Algebra Questions

Consider the polynomial below a List all potential rational roots using the Rational Root Theorem Separate your numbers by commas list of possible rational roots P x 7x 29x 31x 5 b Find all the rational roots Separate your numbers by commas list of actual rational roots c Express P x in factored form with the leading coefficient factored to the front P x

Check 9x 12x 4 4 X M Check

Suppose P x 2x 2x x 2 is divided by x 2 a Identify the quotient Quotient b Identify the remainder Remainder c Express P x in the form quotient divisor remainder Pfr

Q3 Sketch each of the following sets of points in the complex plane separately i e four different sketches for a d After sketching each set determine if each of the sets are i open ii connected iii bounded iv domain 15pts 4 If All correct a Re 3 i z 1 2 b 2 2 14 4 c Im 2 Re z 1 4 d 2 z 4 3i 2 4

Check DUA x 12 13

What is the slope of the line y 2 2 x 3 Choose 1 answer B 1 1 2 O 1 Google Classroom

Consider the systems of equations below from previous exercises for each system write it as Ax b and then try to perform LU factorization on A note this means the b portion of the augemented matrix you Should not include 3x2 6x3 6X4 4X5 5 3X 7x2 8x3 5x4 8x5 9 3x1 9x2 12X3 9x4 6Xs 15 b 2x y 2 180 X 3y 27 300 2x 27 240

Check 81x 36x 4 Check

36x 25 X

8 A coastal geologist estimates that a certain country s beaches are eroding at a rate of 1 5 feet per year According to the geologist s estimate how long will it take in years for the country s beaches to produ

Write the parametric equations in the given Cartesian form x 2t t y 7 3t

7 Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour Based on this information what is a possible amount of time in hours that it could take Wyatt to husk 72 dozen ears of corn

X Check 3x 2x 21 X 2 Check 64

124 x X

X Check 20x 25x X Check x 14x 33 0

2 3x 10 X

Find the basis for the kernel and image subspaces WAL 24 6 A2 12 01 C 1 5 7 3 7 5 3 35 1

Suppose that you decide to buy a car for 59 000 including taxes and license fees You saved 11 000 for a payment The dealer is offering you a choice between two incentives Incentive A is 7000 off the price of the car followed by a three year loan at 6 31 Incentive B does not have a cash rebate but provides free financing no interest over three years What is the difference in monthly payments between the two offers Which incentive is the better deal Use PH 9 PMT The difference in monthly payments between the two offers is S Round to the nearest rent as needed

on the right are four functions each using one of the function representations we ve learned about in this lesson se functions f x g x h x and p t to answer the questions on the left Evaluate f 5 f 5 H Determine z when f x 1 g 57 Determine z when g x 37 h 8 Evaluate g 57 2 Determine when h x 27 p 18 Evaluate h 8 Evaluate p 18 Determine t when p t 13 15 t p t 4 3 2 S f x 3 du 1 2 3 y 2 on 4 X g x 2 15 2 7 10 37 19 23 33 18 37 60 42 57 57 58 76 52 80 1 13 15 18 19 25 28 45 60 85 89 100 94 18 13 75 93 90 48 h x 24x 3 112 17

3 Simplify each expression None of the answers have an exponent 1 5 Ln The imaginary unit i 1 bi is a pure imaginary number a bi is a complex number with real part a and b the imaginary part a bi anda bi are complex conjugates a bi a bi will always result in a real number Check alse Choose Choose Choose Choose Choose

Short Answer Please answer all questions and show your work on all problems Write your answers on the answer sheet at the last page of this packet per 1 A remote control car claims that it can travel at a rate of 132 feet per minute What is this rate in miles hour

Winter coat 13 Which item from the table below has the lowest cost per days worn Y 3 1 a Work shoes b Winter coat c Polo shirt d Gown Clothing item Work shoes Polo shirt 636 Gown Original cost Days worn 60 250 155 25 178 620 26 L 2

1 3 5 7 9 a c d solve for b 0 0 atb dic an x an xx nn in terms of the given variable b dtc a y Box a b x y a fux n d rt d rt 7 1 solve for a solve for r d flexty solve for a atby dxty a Fdxty b b 2 p w b n J P w b C C n p w b solve for n 2 4 6 8 10 xyz n solve for y XZXZ A y mx b y b mx ax b c y kx X by L ax b b y x ab y Y Kx X x Gab q a solve for m y b X 54 solve for k solve for y Im y c ax 5x CK solve for b

22 If a 3 pound pizza is sliced in half and each half is sliced into thirds what is the weight in ounces of each of the slices 1 pound 16 ounces e 4 f 6 g 8 h 16

Use the table to determine the location of the zeros 2 12375 SARSSONHN 4 Y 7 9 8 5 7 16 27 The smallest root is at x The other root is at x

b vertex write as an ordered pair x y 1 3 x c axis of symmetry x d maximum or minimum Maximum e range o 3 Check at y 3 Partially correct Marks for this submission 2 00 3 00 Accounting for previous tries this gives 1 Given f x 2x2 Identify the following a y intercept write as an ordered pair x y 0 0 x b vertex write as an ordered pair x y 0 0 c axis of symmetry x 0 x

Use the table to determine the location of the zeros of the quadratic function 7 8 6 1 5 4 The smallest root is between The other root is between 4 4 3 1 and and 2 8 22 0 48

