Algebra Questions

a 52 b 155 c 263 d 17 e 597 f 833

Verify the identity 1 sin t 5 cos t 36 sin t cos t 36 cos t 1 sin t 5 cos t 36 sin t cos t 6 cos t 36 cos t cos t

4 Write in exponential form a 7 b 10 10 4 915 c 228 d 157 48 e 115 f V101

Verify the identity cos x sin x 2 cos x 1

Verify the identity 1 sin y 1 tan y Use a Pythagorean Identity in the denominator and then use a Reciprocal Identit 1 1 1 sin y 11 Use a Pythagorean Identity

Verify the identity sin x cos x sin x cos x sin x cos x sin x cos x 1

Verify the identity tan 0 cot 0 sec 0 csc 0 Use a Reciprocal Identity to rewrite the expression in terms of sine and cosine as a single rational expression tan 0 cot 0 sin 0 cos 8 cos 0 sin 0 sin 0 Use a Pythagorean Identity to rewrite the expression in terms of a single function and then simplify cos 8 sin 0

Simplify the trigonometric expression 2 5 cos y 5 2 sec y

5 A certain college claims to have an 80 graduation rate If 2000 people graduate one year how many students started school with the class

7 In a baseball game Chris gets a hit 2 times takes a walk once strikes out once and grounds out once In what percentage of his at bats did he get a hit

For the polynomial function f x 5 x 1 x 3 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the x axis at each x intercept c Determine the maximum number of turning points on the graph d Determine the end behavior that is find the power function that the graph of f resembles for large values of x Type integers or iacuons OD There are no real zeros b Select the correct choice below and if necessary fill in the answer box es to complete your choice A The graph touches the x axis at Type an integer or a simplified fraction Use a comma to separate answers as needed B The graph crosses the x axis at 3 Type an integer or a simplified fraction Use a comma to separate answers as needed OC The graph touches the x axis at and crosses at Type integers or simplified fractions Use a comma to separate answers as needed D The graph neither crosses nor touches the x axis c The maximum number of turning points on the graph is 6 Type a whole number d The power function that the graph of f resembles for large values of x is y

9 Alex is shooting foul shots He takes 20 shots and only misses three times What percentage of the shots did he make

4 As a teacher circulates the room she finds that 8 students answered a question correctly and 2 answered the question incorrectly What percent of the room answered the question correctly

6 Sam spent 30 minutes studying for his Math test 15 minutes studying for a Reading test 45 minutes studying for a Science test and 20 minutes studying for an English test What percentage of her study time was spent on Reading

8 Mark is 24 years old which is 75 as old as his friend Troy How old is Troy

2 Kayla records the weather for several days in a row There are 10 suppy days 8 rainy days

2 Peter got 80 on a science test If he answered 12 questions right how many were there overall

3 60 of the animals in a zoo are mammals If there are 45 mammals how many animals are there

Practice 1 At the computer factory there is a defect in 2 of computers produced If the factory produces 400 computers in an hour how many will have a defect

4 Write in exponential form 9 b 10 a 7

For the polynomial function f x 8x x 5 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the x axis at each x intercept c Determine the maximum number of turning points on the graph d Determine the end behavior that is find the power function that the graph of f resembles for large values of x a Find any real zeros of f Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The real zero of f is with multiplicity Type an exact answer using radicals as needed Type integers or fractions with multiplicity The largest zero of f is OB The smallest zero of f is with multiplicity Type an exact answer using radicals as needed Type integers or fractions The middle zero of f is with multiplicity O C The smallest zero of fis with multiplicity zero of fis with multiplicity Type an exact answer using radicals as needed Type integers or fractions OD There are no real zeros The largest

3 Maya s gas tank currently holds 9 gallons of gas It is 60 full How much gas can the tank hold when full

1 If 45 of the students in a school are girls and there are 200 students in the school how many are girls

Exercise 8 5 4 Take the 2 x 2 matrix A and consider the matrix A XI where A is a variable scalar and I is the identity matrix Compute det A XI Using the 2 x 2 formula Solve for A when setting this determinant equal to zero Now for each solution solve the equation Ar Ar for x You have just found your first eigen pair We ll talk more about these in a few weeks

Exercise 7 3 4 Let A be an m xn matrix of rank k If B is an invertible mx matrix try to argue why B A is also ank k

1 point Suppose and Then f g x x 2 x 2 f g x x 2 x fg x x 3 x 2 x 1 f g x x 2 1 x 1 f g x x 2 2x 2 g f x x 2 2 and f x x 1 g x x 1

Find the difference in interest paid over the full term of the loan repaid in monthly installments for a 200 000 loan Loan A 30 year fixed at 7 00 compounded monthly paid monthly or Loan B 20 year fixed at 6 50 compounded monthly paid monthly Payment P 7 1 O 38532 O 217470 They are the same

