Mathematics Questions and Answers May 13, 2020

Describe the end behavior of the right side of the function f x x 2x 7 y approaches infinity as x approaches infinity y approaches infinity as x approaches negative infinity y approaches negative infinity as x approaches negative infinity y approaches negative infinity as x approaches infinity

Let p and q represent the following simple statements p The chair is broken q I eat bananas Write the following compound statement in its symbolic form If the chair is not broken then I do not eat bananas Choose the correct symbolic form below Op q p q p q p q www

Question Details Find an expression for the perimeter of the figure 2 lo y 1 2 y 2 y y 1

For each function below find the indicated inverse function Be mindful of the following when using Derivita To enter a log of any base type log b base argument log argument defaults to the base 10 In argument is the natural log which has base e a f x 7 b g x c h x 10 h y d m x e m y

oblem 3 a Express the complex number 4 3i 3 in the form a bi b Express the below complex number in the form a bi 7 3i i 3 6i c Consider the following matrix A 2 4i 2 4i 1 5i 1 2i Let B A Find b22 i e find the entry in row 2 column 2 of 4

are 22 grams of the isotope a Find the function P t which gives the number of grams of the isotope after t days P t 22 1 2 t 7 Correct Good Job 9 30 b Estimate the number of grams of the isotope after 12 days Round to two decimal places 20 grams Not quite grams Preview P t 22 grams c Estimate the number of days it will take for the isotope to

K Use a sum or difference formula to find the exact value of the trigonometric function sin 11x 12 11T sin 12 Simplify your answer including any radicals Use integers or fractions for any numbers in the

Listen Use the following frequency distribution to determine the class limits of the third class Class 9 11 12 14 15 17 18 20 21 23 Frequency 7 11 8 5 9 lower limit 14 upper limit 18 lower limit 15 upper limit 17 lower limit 14 upper limit 17 Olower limit 15 upper limit 18

Roger has found a home to be purchase for 112 057 and has agreed to pay 10 down Find the amount of Roger s down payment Find the amount of money that Roger would need to borrow through a mortgage in order to purchase the home If Roger found a 30 year mortgage with a 5 6 APR What would Roger s monthly payment be Round your answer to the nearest cent

According to 2010 U S census the population of Fort Pierce was 41 797 The 2020 U S census found that the population of Fort Pierce had grown to 46 608 Use the exponential growth model Y Yekt where t is the number of years after 2010 to write an exponential growth function for the city of Fort Pierce Round the growth constant k to four significant

Given the triangle below find the measure of angle x Round to two decimal places Note picture is NOT drawn to scale but x is obtuse 26 26 X

1 11 x 5x5 2x4 2x 8x A 3x5 10x4 6x B 3x 10x x C 5x 10x4 x D 3x 10x42x

Enter the simplified form of the complex fraction in the box Assume no denominator equals zero 2 x 3 3 x 3 3 X

Determine the zeroes for the following polynomial function Write your answers as integers or fractions in order from least to greatest f x x x 3 2z 1

20 dAR 0 45155 05057 0s0s A OB www OC O D O

10

Give a rule for the piecewise defined function Then give the domain and range OA O C f x 5 if x 2 6 if x 22 Domain 5 6 Range 0 00 5 if x 2 6 if x 2 Domain 00 00 Range 5 6 f x 81 B O D f x 4 f x 5 ifx 2 6 if x 2 Domain 5 6 Range 0 00 5 if x 2 6 if x 2 Domain 00 00 Range 5 6 X

Find functions f and g so that fog H H x 8x 5 Choose the correct pair of functions OA f x 8x 5 g x x O B f x x g x 8x 5 O C f x x g x 5 8 O D f x X 5 8 g x x

2 3n A 3n B 2n C 3n D D 9n

C (3n)

2a Twelve less than the quotient of x and 10

2a.) Twelve less than the quotient of x and 10

1 Approximate the following value using a calculator Round the solution to four decimal places if necessary 2 Note No work needed this question ensures a student is using a calculator properly

