Algebra Questions

a Evaluate log4 256 without a calculator b Which of the following is equivalent to log4 256 using the change of base property Select all that apply In 4 In 256 log 4 log 256 log 256 log 4 log256 4 In 256 In 4 c Use a calculator on your correct answers from part b Are the answers from part a and part b equivalent O Yes

Let x y z be non zero vectors and suppose w 18x18y 4z If z 3x 3y then w Using the calculation above mark the statements below that must be true A Span w x y Span y z B Span w z Span w x C Span w x Span w y D Span w x y Span w z r 6 x 6 y

Rewrite the following logarithmic expression as one logarithm 9 ln x ln y 16 ln z

Simplify each expression a log a b blog 2 c eln 7 d 10log 3

Which of the following is equivalent to the expression below Select all that apply log 7 log 6 log 7 log 10 log 4 log 7 logs 6 log 7 log 6 log In 7 In 2 In 3

Which of the following is equivalent to the expression below Select all that apply logs x7 7 logs x logs logs x 7log x

Which of the following is equivalent to the expression below Select all that apply In 4x 5 ln 4x 5 ln 4 ln x ln 4 5 ln x In 4 In 25 5 ln 4 5 ln x

Which of the following is equivalent to the expression below Select all that apply logis cy log18 x log18 Y logis 2 logis y log18 2 log18 y

Suppose the roots of a Show that r r2 quadratic equation ax bx c 0 are r and r2 b and r r2 in two different ways a a

Which of the following is equivalent to the expression below Select all that apply log22 y log22 2 log22 y log22 2 log22 y log22 2 logan y loga z log22

37 3i 5 1 39 3 2 4

21 6 1 7 3i 22 9 51 11 21

Use the vertex and intercepts to sketch the graph of the quadratic function Give the equation of the parabola s axis of symmetry Use the graph to determine the domain and range of the function f x x 4 g 9 Use the graphing tool to graph the function Use the vertex and one of the intercepts when drawing the graph 6 3 The axis of symmetry is Type an equation Simplify your answer

9 9 2m n 2mm A 16m B D 512 10 10 2a 20 Za b A 9 46 B 16ba D 4q17

5 5 2 v 24 A 2urv R 0 D 1 6 6 21 2 A 16x B D 16pl2

3 2a a b 2ab A C 418 166 3 19 166 B D 1 4 1 C 123 A 4m n I 3 4 40 5 B a m D 8

Divide using synthetic division x5 4x 3x 5x 12x 4 x 3 x5 4x 3x 5x 12x 4 x 3 Simplify your answer Use integers or fractions for any numbers in the expression Do

Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions Zero of 4 having multiplicity 3 f 4 64 f x Simplify your answer Use integers or fractions for any numbers in the expression

Determine the intervals of the domain over which function is continuous Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is continuous on Type your answer in interval notation B The function is not continuous 4 3 2 Ay 5 4 3 2 1 CO NO 5 2 3 4 5 6 X

Find a quadratic function f whose graph matches the one in the figure f x 0 10 10 0 6 SU

Refer to 11 12 What are the coordinates of each image a Ry axts 5 3 Rx 5 3 5 3 b Ryaz 1 6 Ry 196 13 Graph AXYZ with vertices X 2 4 Y 6 0 and Z 7 2 and Its Image after the composition Translation x y x 6 y Translation x y x 2y 3 Graph the image of the figure using the transformation 14 15 reflection across the x axis reflection across 16 Becky draws a triangle with vertices A 6 7 B 9 3 and C 4 2 on a coordinate grid She reflects the triangle across the line y 4 to get AA B C She then reflects the image across the line x 3 to get AA B C What are the coordinates of AA B C and AA B C 17 Graph the figure and its image under the given reflection Square JKLM with vertices J 4 6 K 0 6 L 0 2 and M 4 2 Ry arts 19 A point in Quadrant III is reflected over the y axis and then over the x axis What quadrant is it in now 18 ERROR ANALYSIS Jamil and Ashley are finding the coordinates of the image of 2 3 after a reflection in the x axis Is either of them correct EXPLAIN 1 P 2 3 2 x y x y 3 When reflecting 21 Graph ARST with vertices R 4 1 S 7 3 and T 64 and its image after the glide reflection TRANSLATION x y x y 1 REFLECTION In the y axis Jounill CQ 3 Ashley C 23 The Point 20 ERROR ANALYSIS Sasha says that for any AXYZ the reflection over the y axin composed with the reflection over the x axis is equivalent to a translation of AXYZ EXPLAIN Sasha s error

What is the rule Select the correct choice below and fill in the answer boxes within your choice OA f x if xs if x OB f x if x if x2 3 2 R th 2 3

