Algebra Questions

For each matrix choose one option Either indicate that the matrix is in reduced row echelon RRE form or indicate the ONE condition that the matrix DOES NOT satisfy Matrix 1 O The matrix is in RRE form O 5 0 4 01 5 0000 1 0 There is a leading entry of a row that is NOT one Leading ones DO NOT appear further to the right from row to row O There is a row of zeros that is NOT at the bottom of the matrix O NOT all other entries in a column with a leading one are zero

To enter a matrix type each row as a comma separated list pressing Enter when you need to create a new row You don t need to enter parentheses or brackets Enter the matrix below 8 6 4 6 02

Part 1 of 2 Find the zeros of the function and then describe the behavior of the graph at each zero f x x 10x 25x The zero s is are Use a comma to separate answers as needed

Use the leading coefficient test to determine whether y o or y o as x for the function y 2x x 16 As x y

Multiply and simplify your answer State any restrictions on the domain 62 36 4 6 12 b b X 6 2 LIST FACTORS FROM LEAST TO GREATEST LIST RESTRICTIONS FROM LEAST TO GREATEST

Multiply and simplify your answer State any restrictions on the domain 3x 27 x 13x 36 4x 16 X X LIST RESTRICTIONS FROM LEAST TO GREATEST

Find the vertical and horizontal asymptotes of f x 6 Remember to write the asymptotes as equations and do not type spaces in your answers Vertical asymptotes Horizontal asymptote POSSIBLE POINTS 1 and

S varies inversely as G If S is 3 when G is 0 4 find S when G is 2 a Write the variation Find S when G is 2 a How are these two variables related OA S KG B S kG C O D k S G S 2

POSSIBLE POINTS 1 The length of a pipe in a panpipe in feet is inversely proportion to its pitch p in hertz If the pitch is 25 hertz when the length of the pipe is 18 feet find the length of the pipe when the pitch is 90 hertz feet

Simplify and state any restrictions on the domain 3 15 54 az

P varies inversely with q If P 10 when q 3 find the value of P when q 6 When q 6 P

Pairs of markings a set distance apart are made on highways so that police can detect drivers exceeding the speed limit Over a fixed distance the speed R varies inversely with the time T In one particular pair of markings R is 44 mph when T is 5 seconds Find the speed of a car that travels the given distance in 4 seconds R mph Round to the nearest whole number

Graph the function f x Identify the domain the range the horizontal asymptote and the vertical asymptote Domain i Range i Horizontal Asymptote Vertical Asymptote i POSSIBLE POINTS

5 1 The current I in an electrical conductor varies inversely as the resistance R of the conductor The current is ohms ampere when the resistance is 784 ohms What is the current when the resistance is 9604 2 The current is ampere Simplify your answer Type an integer or a fraction

Multiply the radical expression 2 4 11

Simplify the radical Assume all variables are greater than or equ 250x13

Multiply and simplify the radicals Assume all variables are greater than or equal to 5 8a b74a b 32 7 3 2 2 2 2

Click here to watch the video Simplify the radical 19 19 49

Multiply the radical expression 10p 3p

ck here to watch the video ltiply and simplify the radicals Assume all variables are greater than or equal to zero 18a 3 15a

Simplify the radical expression Assume y 0 12 32y 32112

Click here to watch the video Simplify the radicals Assume all variables are greater than zero 192n 12n 192n7

Simplify the radical Assume all variables are greater than or equal to zero 125x 64 3 9 3 125x 64

Simplify the radicals Assume all variables are greater than 3 16x 3 2x 1

Two neighbors Wilma and Betty each have a swimming pool Both Wilma s and Betty s pools hold 8000 gallons of water If Wilma s garden hose fills at a rate of 650 gallons per hour while Betty s garden hose fills at a rate of 500 gallons per hour how much longer does it take Betty to fill her pool than Wilma It takes Betty hours minutes longer to fill her pool than Wilma

2 Kuta Software EXTRA CREDIT SUM 3 Simplify each difference 1 8k 1 k 4k 8k 2 A 14k 10k 6 B 16k 10k 6 C 16k 5k 1 D 16k 5k 6 Simplify each sum 2 5 7x 8x 7 A 15x 2 C 13x 3 Simplify Your answer should contain only positive exponents 2x y 4 4 y x10 22 B B 13x 2 D 15x 2 D 4x11 All rights reserved 16x14

EXTRA CREDIT SUM 3 Divide 4 x 6x 15x 28 x 4 3 x 4 A x 2x 8 B x 2x 7 C x 2x 6 D x 2x 8 5 x 4 5 x 4 Find each product 5 3a 7a 1 a a 1 A 3a 10a 9a 6a 1 B 3a 7a 1 C 3a 4a 5a 8a 1 D 8 4 26 12g 24g 22