2m n 2m n 2mm A 16m n 9 4n B D 14 512m 6 120 10 10 A C 2a 2a 2a b 46 2 B 16ba D 4a17

Divide the following polynomials using any method of your choosing 2x 7x 2x 9 2x 3 2 x 2x 3

Determine whether B is the inverse of A A 4 3 5 4 O Yes O No B 4 3 54 Is B the multiplicative inverse of A

K Given that sin 0 sin 20 cos 20 2184 7225 13 and cos 0 0 determine the values of the sine and cosine functions for 20 85 Type an integer or a simplified fraction Type an integer or a simplified fraction

The comprehensive graph of a polynomial function y f x is shown How many real zeros does the function f have The function hasrat roma E 12 Ay 150 150 12 Q

Select the correct choice that completes the sentence below The point 1 lies on the graph of y tan x Therefore the point of 4 2 2 lies on the graph of y tan

10 Explain how the graph of the function f x can be obtained from the graph of y Then graph f and give the a domain x and b range Determine the largest open intervals of the domain over which the function is c increasing or d decreasing 1 To obtain the graph of f stretch the graph of y Graph the function f x AY Q 10 Choose the correct graph below

Identify the missing number without using a calculator If no number makes the statement true enter DNE a In 1 e b logo 36 c log3 81 d log 1 e logg 9

Which domain restrictions apply to this rational expression x 4x 4 x 4 Select each correct answer O x 4 x 2 0 x 0 0 x 2 C E

Today the population of the town of Wallingford Pennsylvania is 11 300 people In 1980 ere were 10 000 people while in 1990 there were 10 500 people By what percent did the opulation grow from 1990 to today

1 In an arithmetic sequence the first term is 8 and the sum of the first 20 terms is 790 a Find the common difference

4s 37 19x 3r is equivalen to F 148 11 G 108 21 H 25 22 J 14 11 K 40 24

Find the requested value 2x 1 if x 6 f 6 for f x 6x OA 11 OB 36 O C 48 if 6 x 9 6 7x if x 9

2 What is the value of 2x 4y if x 2 and y 3 a 16 b 8 c 8 d 16

Find a formula in terms of k for the entries of Ak where A is the diagonalizable matrix below A 19 18 20 19 00

Let A 14 19 a a13 b a31 19 10 11 6 c a a22 13 3 15 Find the following matrix entri FI A

Independent Simplify each expression 1 8 6x 6x 3 7m 5m 5 9b 2 6b 7 9 10 6r 2 7r 6 6 10r 4 2x 1 6 6 4n 5n 8 5 2n 6 Dat

Find the exact value of the following logarithmic expression log12 V12

Find the exact value of the following logarithmic expression.

You decide to purchase a car for 22 750 Assuming the sales tax is 5 5 of the purchase price find each of the following a What is the total cost including sales tax b If you make a down payment of 18 of the total cost find the down payment c Assuming you finance the remaining cost at an annual interest rate of 7 05 for 10 years find the monthly

Use long division or synthetic division to divide the following polynomials x 2x2 x 5 x 1

Use long division or synthetic division to divide the following polynomials x3 2x2 x 5 x 1

7 99x119x 76x 96 11x 12 8 8 12 153 48v 45 12 2 A 9x x 6 A 12v 8 2 11x 12 B 12v 4 B 9x x 8 3 C 9x x 8 D 9x x 7 11x 12 2 11x 12 4 9 21 154p 104 p2 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 2 14p C 11p 6p 8 D 11p 9p 11 2 14p 1 2 14p 10 C 12v 7 D 12v 5 3 4v 3 2 3 4v 3 1 4v 3 10 224x 49x 90 14x 14x 1 A x 4x 14 7 8 14x 7 B x 4x 15 7 2x 1 4 14x 7 10

What are the solutions of 2x 16x 34 0 O 4 2i O 8 2i O 8 ti Q 4 1

Which is a factor of 15xy 45x 6y 18 Oy 2 O 5x 3 O 5x 2 Oy 6

Which is a tactor of 15xy oy2 05x3 05x2 oy6 45x 6y 18

Look at the graph of the function f x x 1 3 below and describe its charact 0 1 3 Domain 5 Range Positive Interval Interval of Negative Interval as x as x V V 10 10 0 average rate of change over the interval 2 5 The point 10 0 is the 15 1 00 f x f x V V V