Compute each sum below If applicable write your answer as a fraction 2 2 3 2 3 2 3 0 8 X

oblem 1 Consider a quantum mechanical system with three states At each step a particular particle transitions from one state to a different state Empirical data show that if the particle is in State 1 then it is 3 times more likely to go to State 2 at the next step than to State 3 If it is in State 2 then it is 8 times more likely to go to State 3 at the next step than to State 1 If it is in State 3 then it is equally likely to go to State 1 or State 2 at the next step Let A be transition matrix for this markov chain Find a31 932 and a33 i e find the last row in the transition matrix

a J t sin Precipitation 12 Problem 2 The graph below models the monthly average precipitation in inches at a town on a particular mountain over a 3 year period where x is the number of months after April 2020 11 10 9 8 7 5 4 3 2 1 n 2 3 0 0 5 10 D J x 4 COS 2x 15 20 Month x 2 1 25 30 35

The mean cholesterol level of women age 45 59 in Ghana Nigeria and Seychelles is 5 1 mmol l and the standard deviation is 1 0 mmol l Assume that cholesterol levels are normally distributed Round the probabilities to four decimal places It is possible with rounding for a probability to be 0 0000 a State the random variable Select an answer b Find the probability that a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level of 2 7 mmol l or more c Find the probability that a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level of 7 6 mmol l or less d Find the probability that a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level between 2 7 and 7 6 mmol l e Find the probability that randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level that is at least 8 6 mmol l f is a cholesterol level of 8 6 mmol l unusually high for a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles Why or why not Select an answer B What cholesterol level do 44 of all women age 45 59 in Ghana Nigeria and Seychelles have less than Round your answer to two decimal places in the first box Put the correct units in the second box

On which interval s is the following function concave up f x ln x Select all that apply OI 0 00 0 III 0 00 N 4 0 V 0 4 O VI None of the above

rewrite each fraction in terms of the LCD 1 5x 1 x 2 5x 5x 1 x 3

1 Jenna babysits for 15 per hour She also works as a tutor for 20 per hour She can work up to 13 hours this week and she wants to make at least 200 a Write a system of inequalities where x represents the number of hours she babysits and y represents the number of hours she tutors YA 20 19 label your axes and shade the 18 correct region 17 16 15 14 13 12 11 10 9 b Graph the system of inequalities Make sure to 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 c If she knows she has to babysit for 4 hours this week how many hours should she spend tutoring to make the most money Mark this point on your graph

Rewrite the given expression with positive exponents and completely simplify if possible 5 3 17x 5 3 17x

Write the radical 5 0 2 7 2 5 9x y with a rational exponent

Rewrite the following radical with a rational exponent 5 3y

Simplify the given expression 8 8 ly

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

Evaluate the following expression if possible 3 7p 1 3 F 3 30 Pr

Simplify the given expression 3 3 VY

Simplify the given expression 5 5

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

Which function is the inverse of f x O A f x 36x 2 for x 0 O B f x 6x 2 for x 0 O c f 2 36x 2 for x 0 I O D f 2 6x 2 for a 20

Chris puts one tenth of each paycheck into savings Her current paycheck is 200 She decides to also put into savings any amount she earns over 200 The expression below represents the percent of her paycheck that Chris saves when she makes x dollars more than her current paycheck 100 x 20 x 200 Drag and drop the expressions into the boxes to identify their meaning Original ratio of saved to total money per paycheck Final ratio of saved to total money per paycheck Final amount saved per paycheck

Subtract x x 3 x 3x 5 x 2x 8 x 2x 8 O O O O 2 x 2 2x 2 x 2x 8 2 x 4 1 x 1

Solve for x x 3 x 3 O2 O 2 D 4

Which statement best reflects the solution s of the equation 1 1 2 3 3 x 2 x 3 x 3 O There are two solutions x 1 and x 3 O O There is only one solution x 1 The solution x 0 is an extraneous solution There is only one solution x 1 The solution x 3 is an extraneous solution There is only one solution x 3 The solution x 1 is an extraneous solution

Multiply 2 x 3 4x 2 x x 1 10 x 3 Enter your answer in simplest form in the b

Simplify 5 x 6x x 2 Enter your answer in the b

Simplify x 4x 3 2x 1 2 x x 2x2 3x 1 O O x 3 x 1 x 2x 1 x 3 x x 1 x 3 x 1 I x 3 x 1 2x 1

Add x 1 X O O O x 55 x 4x 2x 1 x x 1 T 1 r T 1 I 3x 1 x x 1 22 1 T T 1

Add x 2 52 4 9x2 1 9x 1 O x 2 3xz 1 6x 2 3x 1 2 3x 1 4x 2 97 1

Solve for x 2 x 4 O 1 1 x 2 32 1 2 3 x 2

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