Mathematics Questions and Answers May 14, 2020

1 B 9 Basics to Multiplying Rational Expressions Simplify each expression A 6b C 3 5 7b 8 9b 9b A 7 k 7 5 7k 5 k 6 C k 5 9 A 2v 56 81b 5 35v 45 A C v 3 4 n 3 49n 14 A 2 k 2 7k 5 2 k 8 k 2 B B b D 14v 18v n 1 6 n 2 B D 5 n 6 n 7 4 36 3a 7 21a 64a 35 3 a 1 k 1 4k k 7 k 8 21n 64n 20 9n 30n 5a a 6 a 10 6 v 2 v 9 100 9v B D 14a 10a 5a 45 B n 3 21n 8 9n

Find all complex zeros of the polynomial function Give exact values List multiple zeros as necessary f x 3x4 20x3 44x 80x 128 8 OA 4 i i 8 OB 4 2i 2i 3 OC 13 4 4 4i 4i 8 D 3 4 21 2i

Problem 5 Let W be the subspace of R spanned by the vectors u 1 0 1 0 u2 0 1 1 0 and u3 0 0 1 1 Use the Gram Schmidt process to transform the basis u u2 u3 into an orthonormal basis 4 v 2 0 2 0 v2 V V V 0 v3 3 V3 6 3 6 2 0 2 0 v V6 NE V6 0 V3 13 13 13 V2 3 3 D v 2 0 2 0 v2 V6 V6 6 0 v3 2 0 0 v 6 16 16 0 1 13 13 13 v3 E v V2 B v1 C v 2 0 2 0 v2 V6

Write the following expression as a sum and or difference of logarithms Express powers as factors In e x 7

Simplify each sum 4 2x 5 6 2x A 1 C 1 5x B 1 x D 3 5x 5 5 2x 6x 3x x A 7x x C 8x x B 15x x D 14x x

11 Solve the following logarithmic equation If multiple solutions exist enter solutions using a comma separated list log 6x 17 log 4x 18 1

Write the equation of the circle The circle with center C 1 4 and radius r 2

Write the equation of the circle. The circle with center C(l, 4) and radius r 2,

Find the exact value of the logarithm without using a calcu log 12144

Find the exact value of the logarithm without using a calcu log 12144

Find the solution to the following lhcc recurrence an 34an 1 an 289an 2 for n 3 with initial conditions a 204 a2 3468

11 2x6 10 13 2 4x 10 15 5 3x 10 12 12 5x 2 14 4 10x 6 16 12 2x 8

Find the perimeter and area of the shown figure 12 108

Find the perimeter and area ot the shown figure.

Sketch the graph of each linear inequality 1 y x 3 A B D 2 44 2 4 2 y 2 4 4 X X

arry and Sally can both produce fish and fruit Sally can produce 1 kg of fish in 4 hours and 1 kg of fruit in 5 hours Harry can produce 1 kg of fish in 5 hours and 1 kg of fruit in 2 hours Each person wants to have 4 kgs of fish and 6 kgs of fruit per week Each person works for 20 hours a week Who has a comparative advantage in fish Who has a

i want to calculate theta 3 and theta 4 please 0 712 Cos 3 Cos 04

i want to calculate theta 3 and theta 4 please e

Combine all 10 equations into one piecewise function Include correct domains for each part of the piecewise function y 2 x 1 5 x 3 y x 5 8 3 x 7

Let f 2 x x 6x 1 and g x 9 2 Determine 3f x 2g r In the space provided type the coefficients of your final solution in arx bx c form 3f x 2g x

What are the solutions for the given equations below 3n 27 O

What are the solutions for the given equations below 2

f log 8 4x The domain of f is 2 00 X

f(c) log(8 ax) The domain of f is (2,00) x .

Express 3 1 4 1 3 9 Simplify your answer Use integers or fractions for any numbers in the expression Use p 3 3 9 as a power of 3

Enter the system of equations that is represented by the augmented matrix below Use x y and z for the first second and third variables respectively You do not need to solve the system Equation 1 Equation 2 Equation 3 3 5 7 2 6 2 0 4 1 4 4 2

Let A and B be any two sets Then a AUB ANB A b ANB AUB De Morgan s Properties A B B U U 11 U A B A U B D

4 For each equation identify the slope of the line it represents and the coordinates of a point on the line a y 5 4 x 1 b y 7 3 x 8 c y 11 x 15 d y 5 x 2 4 e y 6 x 3 8 f y 21 x 16

8 12v 153v 48v 45 12v 9 4 3 4v 3 2 3 4v 3 1 4v 3 A v 12v 8 B v 12v 4 C v 12v 7 D v 12v 5 X