Find two functions f and g such that h x can be expressed as the function indicated Several answers are possib h x 3x x f g f x g x

Simplify Your answer should contain only positive expor 3 24 29 44 2 A 28 A C 1 1 28 D 25 B C

9 8 points Use long division to perform the indicated operation x 4x 11 x 5

9) (8 points) Use long division to perform the indicated operation (x3 4x2

Evaluate each expression using the values given in the table 1 2 X f x g x a fog 1 d gof 3 a fog 1 b fog 2 c gof 2 d gof 3 e gog 1 f fof 3 3 9 6 2 7 2 5 0 0 3 2 b fog 2 e gog 1 1 1 0 1 2 3 3 6 c gof 2 f fof 3

Simplify the radical 9p 8 Select the correct choice below and fill in any answer boxes in your OA 9p 8 OB The root is not a real number A 4 Simplify your answer

Factor the following polynomial using the difference of squares 422 81

Factor the following polynomial using the difference of squares. 422 81

K Find the exact function value CSC CSC T T BOXED Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

8 10 8 8b 3 8b 5b 8 A 6b 56 246 7 B 216 3462 26 8 C 86 33b2 3b 4 D 64b 64b 49b 24 10 7b 6b 7 6b 8b 5 A 16b 546 92b 54b 40 B 16b 18b 40 C 426 92b 125b 86b 35 D 16b 42b 56b 6b 40

7 A B C D 5 12x 8x 16 9 3x x 8 2 2x 3x x 32 6 8 8 6a 7 2a 7 A 12a 56a 49 Bj 12a 49 C 12a 28a 49 D 12a 56a 49

7 99x 119x 76x 96 11x 12 8 8 12v 153v 48v 45 12v 9 4 A 9x x 6 3 4v 3 2 3 4v 3 1 4v 3 B 9x x 8 C 9x x 8 D 9x x 7 2 11x 12 3 11x 12 9 21 154p 104p 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 C 11p 6p 8 2 11x 12 B x 4x 9 D 11p 9p 11 C x 4x 9 D x 4x 7 2 14p 1 2 14p 1 2 14p 11 5x 24x 61x A x 4x 9 30 5x 4 6 5x4 8 5x 4 1 5x 4 5 5x 4 10 12 A v 12v 8 B v

EXTRA CREDIT SUM 2 Q2 Sketch the graph of each linear inequality 1 3x y 2 A B C D 6 4 4 2 Y 2 2 4 X 6 x 6 x x 2 2 x 2y 0 A B C D 43 1 4 2 2 16 4 2 V A x X X

25 9 8k 9 k 10 27 7 4 x 10 6x 2 29 4 a 3 6 1 4a 31 7 2k 8 10 8k 4 26 7 6 k 5 9k 10 28 8 a 2 5 5a 3 30 7 9 6p 3 8 4p 32 3 8r 6 7 r 5

oblem 8 Let V be the set of all ordered pairs of real numbers u with u 0 Consider the following addition and scalar multiplication operations on u u U and v v V u v u v 2 6u2v2 ku ku ku Use the above operations for the following parts Problem 8 a Problem 8 b Problem 8 c a Compute u v for u 6 2 and v 4 7 b If the set V satisfies Axiom 4 of a vector

Find all rational zeros of the following polynomial funct P x x 43 x 55 x X 7 7 x 13

4 Use synthetic division to divide 4x 6x 23x 10 by x 2

4) Use synthetic division to divide 4x3 6x2 23x 10 by x 2.