Suppose you are given a square with an inscribed circle as shown below If the area of the square is 100 m what is the area of the circle Use 3 14159 for T a

A family has a monthly income of 3019 Their monthly expenditures are as shown in the graph below Rent 22 Food 17 Transportation 13 Other Expenses 17 Savings 31 How much money does the family save in a month S

The number of tropical fish that an aquarium can hold depends on the volume of the fish tank The interior dimensions of the fish tank below are 60 cm 50 cm and 50 cm Each fish requires 10 000 cubic centimeters of water How many tropical fish will this fish tank hold

If the mean number of people who attended four basketball games is 4860 what was the total attendance at the four games

10 Circadian rhythms are biological processes that oscillate with a period of approximately 24 h That is a circadian rhythm is an internal daily biological clock Blood pressure appears to follow such a rhythm For a certain individual the average resting blood pressure varies from a maximum of 100 mmHg at 2 00 p m to a minimum of 80 mmHg at 2 00 a m Find a sine function of that models the blood pressure at time t measured in hours from midnight Graphthe function over two periods

Consider the parallelepiped Pin R determined by the vectors u 2 1 1 v 1 3 1 2 and w 1 6 2 8 Use the parallelogram determined by u and v as the base of P a 2 marks Find the area A of the base of P A If needed enter as sqrt z b 1 mark Find the volume V of P c 2 marks Find one vector n orthogonal to the base of P so that the volume of the parallelepiped determined by u v n equals the volume P

The comprehensive graph of a polynomial function y f x is shown How many real zeros does the function f have The function f has real zero s 8 JA Q S

End Behavior As x co f x As x f x Y intercept Zeros and multiplicity Find one other ordered pair on the graph Sketch a graph of f x Choose an appropriate scale XA

5 4 J 2 1 Y intercept End Behavior 24 22 20 18 16 14 12 10 0 10 Degree 6 4 2 0 C 2 Zeros and multiplicity 6 Leading coefficient As x g x As x g x 2 g x Equation of g x in intercept form Challenge Equation of g x in standard form

1 1 4 X 3 5 10 2 3

Use synthetic division to find the function values f x x 16 find f 1 f 1 and f 1 10 f 1 Type an exact answer using radicals as needed f 1 Type an exact answer using radicals as needed f 1 10 Type an exact answer using radicals as needer

Rewrite cos 2 tan 1 G 6 1 as an algebraic expression in u

Question 10 of 14 Step 1 of 1 Find the linear function with the following properties Answer f x 12 17 Correct f 6 6 f 4 12

7 Prove the following identities 4 marks a Sinxtanx secx cosx b Cos x sinx 1 cosx 1

Use the COMPLETING THE SQUARE method to solve the equation After dividing both sides by 2 first what would you then add to both sides of the equation to complete the square 10 20 25 100 2x 20x 9

A lithotripter machine uses an elliptical reflector to break up kidney stones nonsurgically A spark plug in the reflector generates energy waves at one focus of an ellipse The reflector directs these toward the kidney stone positioned at the other focus of the ellipse with enough energy to break up the stone as shown in the figure The lengths of the major and minor axes of the ellipse are 25 millimeters and 160 millimeters respectively How far is the spark from the kidney stone Round your answer to one decimal place mm Spark plug Elliptical reflector Kidney stone

Find the values of the variable that would make the statement true using the square root method x 1 18 0 O 17 1 3 2 O 17 2 2 or 4 2

A picture has the dimension of 8 units by 4 units A frame of equal width surrounds the picture as shown in the diagram If the area of just the frame is 108 units what is the width of the frame 1 unit O2 units 2 5 units 3 units 8 units 4 units X

Solve the following by FACTORING and using the ZERO PRODUCT PROPERTY 3x 36x 60 0 In the blank list only the smaller of the 2 solutions just the number only

Which of the below is the completely factored form of the polynomial shown 2x 20x 48 2 x 6 x 4 x 4 x 16 x 4 x 24 2 x 2 x 12

Which of the below is the completely factored form of the polynomial show 4a 96 2a 3b 2a 3b 2a 3b 2a 36 4a 9b a b

The function defined by f x x4 5x3 48x 252x has the graph as shown Use the graph to factor the polynomial What is the factored form of the polynomial Simplify your answer Type your answer in factored form 10 1400 1400 10

What is the GCF of the expression below that could be use to rewrite the polynomial in factored form 24p 30p 3p op 24p 6p3