What is the vertex of the following parabola y 4x 24x 23 3 13 3 13 3 24 3 24

Factor f x 3x 5x 58x 40 into linear factors given that 4 is a zero of f x f x 3x 5x 58x 40 Factor completely

Find the sum of the first 21 terms of the arithmetic series 48 54 60 66 21

Find the sum of the first 21 terms of the arithmetic series. 48 54 60 66

a 3 3 3 3 11 5 7 1 27 13 15 x 8 15 17 19 1 n 11 21 12 b 2 5 x 10 7 x 15 3 k 5 V 5 2 3 2 3 2 x 2 14 9 4 8 10 12 6 2 21 1 14 16 m 12 5 18 x 2 2 3 11 v 4 n 5 6 3 m 14 4 b 8 8 1 P 6 n 3 3 2 2 1 7

Which is the only relationship below that could NOT be modeled by a linear function Hours Worked Pay Hours Worked Pay 3 36 Hours Worked Pay 5 50 Hours Worked 0 Pay 450 1 20 4 48 6 60 1 450 2 30 5 60 7 72 3 450 3 40 6 72 8 86 12 450 4 50 8 96 9 102 30 450 5 60 www

Use the Quotient and Reciprocal Identities to match equivalent expressions sin 0 1 1 1 1 1 1 cos 0 a cos 0 csc sin 0 sec 0 cot e cos e tan e sin 0 sin e b cos 0 c tan e d csc 0 e sec 0 f cot 0 1

7 3x 22x 35 A 3x 7 x 5 B 2x 7 x 7 C 3 x 7 x 5 D 3x 7 x 5 8 8 15x65x 70 A 5 3x 7Xx 2 B 5 3x 7 x 2 C x 7 3x 2 D al3x 7

Change the exponential statement to an equivalent statement involving a logarit ex 19

Change the exponential statement to an equivalent statement involving a logaritl eX19

Rewrite the expression In 39 In 6 so that it includes the expressions In 3 and 39 and 6 do not appear inside a natural logarithm Expression

Is 33 52 a factor of 34 52 Explain why or why not Choose the correct answer below O A No because the exponents on the 5 terms are the same B Yes because 34 52 3 33 52 OC No because 33 52 cannot be written as a number times 34 5 D Yes because the two terms have the same factors P

Solve the system of equations x 2 y 2 x

Solve the system of equations.

Test Find the 18th term of the arithmetic sequence 4 9 14 19 The 18th term is Ques

Ques les Find the 18th term of the arithmetic sequence. 4, 9, 14, 19, The 18th term is I

Find the value 16 In ve 16 e 0 In Ve Simplify your answer Type an integer or a fra

Find the exact value of the logarithm without using a calculator log 28 log8 8

Find the exact value ot the logarithm without using a calculator log C 8 log 8

5 Solve the following exponential equation 1 25 55 6

5. Solve the following exponential equation 1 55tt6

A local realtor sold 5 houses this quarter The prices of the houses were 85 000 127 500 197 000 240 000 750 000 Find the mean and the median Explain which is a better measure of the average for this situatio and why you think so This question must be answered in 2 4 complete sentences

2 7i 3 4i 6 points Given the following expression a 1 point State the conjugate b 4 points Simplify the expression in a bi form

x 1 x 15 2x zoom in 3x 2 1 What is the expression that represen the area of the shaded part of the figure Type a response

State Cayley Hamilton theorem and use it to find A 1 and A4 Where A 1 2 3 2 1 4 L3 1 1

Determine the exponential regression of the data below using either a calculator or spreadsheet program 21 6 19 23 13 33 8 47 5 54 2 62 Select the correct answer below Of x 93 264 1 106 Of x 93 264 1 106 O f x 93 264 1 106 O f x 93 264 1 106

Use the change of base theorem to find the logarithm log 83 Use the change of base theorem to rewrite the given expression in terms of n log 83 Do not evaluate Do not simplify

Partner Practice 1 Identify all values for x below that are a solution to the inequality 2x 4 10 a 2 b 1 c 3 d 5 e 10

6 44 Example Find u P2 R such that 1 p t cos t dt 1 for every p P R S L PU p t u t dt

Graph the hyperbola Give the domain range center vertices foci and equations of the asymptotes 25y 49x 1225 Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers or fractions 1225 Choose the correct answer below Give the equations of the asymptotes for the

7x 35 2 x 7 10x x 7 D 3 7 2 11 x 2 8 8 10p 10 p 4p 5 A P S B P 5 10 C P S D P3 0 3 5 3 5 1

