Quadratic equations Questions and Answers

Factor the expression completely over the complex numbers y4 24y 144 Enter your answer in the box

ent Marshall uses the polynomial identity polynomial identity x y x What values can Marshall use for x and y Interim Checkpoint Algebra 2 Checkpoint 1 Part 1 O x 8 and y 64 O x 2 and y 6 O x 64 and y 0 O x 10 and y 2 2xy y to show that 8 64 16 17 18 19 20 21 22 23 24

Solve for x 3x 2x 2 0 Enter your simplified answers as exact values in the boxes X or x

intent What number needs to be added to both sides of the equation to complete the square x 9x 8 Enter your answers in the boxes x 9x 8 Basic 8 Interim Checkpoint Algebra 2 Checkpoint 1 Part 1 9

tent E III Solve the system of equations using the linear combination method 2x 5y 1 3x 4y 13 Enter your answer in the boxes Basic 7 8 Interim Checkpoint Algebra 2 Checkpoint 1 P 9 X y

What is the solution to the inequality 2 2 3 52 9 Enter your answer in the box

47 The larger of two numbers is 17 more than the smaller When added together the sum of the larger number an four times the smaller number is 157 What are the two numbers larger number smaller number 48 Evaluate 3 14

O x 6 Ox 40 25 Ox 40 25 O 6 11 Simplify 6c 2c 8c x 12 Given the formula PV nRT solve for the variable T Hint click the button next to the answer box to make sure your answer is formatted correctly Use parentheses if needed T x 13 Let x 1 y 2 and z 4 Evaluate 2x 1 3x 3y 07 O 11 O 5

x 1 y 1 36 x 1 y 1 16 Choose the correct graph below O A O B L Q O C Q 2

18 Solve the following proportion for a 2 29 36 87 19 Solve for x 9 x 24 8 5x 16 39 O 49 O 53 O 48 20 Use properties of exponents to simplify and then write the answer in radical form 2 rty Oxy

x y 2 0 x y 3y 4x 2 you wish 1 2 EXE Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type an ordered pair Type exact answers using radicals as needed Use a comma to separate answer as need OB There is no solution

K Write the form of the partial fraction decomposition of the rational expression It is not necessary to solve for the constants 4x 5x x 6 What is the form of the partial decomposition of the given expression A B OA x 6 x 6 Ax B OC x 6 Ax B OE x 6 Cx D 6 Cx D Ex F x 6 x 6 SCOOB OB O D Ax B x 6 Ax B x 6 Cx D x 6 x 6 Ax B OF 2

x x 8 3 2 X X x x 8 3 X X Use integers or fractions for any numbers in the expression

the fountain poor area removed has an area of 45 square meters and a perimeter of 48 meters Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool Each length of the large square floor is meters and each length of the small square is meters

e the given conditions to write a system of equations Solve the system and find the numbers e sum of two numbers is 13 If one number is subtracted from the other the result is 3 Find the numbers e two numbers are se a comma to separate answers

measure of the three interior angles What is the measure of angle x X What is the measure of angle y y 0 Thed with variables Find the

The right triangle below is dilated by a scale factor of Find the perimeter and area of the right triangle below as well as the perimeter and area of the dilated right triangle Express your answers as whole numbers decimals or fractions in simplest terms no mixed numbers Figures are not necessarily drawn to scale 25 65 60 Perimeter of given right triangle Area of given right triangle units units Perimeter of dilated right triangle Area of dilated right triangle units units

Subtract 3x 5x 2 2x 5x 4 The constant in the final answer is Select one O a 4 O b 6 O c 6 Od 4

Does the function x x have any horizontal or diagonal asymptotes x 3 x 4 x 10 x 2 Yes the horizontal asymptote is y 1 Yes the horizontal asymptote is y 0 It has a diaogonal asymptote It does not have any horizontal or diagonal asymptotes

K The area of the rectangular piece of cardboard shown below is 198 square inches The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides If the box is to have a volume of cubic inches find the length and width of the cardboard that must be used W The length of the cardboard is inches and the width is inches SZER

The Royal Fruit Company produces two types of fruit drinks The first type is 35 pure fruit juice and the second type is 85 pure fruit juice The compan attempting to produce a fruit drink that contains 40 pure fruit juice How many pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 40 pure fruit juice First fruit drink Second fruit drink pints pints X

Solve for x 4 In x 2 7 Do not round any intermediate computations and round your answer to the nearest hundredth

Solve cos 2 x cos x sin 2 x for 0 degrees x 360 degrees

39 Solve for x 7 18 Check all that apply 11 0 25 0 21 0 24

Round your answer to the nearest hundredth if necessary 46 Use Substitution to solve format your answers as fractions if necessary 30y 12x 90 8y x 15 C y x 47 Solve 82 45 3x 10 C 48 How many milliliters of water must be added to 70 ml of 35 corn starch solution to produce a 30 solution Round your answer to the nearest hundredth

O 6 15 Ob 15 Ob 26 43 Given the formular x tx p i solve for the variable p Hint click the button next to the answer box to make sure your answer is formatted correctly Use parentheses if needed p x 44 Evaluate the expression 18