17 Find all roots of the equations a z4 222 4 0 b w w 1 0 c z 1 0 d z 22 522 8 4 0 e 3 12z 10 0

9 3 7 6 7r 11 3 5 3 10 4 28x 7x 12 2 5 6 2

9) 3 7r3 .6 7r2 10) 12)

Maximum mark 4 without GDC The second term of an arithmetic sequence is 7 The sum of the first four terms of the arithmetic sequence is 12 Find the first term w and the common difference d

SUM 2 Q2 Solve each system by elimination 5 6y 42 18x 4x 8 3y A 4 1 C 1 4 B 4 1 D 1 4 66 3y 3x 15 9 3x 2y A 7 5 C 7 10 B 7 8 D 1 6

1 point Find a linearly independent set of vectors that spans the same subspace of R as that spanned by the vectors A linearly independent spanning set for the subspace is 1 2 0 0

36 The certificates of deposit pay 2 annually and the municipal bonds pay 4 annually Over a five year period the investor expects the blue chip stocks to return 10 annually and the growth stocks to return 14 annually The investor wants a combined annual return of 6 and also wants to have only one fourth of the portfolio invested in stocks

9 1 7 99x 119x 76x 96 11x 12 2 A 9x x 6 11x 12 3 11x 12 B 9x x 8 C 9x x 8 D 9x x 7 2 11x 12 9 21 154p 104 p 172p 2 14p 2 A 11p 9p 12 1 7p 4 5 B 11p 7p 10 C 11p 6p 8 D 11p 9p 11 2 14p 1 2 14p 1 2 14p 11 5x 24x 61x 30 5x 4 6 A x 4x 9 5x 4 8 B x 4x 9 C x 4x 9 D x 4x 7 5x 4 1 5x 4 5 5x 4 8 8 12 153y 48v 45 12 zoom 4 A v 12v 8 3 4v 3 2 B v 12v 4 3 4v 3

Determine whether or not the graph shown is the graph of a polynomial function 10 8 6 8 6 16 40 3 5 O not a polynomial funct O polynomial function

Find the zeros and give the multiplicity of each for f x x x 4 x 2 Note to be counted as correct you must get One zero is a Another zero is x The last zero is x all answers correct and has a multiplicity of and has a multiplicity of and has a multiplicity of help numbers help numbers help numbers

OA a 26 7 b 44 5 c 30 d 45 This question 1 point s possible For the given data set find the a mean b median c mode or state that there is no mode and d midrange The ages of teachers in the mathematics department of a certain high school are shown below 30 55 33 60 30 55 30 46 46 43 OB a 42 8 b 44 5 c 30 d 45 OC a 31 3 b 44 5 c 30 d 45 Some acco

10 If a taxi charges a pickup fee of 3 50 and 50 per mile write an expression for the cost of traveling m miles 3 50mt 0 50m

a Which expression below is equivalent to 30 2x 5 50 2x 5 b 3x 3x 2 5 7x 1 0 2x 7 x 1 d 20x 2x 3 5 10 Combine like terms in the expression below x3 2x 4x 2x

11 Show the solution to the following system FOLLOW DIRECTIONS ON DRAWING y 7 y x 2 y 2x Show Your Work

Find the A P R annual percentage rate necessary for 9000 to grow to 24 000 in 9 years given the indicated method of compounding Express each answer in decimal form rounded to four decimal places a Compounded every 3 months A P R T 11 0479 Not quite b Compounded continuously A P R T 10 8981 Not quite Preview T 11 0479 Preview r 10 8981

f x Simplify your answer Use integers or fractions for any numbers in the expression 12 RA 12

(Simplify your answer Use integers or fractions for any numbers in the expression.)

9 1 2x y4 8x 8xy 5 4x y 6xy 8x4y x4 A 5x y 9x 10xy 4 B 2xy 9x 10xy 4 C 5x y 9x 10xy 10 D 2xy 9x 14xy 4

Graph f x 4 and g x log ax in the same rectangular coordinate system O Q CXS

4 log In

Evaluate the following expression if possible 3 3 X 7 x 3 3 5 5 10 ME PC

Evaluate the following expression, if possible.