2 x x 6 0 a What is the axis of symmetry What is the vertex b What is the solution based on the graph If the exact roots cannot be found state the consecutive integers between which the roo are located Explain your answer c Upload a picture of your hand drawn graph Label vertex and one point on either side of the vertex

1 What are the solutions for the equation Give a reason for your answer x 2x 3 0 y 0 X

3 A model for a company s revenue from selling a software package is R 2 5p 500p where p is the price in dollars of the software a What price will maximize the revenue Give a reason for your answer b What is the maximum revenue Give a reason for your answer

ws online is included in the membership fee but there is an additional fee of 1 50 to rent each movie that embership fee for an online television and movie service is 9 80 The cost of viewing television For one month Jill s membership and movie rental fees were 12 80 How many movies did Jill rent online that month a 1 b 2 c 3 d 4 19 If a 3 pound pizza is sliced in half and each half is sliced into thirds what is the weight in ounces of each of the slices 1 pound 16 ounces a 4 b 6 c 8 d 16 20 Nate walks 25 meters in 13 7 seconds If he walks at this same rate which of the following is closest to the distance he will walk in 4 minutes e 150 meters f 450 meters g 700 meters h 1 4000 meters

1 Use a calculator to graph and then identify the following for the parabola y x 2x 1 a vertex b axis of symmetery c maximum or minimum value d domain e range

21 The monthly membership fee for an online television and movie service is 9 80 The cost of viewing television shows online is included in the membership fee but there is an additional fee of 1 50 to rent each movie online For one month Jill s membership and movie rental fees were 12 80 How many movies did Jill rent online that month e 1 f 2 g 3 h 4

2 Show the steps you would use to graph the function without using a calculator y a Find the vertex b Find the y intercept c Find the point on the other side of the axis of symmetry from the y intercept HN 1 2x x 2x 8

Simplify cot t cs t sin t to a single trig function

lowest price per ounce The table at left gives the number of ounces and prices of different bottles of body wash Which has the a Bottle A b Bottle B c Bottle C d Pack D Bottle A Bottle B Bottle C Pack D with 6 bottles Ounces 12 21 32 24 each Price 0 99 2 97 3 97 34 50 ber

18 The monthly membership fee for an online television and movie service is 9 80 The cost of viewing television shows online is included in the membership fee but there is an additional fee of 1 50 to rent each movie online For one month Jill s membership and movie rental fees were 12 80 How many movies did Jill rent online that month a 1 b 2 3

interval 3 3 X d Interval 2 2 2 12 X f x 3 0 2 3 1 4 0 3 1 0 2 3 5 20 0 LO 5 12 2 4 5 6 12 10

17 Nate walks 25 meters in 13 7 seconds If he walks at this same rate which of the following is closest to the distance he will walk in 4 minutes a 150 meters b 450 meters c 700 meters d 1 4000 meters

19 If a 3 pound pizza is sliced in half and each half is sliced into thirds what is the weight in ounces of each of the slices 1 pound 16 ounces a 4 b 6 c 8 d 16

Solving Quadratic Equations By Completing the Squarebate Solve each equation by completing the square 98 28 1 p 14 p 38 0 P 1yp 51 51 3 a 14a 51 0 a2 149 8 8 5 x 6x 8 0 x 6x 7 x 14x 15 x 14x 9 4r 91 7 11 k 4k 1 5 59 59 2 v 6v 59 0 va bv 4 x 12x 11 0 x2 1DX 6 n 2n 3 0 n 20 21 22 8 k 12k 23 0 k 12k 10 x 10x 26 8 12 b 2b 20

peas Faba beans Field peas Lupins 240 70 225 150 a 3 00 b 5 50 c 6 67 d 7 34 of plants pl Area m 2 5 3 3 50 He spent the rest of the money on bowling a number of games If it took Zhang Lei 45 minutes to bowl each 16 Zhang Lei spent 20 00 during his last outing at the bowling alley This included a one time shoe rental fee of game and he spent 2 hours and 15 minutes bowling how much did it cost per game

the greatest planting density in plans per square meter PL 15 The table at left gives the numbers and planting area of several plants in a garden Which plant variety has m2 a Chickpeas b Faba beans c Field peas d Lupins Plant variety Chickpeas Faba beans Field peas Lupins Number of plants pl Area m 240 6 70 225 1 50 2 5 3

O Nate walks 25 meters in 13 7 seconds If he walks at this same rate which of the following is closest to the istance he will walk in 4 minutes e 150 meters f 450 meters g 700 meters h 1 4000 meters

12 A line in the xy plane has a slope of and passes through the origin Which of the following points lies on the line a 0 b 2 3 c 6 4 d 9 4

11 In the xy plane the line determined by the points 2 k and k 32 passes through the origin Which of th following could be the value of k a 0 b 4 c 8 d 16

10 Graphene which is used in the manufacture of integrated circuits is so thin that a sheet weighing one ounce can cover up to 7 football fields If a football field has an area of approximately 1 acre about how many acres could 48 ounces of graphene cover a 250 b 350 c 450 d 1 350 009 5

Bonus Lett 2 that H X exph show Fast enten 1 X 4 O is a constant

For all positive integer numbers n the statement Sn 2 6 12 n n 1 n 3 n n 1 n 2

5 Elena is conducting a study about the effects of toxins in the water on the hormones of fish Elena surveys 350 male fish in a river and finds that 150 of the male fish have egg cells growing inside them According to Elena s survey what is the ratio of male fish with egg cells to male fish without egg cells in the river