Algebra Questions

If o 3 are acute angles such that sin a and cos 3 calculate cos a 3 If your answer is a fraction type it using the symbol For example if the answer is write 3pi 2

Vrite the given sentences as a system of inequalities in two variables Then gr ne system The sum of the x variable and the y variable is no more than 5 The y variable ess than the difference between the square of the x variable and 2 Complete the system of inequalities in two variables first sentence 18 second sentence Type inequalities Simplify your answer

5 Consider the sequence an defined by the recursion for n 3 4 5 an an 1 1 4 An 2 a Calculate h such that an h 1 fulfills the recursive definition 1 b What is the limit of the sequence an if it exists

Calculate the 3x3 determinant 6 0 1 3 277 1 3

52 22 6 Consider the matrix A a Find an orthogonal matrix P and a diagonal matrix D such that A PDPT b Compute A77 and leave your answer as a product of 3 matrices leave numbers in calculator form

In the diagram shown below two ships are at points P and Q The ships are in the same vertical plane as an airplane at point R When the height of the plane is h 3650 feet the angle of depression from point R to point P is 58 degrees and the angle of depression to Q is 41 degrees Determine the distance between the two ships Enter an exact expression or round to the nearest whole number To present an angle in degrees type deg or use the MathPad degree symbol For example sin 30deg P distance from P to Q ft Q

For this problem consider a triangle with side lengths A B C with opposite angles a B Y respectively Suppose that A 2 B 5 C 39 Calculate y in degrees Enter only a numerical value Do not type degrees 30

Use a system of linear equations to find the quadratic function f x ax bx c that satisfies the given conditions Solve the system using matrice 2 2 f 1 2 2 14 F x

Use the dot product to find the magnitude of u u 9 12

Multiply 8 14 21 Enter your answer in simplest radical form in the box

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

III x 4 y x 1 y 2x 2 y 4 y x 1 y 2x 2 x 4 y x 1 Interim Checkpoint Algebra 2 Checkpoint 1 Part 1 WEX 543211 Simp 345 D

tent III Simplify 261 o i 01 0 1 Inte

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

Simplify 3 2i 5 4i 0 2 22 8 6i 0 2 2i 0 8 2i

Multiply 7x 4 4x 3 Enter your answer in standard form in the box 7 8 B

Gerry is a restaurant manager and plans to advertise her restaurant The advertising budget is 5000 and she plans to run television and online ads She would like to run at least 5 television ads and 10 online ads A television ad costs 500 and an online ad costs 150 Let x represent the number of television ads and y represent the number of online ads Two of the constraints for this situation are 5 and y 10 What is the other constraint for this situation Enter your answer in the boxes

Which expression is equal to O O 3 3 5 3 5 5 5 3 3 9 45

Factor the expression over the complex numbers x 24 Enter your answer in the box

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

11 Solve for x 10 5 25 45 Enter your answer as one inequality in the box 7 Interim Checkpoint Algebra 2 Chee 8 9

Factor 3ab 66 2bc ac O O O a 2b c 3b a 2b 3b c a 2b c 3b a 2b 3b c

Add 4x 5x x 1 2x4 7x 6x 2x Enter your answer in standard form in the box

What is the product of 5 Enter your answer in standard form in the box Basic 7 4 8 of 5 2i and 3 4i 5 9 6 X X X

What is the radical form of the expression 2z y5 O 2x y8 8x12y15 64x32 y 40 2x 2 y 15 Interim Checkpoi

Simplify 7 50 6 24 Enter your answer in simplest radical form in the box

VUITE IN A 0 2x 3x 5 X X X x 3 i 50 4 3 i 31 4 3 i 15 2 3 6i 4

What are the roots of the equation 2x x 6 Select each correct answer 3 10 2 0 1 1 3 0

E 2x 3y6 5 3 2 5 4 3 2 1 54 3 C Interim Checkpoint Algebra 2 Checkpoint 1 Part 1 O 5 3 2 1 5 4 3 2 1

we JII Subtract 2x 2x 8x 2 x 5x 2x 7 Enter your answer in standard form in the box Basic 7 Interim Checkpoint Algebra 2 Checkpoint 1 Part 1 8 9 0