Determine if the function is even odd or neither f x 0 75x x 2 O Odd O Even

Determine if the function is even, odd, or neither. f(x) 0.75x2 IXI 2 O Odd O Even

M Ex 4 Write an equation for the line with slope of 2 3 and passing through the point 1 4 Answer in general form

Which of the below is a binomial factor of the polynomial shown w 8w 16 O w 2 O w 8 w 4 w 16

Find the midpoint M of the line segment joining the points A 1 7 and B 7 7 M D

1 Find the area of the triangle using the formula A bh and then verify that Heron s formula gives the same result 1 bh Use the formula A 2b The area is 48 Use Heron s formula The area is C 10 16 10

Question 1 13 Jse the dropdown menu to indicate the ustification of the previous step to the current step when solving the equation 3 5 2d z Statement 3 1 5 2d z 3 2 2d2 3 3 d 2 8 4 d 4 16 21 21 Justifi 1 Giv 12 3 4

Express y as a function of x The constant C is a positive number In y In x In x 10 In C

2 Is x 4 a solution to the equation 4x 5 21 No

2) Is x 4 a solution to the equation 4x 5 21 No.

16 x y x y 5 A 51 F X B 380 C 9 D 19 E 22

16. A) B) D) 19 E) 22

Use the quadratic formula to solve x 3x 1 0 3 5 3 5 2 2 O O 3 13 3 13 2 2 3 5 3 5 2 2 3 13 3 13 3 13 2 2

5 3 3 5 3 A 12 2 15 B 12 C 8 2 15

A 122 15 B 12 c 8 15

Solve the equation over the interval 0 2x then support your solutions graphically 2 cos 2x 2 cos x 0 Select the correct choice below and if necessary fill in the answer box to complete your choice O A 2 4x The solution set is 0 33 Use a comma to separate answers as needed Type exact answers using a as needed OB The solution is the empty set

inner products T a u v where u 12 T v 5 b x y where x 10 14 3 y 0 49 00 c 2u v v using u and u above Compute the norms of u v x and y above simplify only where reasonable Compute the distance from u to v above Find the angle between u and u above calculator needed Draw two vectors in R2 which are not perpendicular Verify this by showing that a

The function f x 2x 3 is graphed at the right Determine the y intercept for the function f x which is shown O 1 5 0 O 2 0 0 3 0 2 6 5 4 3 f x 2x 3 2 1 S 3 2 1 F 1 n 2 Asymptote y 3

Graph the hyperbola x y 9 Give the domain range center vertices foci and equations of the asymptotes for the figure The hyperbola has a center at 0 0 Type an ordered pair The vertices are 3 0 3 0 Type ordered pairs Use a comma to separate answers as needed The foci are 3 2 0 3 2 0 Type ordered pairs Type an exact answer using radicals as needed

Simplify each difference 2 3n 6 3n 4n 7 7n A n 4n 12 6n B n 4n 14 6n C n 4n 12 D n 4n 13

Solve the equation ex 6 O A 10 OB 4 O C O D X 6 18 5 12 5

3x If f x In x g x e x and h x x find the following a fog x What is the domain of fog b gof x What is the domain of g of c fog 7 d foh x What is the domain of f o h e foh e a fog x Simplify your answer The domain of fog is b gof x Simplify your answer The domain of g of is Type your answer in interval notation c fog 7 Simplify your answer d f x

12 Given the function f x x2 1 where n is a Natural number using calculus methods determine the intervals of concavity Show all work for full marks

S I 350 at 4 for 5 years Find the Principle P

S.I. 350 at 4 for 5 years Find the Principle (P)

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

A C C If a 8 b 8 and ZC 60 then find the length of side c b B a

Write the Roman numeral as a Hindu Arabic numeral MMDCLXVI OA 2 656 OB 2 666 OC 2 565

Write the Roman numeral as a HinduArabic numeral. MMDCLXVI 2,656 2,666 2,565

Expand a q 5 a q 5 Simplify your answer

Expand. 5 (Simplify your answer.)