3 5 Simplify Your answer should contain only positive exponents 11 a 4 12 12 4k A 16a A k 2 C 1 C 13 1 256a4 15 3 3 3 2v 4v A 4p 1 B B 1 D 3 B 4 D 2v 14 16 4 4 A 4 4 C 4 14 16 A B 64k D 16k 13 17 B B 3 x 2

Use the graphs for f x and g x to evaluate the expressions below Write your answer as a whole number or a reduced fraction 6 5 4 3 2 1 1 f x 2 1 f 3 g 1 f 3 g 5 CA A 10 X 160 16 5 4 3 2 1 g x 1 1 g 5 f 4 g 1 f 4 2 st X 160

4 x 3 equation a Write the value or values of the variable that make a denominator zero These are the restrictions on the variable b Keeping the restrictions in mind solve the equation 3x 2 x 3 9 a Write the value or values of the variable that make a denominator zero Use a comma to separate answers as needed b Solve the equation ACCES

Graph the function Based on the graph state the domain and the range and find any intercepts x 2 if x 2 x 2 if x 2 f x e Choose the correct graph of f x

B P C B 11 6 8 Prove that ZPAB ZPCB and then use similar triangles to conclude AC PC

For the triangle shown find the length AD Assume u 19 v 19 2x 10 and y 10 Round your answer to two decimal places AD B The area is V Find the area of the triangle ABC C 131 2 a 45 3 ft and b 35 7 ft square ft D A C

Solve the equation 4 0 5x x X 5 The solution set is 6 Simplify your answer

Solve the equation. 4 3 The solution set is 1. (Simplify your answer.)

Find the volume of the parallelepiped with one vertex 2 2 0 and adjacent vertices 6 4 2 3 4 1 and 7 3 2 Volume

Mario bought a new car for 25 000 The value of the car is decreasing at a rate of 12 5 every year After 3 years the value of the car will be about how much Round to the nearest whole dollar Use A p 1 r 16 748 16 750 35 596

Exercise 4 Find complex solutions of the follow ing equations Hint assume z a bi where a b R 1 z z 1 0 2 z 2iz 5 0 3 24 3iz 4 0 4 3z 5iz 2 0 5 422 9 0

Simplify the following trigonometric expression by following the indicated direction Multiply cos e cos 0 sin 0 1 sin 0 1 by sin 0 1 sin 0 1 Simplify your answer

11b Evaluate your expression for x 2 and y 4

AlbJEvaluateyourgxpressiomfor

Find the mean for the data items in the given frequency distribution Round to the nearest tenth if necessary Score x 1 2 3 4 5 6 7 8 9 10 5 5 7 4 6 2 06 7 Frequency f 5 2 1 6 7 10 9 12 11 11

Prove that every positive rational number can be expressed uniquely as a finite sum of the form a a2 2 az 3 where an are integers such that An n

10 224x49x 90 14x 14x 7 8 14x 7 1 2x 1 4 A x 4x 14 B x 4x 15 C x 4x 11 D x 4x 13 14x 7 10 14x 7

Write in point slope form an equation of the line that passes through the point 5 8 with slope 2 0 0 0

nd the indicated term for the geometric sequence 9 9 9 024 256 64 3 the 8th term The 8th term of the g

PopQuiz On Halloween CC GG and JJ collected 75 candies CC got five more candies than GG and GG got 10 less candies than JJ How many cadies did each one get

6 end 10th tem The end 8 sequence o the b the third is 39 tem of sun of 230 Find is the first tem of sum of the an the the first arithmetic sequence first to terms sequence 13 terms is of the 416

The atmospheric pressure p on a balloon or an aircraft decreases with increasing height This pressure measured in millimeters of mercury is related to the height h in kilometers above s 0 145h level by the formula p 760e a Find the height of an aircraft if the atmospheric pressure is 231 millimeters of mercury b Find the height of a mountain if

For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is Type your answer in interval notation C 81 6 AY 10 6 h b 4 6 8 10

Use the given display to find the median Round to the nearest tenth if necessary Frequency Listen 20 10 5 4 N 21 7 201 10 20 30 40 50 Score

Use the parent function f x b to graph h 1 11 The domain of h is The range of his The equation of the