Exercise 8 5 2 Use the fact that A A 1 I and Proposition 8 2 8 to solve for det A in terms of det

Try It In a basketball game Mike makes 60 of his shots If he makes 12 baskets how many shots did he take p 72

LINE y 3x 1 5 Determine the y intercept of a line with a slope of 2 that is a tangent to the curve y 2x 6 4x

4 On a test there are 6 true false questions 5 multiple choice and 4 short responses What percent of the questions on the test are true false

Dollars The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars Use the information in the figure to answer the question 3500 3000 2500 2000 1500 1000 500 400 600 200 800 Binoculars Produced and Sold R x 3x 2700 binoculars 750 binoculars O1500 binoculars 2250 binoculars C x 1500 x Break even Point 750 2250 How many binoculars must be produced and sold for the company to break even

A catering company prepares and sells food items Let x be the number of items prepared and sold in one month The cost function is C x 1200 120 x The revenue function is R x 150x Find the profit or loss when 200 flat screen TVs are sold When the company prepares and sells 200 items in one month the profit is 6000 When the company prepares and sells 200 items in one month the profit is 7200 When the company prepares and sells 200 items in one month the profit is 4800 When the company prepares and sells 200 items in one month the loss is 4800

store sells small notebooks for 8 and large notebooks for 16 If a student buys 6 notebooks and spends 80 how many of each size did he buy He bought small notebooks and large notebooks Type whole numbers

4 80 of a class completed the homework one night If there are 20 students in the class how many students completed the homework A 8 B 16 C 18 D 25

The price of a home is 250 000 The bank requires a 15 down payment and two points at the time of closing The home is financed with a 20 year mortgage at 6 5 compounded monthly Find the amount of the monthly payment Payment 11 1 1 1584 34 1863 93 2798 18 1552 66

3 Melissa has 5 pens 3 pencils and 2 markers in her pencil case What percentage of her writing utensils are pencils A 3 B 13 C 30 D 43

frth f8 h 3 xh 41 17 4 x F 3x 3h 5245444 h 3x 1 5444 3241 5x 4

se a coterminal angle to find the exact value of the following expression Do not use a calculator 9x 4 sin

Linda needs to have her car towed Little Town Auto charges a flat fee of 85 plus 2 per mile towed Write a function expressing Linda s towing cost c in terms of miles towed x Find the cost of having a car towed 11 miles c x 2x 22 c x 2x 85 Oc x 2 85 c x 2x 85 97 87 107

Use the graph of y f x to answer the following y f x Part 0 9 Part 1 of 9 a Determine f 0 f 0 3 2 1 4

The price of a home is 260 000 The bank requires a 20 down payment After the down payment the cost of the home is financed with a 15 year fixed rate mortgage at 7 Find the mortgage loan amount 241 800 52 000 208 000 O 260 000

Select all functions that will successfully return value s based on the parameter list inputs back to the invoking program such that the values can be used for later computation after the function has ended Odef mystery1 x y a b y x return a b Odef mystery2 w1 w2 x y w2 w1 print x y def mystery3 X V V X

The cost of a home on a particular island is 1000 000 The bank requires a 15 down payment and three points at the time of closing The cost of the home is financed with a 30 year fixed rate at 8 Find the amount that must be paid for th three points at closing 25 500 O 30 000 O 68 000 80 000

The functions f and g are graphed in the same rectangular coordinate system shown to the right If g is obtained from f through a sequence of transformations find an equation for g What is the equation for g g x fixtED 15 ALTHO

Suppose that you borrow 30 000 for four years at 8 compounded monthly towards the purchase of a car Find the the amount of the monthly payment Payment 857 2095 O 732 O 7625 A 11 nxt

Find how much money will be in the account after the given number of years at the given rate of compound interest Principal 7000 Rate 4 compounded semiannually Time 4 years Use one of the formulas below to solve the problem Future Value A P 1 nxt Present Value P 7577 03 9579 98 8201 62 8189 01 nxt

Determine the periodic deposit at the end of every month Rate 7 5 compounded monthly Time 3 years Financial Goal 44 000 Periodic Deposit P 1094 3304 1172 975 4

The price of a home is 180 000 The bank requires a 5 down payment at the time of closing The cost of the home is financed with a 30 year fixed rate mortgage at 7 5 Find the required down payment 13 500 O 135 000 O 90 000 O 9 000

from the annuity in Q 14 Periodic Deposit 2500 at the end of every three months Rate 4 5 compounded quarterly Time 12 years Value of Annuity A 260 187 37 965 33 735 20 911 nxt A n