Consider the function Which graph below corresponds to the following traces 18 2 B f x y m 1 0 2x xy 6 1 The trace for z 1 35 2 The trace for y 0 75 3 The trace for x 0 3 4 The trace for y 2 C 2 118 D

18 T B P 10 2 0 10 2 0 b 10 Find the coordinates of x in the ordered basis B a b Hint The preview shows the picture of a with the coordinates you pr

Simplify each expression 1 6k 7k 3 n 10 9n 3 5 r 10r 7 11r 12r TIS 2 12r 8 12 4 4x 10x 6 2x 11 6x 8 v 12v Date

Find the 11th term of the arithmetic sequence 11 7 3 3 5 a11 Simplify your answer

Find the I Ith term of the arithmetic sequence. 11 7 (Simplify your answer)

a Find the center radius form of the equation of the circle with center 3 5 and radius 4 b Graph the circle a The center radius form of the equation of the circle is x 3 y 5 16 Type an equation b Use the graphing tool to graph the circle Click to enlarge graph 4 10 B Ay 10 8 6 4 2 2 8 40 x

8 Solve each equation below 4 pts each a 0 05 1 15 5 c log 2x 4 2 b log x log x d 4ln 6x 5 15 2

Decide whether the equation is an identity a conditional equation or a contradiction Give the solution set 2 5x 5 10x 10 0 OA Contradiction B Identity all real numbers C Conditional 0 D Conditional 5

discuter en fonction des param tres ventuels 2x b y z x 2a y z x 6a b y 6a b z

Synthetic Division Divide 1 3 2v v 2 v 6 A v v 3 2 v 4 2 v B v v C v v 3 3 D v 2 v 2 2 2n 3n 2 n 1 1 A 2n n 1 n 1 3 B 2n n 2 C 2n n n 3 D 2n n 3 n 1 3 n 1 3 n 1

Ex 7 Write an equation of the line in general form that is parallel to the line y 3x 5 and passes through the point 6 5 m 3

Multiply and simplify 2 2 7 7 2 5 7 2 2 7 7 2 5 7

Multiply and simplify. F) 5di)

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

Divide 2 15 12 A B C 5 2 15 3 2 15 V12

Divide. 2 15 12 2 15 2 15 12

1 Given the following examples determine if the function graphed is one to one If the function is one to one graph its inverse If the function is not one to one explain why n 2 points each Function 0 5 5 5 One to One no Graph of Inverse OR Explanation of why Inverse does not exist It is infinite FOR D

1 Solve the following exponential equation 1 625 54 3

I. Solve the following exponential equationi 1 625

A ZA LB ZC b 43 33 C degrees C a b C 15 PO B

43 ZB 33 degrees 15

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

X 3 1 0 4 g x 5 1 1 9 h x x x 4 O 5 O 3 O 3 O 5

The diagram shows the stem and leaf tables of the weights of two groups 20 years olds from towns A and B town A 7 5100 642 6 5 1 7 9 9 8 7 4 0 8 6 4 2 2 2 1 6 7 8 9 10 2234 1 7 8 0 4 4 4 6 0 2 3 5 2 3 3 4 59 6679 How many people were weighed in town B What was the modal group in town B What was the modal weight in town A What was the median weight

Find QR R Q 5 S Write your answer as an integer or as a decimal rounded to the nearest tenth QR

Click here to watch the video Given that cos 1 A 5 5 and 0 x 2 determine the exact value of cos a cos 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Ratic

5 n 4n 4 n n 2 A B C D 7 A B C 5n 1 5n 8 n 1 D n 2 n 2 7x 35 x x 20 x 2 n 1 5n 8 1 5n 1 5 x 7 7 8 5 2 x 4 x 1 2 1 7 1 4 5 0 9 10x x 7 x 2 2 1 6 8 6 12k 24 12k 32 A B 8 C D A B C 3 k 2 3k 8 D 5k 4 7k 9 k 10 10p 10 p 4p 5 k 5 k 5 k 10 P 5 4p 4p P 5 10 0 P 5 P 5 10 8 3 7 5 7 10 7 0 3 5 3 5 1 1

Select the correct asnwer The volume of a rectangular prism is a minimum of 25 cubic feet The height of the prism is 3 feet more than its width and its length is at most 5 feet more than the width Carla wrote this system of inequalities to represent this situation where Vis the volume of the prism and wis the width V w 8w 15w V 25 A OB C OD Carla

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

y 2 x 1 x y 1 Ty 4 3 2 3 2 1 0 2 3 1 2 3 4 X 1

1 Combine like terms in the expression below 2 x 4x 10 3x 4x 12

1.) Combine like terms in the expression below 12) 2(x3 4x2 10)

15 5 3x 10 17 10 12 x 16 12 2x 8 18 2x

15.) 5 10 16.) 1701012 1 s 3 5

Find the vertex of y x 6x 6 using the vertex formula Step 1 Find the x coordinate of the vertex For any parabola y Az Bz C the x coordinate of the vertex will always be t Using this formula what is the x coordinate of the vertex for the parabola y x 6x 6 Step 2 Find the y coordinate of the vertex lue the vertey of the serab