Algebra Questions

25 Express using rational exponents 8x7y 2 F

27 Express the following using exponents 4x y O 2x y O 2x y 3 O 2 x y 2 x y

7 Teratogenic studies of insulin glargine were undertaken in rats at doses up to 0 36 mg kg day This is equivalent to which of the following a 360 cg lb day b 792 mcg lb day c 360 mg lb day d 163 6 mcg lb day

8 Use the graph of y f x to find f 2 and f 1 2 2 OU 2 4

By determining f x f x 4x lim h 0 f x h f x h find f 3 for the given function

Solve the quadratic inequality 16 9x 0 two different ways and show that the result is the same with both methods Show steps for solving algebraically If solving graphically sketch and label the graph and explain

16 15 654321 Is it a function Domain Range Is it a function Domain Range Is it a function

3 Consider the matrix in Matlab notation A 1 a a 1 where the value of a gets close to 1 i e a 0 9 0 99 0 999 etc Study how it maps the unit circle x y Ax

2 10 points Consider the linear system where a and are constants x 3y z a 2x By z 1 2x 3y 4z 3 Find conditions on a and or such that a The system has a unique solution b The system has no solution c The system has infinitely many solutions Show Transcribed Text Please only answer if confident with the answer Please show all the steps and give detailed accura solution to the question Ensure to verify the answers as well Question is worth 10 marks so pleas

R is a linear transformation and that BD by rotating B counter clockwise by 45 degrees and doubling its length Also suppose That T T Suppose that T R we can find the image of T a What is T b What is T 1 1 c Find a matrix M so that for every x

29 Express in simplest radical form 6 25xBy 2 20 x 18 O 8x4y6 12 O 2x y 2x y O 8 x y

9 Express the following in simplest radical form 4 x 7 y t O 2xy O O 4xy 1 4xy

29 Express in simplest radical form 5 6 7 220 x 18 y 14 ryk

List the points in the graph at which the function is not differentiable Ay Hon 1 xo X x2 X3 X4 X5 Select all that apply A X3 C X DE X X 000

hich of the following are NOT functions I x y 1 II y x 1 III y x 1 IV x 1 8 22

After his lunch G del tells you that he ate either apples or bananas also that if he had corn then he had a decaf coffee also that he didn t drink either decaf coffee or espresso Define propositions A through E for relevant parts of G del s statements For example define A to be G del ate apples and so on Write each of the statements G del made about his lunch in terms of the propositions A through E Note that since G del is a logician he uses the word or to mean a logical OR rather than the or used by everyday mortals It is not widely known but G del lied about everything every statement he said was false Determine what G del had for lunch Justify your answer

13 In AABC leg a 16 and hypotenuse b 24 What will the leg c equal if this is a right triangle

21 Given two circles whose radii are 35 and 28 the ratio of their areas is O5 to 4 O 25 to 16 O 10 to 16 O 25 to 8 22 How much water should be added to 55 oz of 55 acid solution to dilute it to a 45 acid solution O 11 64 oz O 1 222 oz O 12 22 oz

26 If c represents the hypotenuse of a right triangle solve for the unknown side length a 279 b c 705 Round your answer to the nearest hundredth

7 Express the following using exponents 64x30 y7

23 How much water should be added to 50 ml of 80 percent acid solution to dilute it to a 70 percent acid solution ml 24 How many ml of 40 percent acid should be added to pure acid to make 40 ml of 45 percent acid Write your answer as a decimal rounded to the nearest thousandth if necessa x ml 25 An investment firm invested 3000 into two accounts 2200 went to an 12 annual rate account The rest went to a 7 annual rate account The interest the first year amounted to YOU

Question 11 If an island s only residents are penguins and bears and if there are 18 heads and 50 feet on the island how penguins and how many bears are on the island A 13 bears 5 penguins 11 bears 7 penguins B C 7 bears 11 penguins 5 F 8 bears 10 penguins

3 If there are 43 people in a school choir and 10 are girl what is the probability that a person chosen at random will be a boy State your answer as a fraction x 9 Solve for x 25 O 11 O 1 O O cannot be done 69 10 What is the scale factor if a 10 by 12 photograph is enlarged

If each side has a scale factor of 1 in to 4 ft the actual perimeter is and the actual area is O64 ft 48 ft O48 ft 64 ft2 O192 ft 64 ft O64 ft 192 ft 27 If there are 89 people in a track team and 17 are boys what is the probability that a person chosen at random will be a girl O 72 89 O about 81 both of these

O 128 04 O 7 35 12 What is the scale factor if a 10 in by 16 in photograph is enlarged to a poster that is 8 33 ft by 13 33 ft O 1 2 O O 10 1 2

13 How much water should be added to 85 ml of 60 acid solution to dilute it to a 45 acid solution Round your answer to the nearest hundredth if necessary ml 14 Mrs Wilson bought stock valued at 55 00 per share and sold it for 75 63 What was the percent of profit O 68 O 137 O 32 O 37 1 1 2