29 Graph the equation y 0 6x 10 If you have a graphing calculator you may use it Find y when x y 30 What is the mode in the following data set 51 46 56 59 53 41 35 46 61 61 36 60 46 52 42 33 Round your answer to the nearest tenth 31 Solve the following system of equations using the elimination method 4x y 2 4x 2y 6 O x y O x 0 y 1 O 1 v 1

following graph 3x ly 6 and 6x 3y 6 O1r ly 20 and 6x 1y 2 O 1x 3y 2 and 8x ly 6

Analyze the following graph of a system of two equations Identify the coordinates of the solutions to the system More than one answer may be correct check all that apply 0 3 1 2 3 3 0 0 3 0

1 The air pressure decreases as we rise in altitude and increases as we decrease in altitude The graph shown below gives the air pressure as a function of altitude compared to sea level h 0 Determine the domain of this function pressure 100 80 60 40 20 0 O 0 h 25 O 0 h 75 O 0 h 100 25 50 altitude 75

21 Given the two points 3 5 and 3 1 what is the slope of a line passing through both these points Om 6 m 0 Om 6 Om 1 1 Om undefined 22 Simplify completely 180

16 What property is shown here 3x6 5 3 6 5 O Commutative Property O Associative Property O Distributive Property O None 17 The distributive property is best illustrated by which equation O 10a 4b 2 5a 26 O 10a 4b 4a 106 O 10a 4b 10 4 a b 10a 4b 2 5 a 2 2 6

Two ordered pairs that are solutions of the equation 2y 3x 8 are O 0 4 7 2 O 0 4 2 7 4 0 4 2 O 4 0 2 7 6 Simplify completely 6 5 O 6 11 5 O6 11 5 5 O 6 11 5 5

43 What is the mathematical property demonstrated in the following equation 5x7 7x5 O Distributive Property O Associative Property O Commutative Property O None 44 There are 36 bikes in a store 18 pairs 2 pair s are orange 15 pairs are green and the rest are purple If you took out a purple bike and you didn t put it back what is the probability that you pull out another purple bike If you enter your answer as a decimal round to the thousandths place

According to the Motley Fool in a recent year there were 146 7 million personal federal tax returns filed and the average amount of tax paid per filer was 9882 Write each of these numbers in scientific notation 146 7 million is 1 467 x 10 9882 9 882 x 10 Part 1 4 Part 2 of 4 How much money total did the government take in from these taxpayers Perform the calculation in scientific notation and write how your answer would be pronounced Round your answer to six decimal places The government took in S dollars x 10 which is Choose one Choose one Choose one trillion X

B Felicia purchased an investment property for 102 450 Her annual expenses for mortgage interest taxes repairs and depreciation total 7 105 She rents the house to someone for 975 a month What is the annual net income of the investment property 3 points

12 Richard purchased a 1 000 bond at a quoted price of 88 5 The bond pays annual interest at a rate of 4 What is the cost of the bond and the annual interest earned 4 points

Myra paid 1 975 for 50 shares of stock They sold for 45 60 a share There was no commission charge What was their profit or loss 3 points

It is estimated that there were 51 3 billion pieces of trash on 79 million miles of roadways in a recent year On average how many pieces of trash were on each mile of roadway About pieces of trash were on each mile of roadway Use scientific notation Use the multiplication symbol in the math palette as needed Type an integer or decimal rounded to four decimal places as needed

8x 3x 3x 1 The degree of the first term is of the polynomial the leading term the leading coefficient and the degree of the polynomial

Suppose that 18 000 is invested at 3 compounded quarterly How much is in the account at the end of 5 years Use the compound interest formula A P1 A P 1 The amount in the account at the end of 5 years is Do not round until the final answer Then round to the nearest cent as needed

9 5 8 3 2 6 3 3 2 Round to the nearest thousandth

inches long by 2 4 inches high a What is the surface area of the pencil box 0 5 in b Layne just placed an eraser with the dimensions shown below in the pencil box What is the volume of the pencil box not taken up by the eraser eraser 2 in shape 2 in 5 5 in 0 4 2 4 in

R Find the shortest distances between a the point 2 1 5 and the line x b the point 0 3 8 and the line 21 1 x2 2 x3 3 1 4 c X the point 11 2 1 and the line of intersection of the planes X 1 0 and 3 2 A 5 x A 3 E 1 3 1

Suppose the vector C 6 is in the nullspace of the matrix d 1 5 287 3 2 19 4 1 7 Determine c and d giving your answers exactly or accurate to 2 decimal places c Number d Number

The area of the rectangular piece of cardboard shown below is 238 square inches The cardboard is used to make an open box by cutting a 3 inch square from each corner and turning up the sides If the box is tw cubic inches find the length and width of the cardboard that must be used W L The length of the cardboard is inches and the width is inches

For the differential equation y 5y 4y 88e7t a State the characteristic polynomial for the differential equation b List the roots of the characteristic polynomial c List y and y2 d Find the homogeneous solution to the differential equation In your answer use A and B to denote the arbitrary constants Y t e Find the non homogeneous solution to the differential equation Y t f State the general solution y t g Find the particular solution satisfying y 0 3 and y 0 8 y t

7 10 pts Given the following piecewise function graph it and then answer the other questions if x 2 x 1 2 x Domain Range What is f 4 What is f 2 What is f 8 f x if x 20 if 2 x 0

Find the inverse of each function 11 5 x x X 3 x 1 2 2 2x 2 2 Y f x x 1 2 7 n 5 2 n 9 f x 5 1 x 6 S x x 6 3 8 f n Sn 8 3 10 f x 5x 1

D 6 points Find the exact values in the form a b e of the other two roots of y x 68x 32 given that 8 is one of its roots