3x 9x 4 units 3x 4 x 1

What is the most completely factored form of the expression 45x 40x a 40 5x x b 5 9x 8x c 5x 9x 8 d 5x 9 8x