Algebra Questions

What are the solutions for the given equations below

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

Select Yes or No to indicate whether each ordered pair is a point of intersection between the line y x 1 and the parabola y x 1 Ordered Pair 0 1 1 2 2 0 Yes No 0 0

A radical expression is shown below What is the simplified form of this expression 150

What are the solutions for the given equations bel 2x 7 1

Solve the system of equations x 2 y 2 x

Solve the system of equations y 6x 16 y x 7

A The system of equations below is represented by which of the following graphs P y 3 x 1 y 2x 5 C 19 dn 44 Y o d B D 39 40 17 T 24 24 44 7 9 5

2 y 4x 6y 4 0 6 5 4 3 2 1 5 4 3 2 1 0 T 2 3 2 N 3 4 5 to 6

Determine if the point P 3 6 is on a circle centered at 1 3 with a radius of 5 units

The complex number 6 3i represents which radical expression below A 6 9 B 6 3 C 6 9 D 6 6

2 Find the exact value of the following logarithmic expression logs

The complex number 9 6i represents which radical expression below A 9 36 B 9 36 C 9 36 D 9 36

ne complex number 9 3i 5 represents which radical expression below 0 A 9 45 B 9 i 15 C 9 45 D 9 45

7 At a local garden shop the price of plants includes sales tax The cost of 4 large plants and 8 medium plants is 40 The cost of 5 large plants and 2 medium plants is 28 a Ifl is the cost of a large plant and m is the cost of a medium plant write a system of equations that models this situation b Could the cost of one large plant be 5 50 and the cost of one medium plant be 2 25 Justify

3 The graph of a quartic function f is shown on the ry coordinate plane Write an equation for f 2 A 12 8 0 4 8 1 2 16

The value of Tony s investment was 1140 on January 1st On this date three years later investment was worth 1824 The average rate of change for this investment was 19 p 4 year 1 day 2 month 3 quarter

4 If the function f x 1 0 1 2 3 3 0 1 1 2 x has the domain 0 1 4 9 what is its range 2 0 1 16 81 4 0 1 1 2 2 3 3 16 16 81 813

6 Solve algebraically for y 4 y 3 4 2y 1

2 A function is defined as K x 1 54 2 0 2x P 1 5x 3 The value of K 3 is 4 3 36 18

5 Is the product of 16 and rational or irrational Explain your reasoning

L Given 7x 2 58 which number is not in the solution set 1 6 2 8 4 12 3 10

7 Decide if each set of conditions is possible If so give an example If not explain why not a A 5th degree polynomial with no turning points b A 3rd degree polynomial with three turning points c A 4th degree polynomial with two turning points

Use the parent function f x b and transformation techniques to graph g x e 3 3 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of g Select all transformations that apply Vertically compress the graph of f by a factor of 3 Horizontally compress the graph of f by a factor of 3 Horizontally stretch the graph of f by a factor of 3 Shift the graph of f 3 units down Vertically stretch the graph of f by a factor of 3 Reflect the graph of f about the y axis Shift the graph of f 3 units to the left Shift the graph of f 3 units to the right Shift the graph of f 3 units up Reflect the graph of f about the z axis

5 The graphs of a function and its derivatives y f x y f x and y f x are shown Determine which graph is which f x f x f x Let A represent graph with thin solid line Let B represent graph with thick solid line Let C represent graph with dotted line

1 For F ax by find F dr across the first quadrant of the circle with radius 2 centered at the origin and oriented counterclockwise 8 points

Choose the end behavior diagram that best describes the function f x 6 x 1x Choose the correct diagram below O A O C O B O D

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

Let g x 2 3x 4 x 1 x 3 be a polynomial function Name all horizontal and vertical intercepts of the graph

The graph of a logarithmic function is given Select the function for each graph from the given options y log g x y log gx y 1 log gx y log gx 1 y log g x 1 y log g 1 x y log gx y log g x Drag each function given above into the area below the appropriate graph depending on which function is represented by which graph 65 Q 66 Q 67 Q68 12 10 8 6 4 2 X 2461 L X N 468 Q

D 790426ab090 2 simplify 6a 5a 8 2 4a 6a O O 2a 14a 4 2a 11a 4 O 2a 14a 1 2a 11a 10 3 Simplify 6n 4n 3 8n 6n 1 12n 4 O

3 Which value for x below is a solution to the equation 2x 8x 20 5x a 1 b 2 p 4 d 5

The pH of a chemical solution is given by the formula pH log 0 H where H is the concentration of hydrogen ions in moles per liter Values of p 10 range from 0 acidic to 14 alkaline Answer parts a through f po ype all meyer un autcimal d What happens to pH as the hydrogen ion concentration decreases pH decreases O pH increases e Determine the hydrogen ion concentration of a solution with pH 3 2 H M Round to six decimal places as needed f Determine the hydrogen ion concentration of a solution with pH 7 8 COB

5 no calculator what is the value of 4x 5 if x 3

Which expression below is equivalent to 3 2x 4 3 x 5 3x 27 03x 27 9x 27 3x 3

5 poir After 3 days a sample of radon 222 decayed to 58 of its original amount What is t half life of radon 222 to 2 decimal place

2 Which values for x below are solutions to the inequality 5 x 2 a 10 b 20 c 2 2 d 6 e 9

The pH of a chemical solution is given by the formula pH log 10 H where H is the concentration of hydrogen ions in moles per liter Values of pH range from 0 acidic to 14 alkaline Answer parts a through f a What is the pH of a solution for which H is 0 001 pH Type an integer or a decimal b What is the pH of a solution for which H is 0 0001 pH Type an integer or a decimal c What is the pH of a solution for which H is 0 00001 pH Type an integer or a decimal d What happens to pH as the hydrogen ion concentration decreases

2 Identify the value for x that is not a solution to the inequality 4 4x 8 a 0 b 2 c 3 d 10

4 Simplify 4x 8x 3x 6x O O 21x 0 7x 14x 12x 14x 12x 17x 4x 14x

3 Simplify 6n 4n 3 8n 6n 1 O O 12n 4 17n 4 11n 17n 4 4n 17n 4 4 Simplify

Questions 8 9 10 11 12 Find the area of the shaded region 2x 3 2 simplify 3x 2 4x 5 6a 5a 8 2a 14a 4 x 8 zoom in 2 4a 6a 1 Write an expression that represents the area that is shaded Type a response

Consider the following f x 1 X 4 a State the domain of the function all real numbers x except x 4 O all real numbers x O all real numbers x except x 4 O all real numbers x except x 4 and x 4 all real numbers x except x 1

2 Identify the value for x that is not a solution to the inequality 4 4x 8 a 0 b 2 c 3 d 10

Find the exact value of the logarithm without using a calculator In 2 e 12

Fill in the blank with an inequality symbol for the following statements that can be satisfied by the value x 2 3x 4 2x 2 3x 4 2x 4 2x 4 4x 3 x 4 12 10 2x 5 5x 10 4x5 2x 24 x 1

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

Quickwrite Is x 4 a solution to the equation and the inequality shown below 3x 2 10 3x 2 10 a equation only b inequality only c both the equation and the inequality d neither the equation nor the inequality Explain

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

9 Which value of x below is a solution to the inequality 3x 2x 8 0 a 3 b 2 c 1 d 0