5 Islamic calligraphy is the art of A writing in a beautiful and elegant manner OB weaving textiles with floral and geometric designs C painting rapidly in watercolor on wet plaster OD sculpting a pot and decorating it with geometric shapes

variation is 23 What is the median in the following data set 32 15 27 18 28 18 28 22 41 17 31 12 36 Round your answer to the nearest tenth 24 Simplify 5w 12 8 w 5 0 12 the constant of 25 Solve for a 10x 7 30x 21 O x 0 Ox all real numbers O has no solution 26 Convert to slope intercept form 8 321 12 x

35 What is the scale factor if a 6 inch by 6 inch photograph is enlarged to a poster that is 4 ft by 4 ft 4 ft 48 in 0 t t O Ott 08 O 1 5 36 How many ml of 60 percent acid should be added to pure acid to make 50 ml of 85 percent acid O 18 75 ml O 1 88 ml 9 38 ml 37 Rewrite the following expression as a fraction times the variable 9a

rational O irrational 39 Simplify completely 16 40 Bill is going into business selling homemade sandals The supplies for each sandal cost him 3 07 and he wants to earn at least 18 00 for each sandal to compensate for his time The best cost equation the cost of the sandal when you sell it for this situation is Use x to represent the number of sandals C 41 Change the equation x 8y 5 0 into an equivalent equation written in the slope intercept form O y x 1 Oy x 1 O y fx 1

42 The temperature from midnight to noon on March 15 can be modeled using the function T h 4 2 h 42 where T temperature and h hours relative to noon note h 0 represents noon Find the domain of the function O 12 h 0 O 0 h 12 O 6 h 0 O 12 h 12 43 75 of 400 is O 10 O 30 O 100 O 300 44 Linear relations are not functions when they appear graphically as O horizontal lines Overtical lines

O 9 and 1 O9 and 1 O 9 and 1 33 Write and solve the equation based on the following diagram x X X 1 34 The point 3 0 is found in quadrant O IV O I ON

45 Solve the inequality set Graph the solution on a numberline 13 11 and x 6 5 O 2 and x 11 O 2 and x 11 O 11 O 2 O all real numbers Ono solution 46 Graph the following system on a sheet of paper or graphing utility 3 and y 5 Determine which of the following points if any satisfy the system More than one answer may be correct check all correct answers 4 9 0 1 3 9 0 5 2 11 3 1 8 11

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

25 Solve for a 10x 7 30x 21 x 0 O X O has no solution all real numbers 26 Convert to slope intercept form 8x 3y 12 y 27 Graph the equation y 0 8x 1 If you have a graphing calculator you may Find a when y 1 3

29 Replace the with the correct symbol or which will make a true statement from the following expression 1 2 V 11 30 Is AGHI a right triangle if the length of the three sides are 13 11 and 21 O cannot be determined O no O yes 31 Solve the systems of linear equations using a graphing method y 3x 17 y 4x 11 O 5 4 O 4 5 O 5 5 Ono solution parallel lines

10 the ratio of their areas is what Mark all correct answers more than one answer may be correct 02 1 4 to 1 2 to 1 04 1 y k 2 1 04 1 6 Solve the equation below and find the variation constant k Find y when x 86 if y varies inversely as x and y 101 when x 13 Round your answer to the nearest thousandth if necessary x 7 Solve for x x 1x 1 Write your answer as a fraction

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

K Graph the solution set of the following system of inequalities x 1 y 1 36 x 1 y 1 16 Choose the correct graph below O A Ay OB Ay Q O C Q OD

15 Find the mean the median and the mode of the temperatures 61 89 93 102 45 89 O mean 95 8 median 97 5 mode 89 O mean 79 8 median 89 mode 1 O mean 95 8 median 89 mode O mean 79 8 median 97 5 mode 89 real numbers x irrational numbers whole numbers 16 To which number set s does the following number belong 11 Multiple answers may be correct Mark all correct answers rational numbers 89 integers 89

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

1 There are 48 socks in a drawer 24 pairs 2 pair s are silver 6 pairs are white and the rest are indigo If you took out a indigo sock and you didn t put it back what is the probability that you pull out another indigo sock If you enter your answer as a decimal round to the thousandths place x 2 Evaluate 5 5 9x8 5 O 84 O 77 O 80 82 3 Use Substitution to solve 1x 22 2y y x 2 3 y quation of a line passing through points 28 71