7 The local hardware store found that 1 out of every 10 generators they recently received were not properly assembled If they received 765 generators about how many generators can they expect to be faulty O 76 5 generators O77 generators O 765 5 generators O765 generators 18 There are 9 navy books and 3 brown books in your bookshelf If you close your eyes and take one book out of your bookshelf what is the probability that the book will be navy Write your answer as a fraction x

35 Given the set of all odd integers from 1 to 63 what is the probability of choosing a number that is a multiple of 7 If you enter your answer as a decimal round to the thousandths place 36 Solve for a O 1 73 O 1 53 O 0 92 O 1 3 6x 2 93403 7

28 Consider a typical die each side with one more dot than the previous side beginning with one dot There are six sides to the die a cube You throw a three on your first throw If you picked up the die and threw it again what is the chance of getting a three again If you enter your answer as a decimal round to the thousandths place x 29 Given two circles V and W with radii 3 in and 7 in respectively the ratio of the areas is Oin Oin both of these choices are equivalent

31 Given two circles whose radii are 2 and 6 the ratio of their areas is what Mark all correct answers more than one answer may be correct 1 9 1 to 9 1 to 3 1 3 1 3

32 An investment firm invested 2000 into two accounts 1500 went to an 10 annual rate account The rest went to a 3 annual rate account The interest the first year amounted to O 164 O 157 O 165 O 174

1 point What function does the following graph represent 3 2 f z 2 f x z f x z 100 PG 1 2 0 2 2

mplify the first trigonometric expression by writing the simplified form in terms of the second expressic tan x cot x sec x sin x

What will it cost to carpet a rectangular floor measuring 24 feet by 18 feet if the carpet costs 21 92 per square yard It will cost www

Find the area of the figure A Simplify your answer m m E 3 DE 11 m 17 m 7 30 m

F 24 Use the following similar triangles AABC ADEP If AC 10 when DF 19 and AB 13 what is DE Solve mathematically Round your answer to the nearest tenth B E

What is the scale factor if a 6 in by 6 in photograph is enlarged to a poster that is 1 5 ft by 1 5 ft O 3 O 04 O 8 Given the set of all even integers between and including 30 to 6 what is the probability of choosing a multiple of 3 from this set O O C 13 O 17

20 The Drama Club receives 1259 25 by selling 341 tickets to the opening night of the musical If the full price of a ticket is 5 25 and discount tickets for students and seniors are 0 75 each how many full price tickets were sold 21 Given two circles J and K with radii 5 in and 8 in respectively the ratio of the areas is O O both of these choices are equi ont

22 Given two similar triangles AABC and ADEF if AB 11 and DE 16 and AC 15 then what is the length of side DF Round to the nearest tenth O 11 7 O 21 8 O 21 3 O 10 3 23 How many ml of 10 percent acid should be added to pure acid to make 50 ml of 35 percent acid Write your answer as a decimal rounded to the nearest thousandth if necessary ml

16 How much water should be added to 105 oz of 60 acid solution to dilute it to a 40 acid solution O 52 5 oz O45 65 oz O 5 25 oz O impossible to do 17 Given two circles X and Y with radii 1 in and 12 in respectively the ratio of the areas is Write your answer as a fraction

27 If there are 11 girls in a class of 16 what is the ratio of girls to boys in the class O Of O O 28 The perimeters of two similar figures are 42 in and 48 in What is the ratio of lengths of corresponding sides State your answer as a fraction x

11 The Triple E Lumber store found that 1 out of every 10 chain saws they recently received were not properly assembled If they received 435 chain saws about how many chain saws can they expect to be faulty O435 5 chain saws O 43 5 chain saws O 44 chain saws O435 chain saws 12 How many ml of 10 percent acid should be added to pure acid to make 70 ml of 50 percent acid O 44 33 ml 38 89 ml

18 Given two circles whose radii are 35 and 28 the ratio of their areas is 25 to 8 O 10 to 16 O 25 to 16 O 5 to 4 19 The Town Theater receives 3913 5 by selling 537 tickets to the opening night of the musical If the full price of a ticket is 9 25 and discount tickets for students and seniors are 5 50 each how many discounted senior student tickets were sold

O 5 55 O 118 26 O 55 48 O 11 83 14 If there are 97 people in a room and 17 are boys what is the probability that a person chosen at random will be a girl State your answer as a percentage rounded to the nearest hundredth x 15 Using the set N 2 3 5 7 9 what is the probability of choosing an even number

9 There are 54 pencils in a box 27 pairs 1 pair s are silver 6 pairs are green and the rest are black If you took out a black pencil and you didn t put it back what is the probability that you pull out another black pencil If you enter your answer as a decimal round to the thousandths place x

One side of a square flower bed is 13 feet long How many plants are needed if they are to be spaced 13 inches apart around the outside of the bed flowers

Use the quotient to a power rule to simplify 4 y 5 3 3

Simplify the following expression by combining like terms 2 z 2 4z

Use the negative exponent rules to simplify 9y 2 C 2 7

Use the distributive property to find the product 4x 5x 4 0 power