descriptionIn this discussion, you will explore systems and approaches used to solve equations.InstructionsStep 1: Respond to the following:In this module, you have studied several different methods for solving a system of equations. Specifically, you should be familiar with graphing, substitution, elimination-by-addition, matrix approach, and Cramer’s rule. Answer the following questions about these methods to create your post: Is there a method that you feel is best for certain types of systems? What is it and what type of systems do you think it is best used for?What is your favorite method to use to solve systems of equations? Why is it your favorite?What is your least favorite method and why?

Question 51 What is the point of symmetry for the circle (x + 2)2 + (y – 4)2 = 25? (–2, 4) (2, –4) (–4, 2) (4, –2)2 points Question 52 Where are the vertices of the following graph? (-9, 0) and (9, 0) ( , 0) and ( , 0) ( 0 ) and ( 0 ) (0, 2) and (0, -2)2 points Question 53 What is the length of the major axis of the following graph? 8 4 18 92 points Question 54 What are the foci of the following graph? (-7, 3) and (5, 3) (-1- , 3) and (-1 + , 3) (-1- , 3) and (-1 + , 3) (-8, 3) and (6, 3)2 points Question 55 What is the equation of the ellipse with vertices (6, 0), (-6, 0) and co-vertices (0, 2), (0, -2)? 2 points Question 56 What is the equation of the ellipse with foci (0, 7), (0, -7) and vertices (0, 8), (0, -8)? 2 points Question 57 The ellipse has symmetry only through the line x = -5. TRUE FALSE2 points Question 58 What are the co-vertices of the following graph? (0, 1) and (0, -1) (1, 0) and (-1, 0) (0, 8) and (0, -8) (8, 0) and (-8, 0)2 points Question 59 What is the equation of the following graph? 2 points Question 60 What is the center of the following graph? (1, -2) (4, -2) (-1, -2) (2, 0)2 points Question 61 Write the equation of a hyperbola with a center at (-5, -3), vertices at (-5, -5) and (-5, -1) and co-vertices at (-11, -3) and (1, -3). 2 points Question 62 Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5). 2 points Question 63 The symmetry if the hyperbola occurs at the lines x = 3 and y = -5. TRUE FALSE2 points Question 64 What are the odds of picking an “m” in the word Mississippi? 1:09 1:10 1:11 1:122 points Question 65 What is the probability of picking an “m” in the word Mississippi? 2 points Question 66 Experimental probability is based on performing trials. TRUE FALSE2 points Question 67 What is the probability of rolling a number less than 5 on a six sided dice? 2 points Question 68 A bag contains 4 white marbles, 3 black marbles, and 5 red marbles. Find the probability of picking a red marble? 2 points Question 69 Josie had a choice of 3 breads, 4 choices of meat, and 4 choices of cheeses to make a sandwich.How many different sandwiches can she make? 24 36 48 602 points Question 70 A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of picking a red marble, replacing it, and then picking another red marble? 2 points Question 71 A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of picking a blue marble, replacing it, and then picking another blue marble? 2 points Question 72 A bag has 4 green marbles, 3 red marbles, and 3 yellow marbles. What is the probability that you pick a green marble, do not replace it, and pick a red marble? 2 points Question 73 A bag has 4 green marbles, 3 red marbles, and 3 yellow marbles. What is the probability that you pick a yellow marble, do not replace it, and pick another yellow marble? 2 points Question 74 In how many ways can a student arrange 6 textbooks on a locker shelf that can hold 4 books at a time? 30 120 240 3602 points Question 75 In how many ways can a music teacher arrange 24 students in 3 rows? 12,144 9240 10,626 79802 points Question 76 A test consists of 20 problems and students are told to answer any 10 of these questions. In how many different ways can they choose the 10 questions? 168,394 184,756 192,548 203,8322 points Question 77 A pizza place offers 5 different cheeses and 10 different toppings. In how many ways can a pizza be made with 2 cheese and 4 toppings? 2100 1800 1500 12002 points Question 78 Expand (2x - y)5. 32x5 + 80x4y + 80x3y2 + 40xy2 + 10xy4 + y5 32x5 - 80x4y + 80x3y2 - 40x2y3 + 10xy4 - y5 32x5 - 80x4y - 80x3y2 - 40xy2 - 10xy4 - y5 32x5 - 80x4y + 80x3y2 - 40xy2 - 10xy4 + y52 points Question 79 Expand (2x - 3)5. 32x5 - 240x4 + 720x3 - 1080n2 + 810n - 243 32x5 - 240x4 - 720x3 - 1080n2 - 810n - 243 32x5 + 240x4 + 720x3 + 1080n2 + 810n + 243 32x5 + 240x4 + 720x3 - 1080n2 - 810n + 2432 points Question 80 What is the fourth term of (x + y)8? 56x3y5 36x3y5 36x4y4 56x5y32 points Question 81 Find the mean of the following set of data. Round your answer to two decimal places.48, 65, 57, 54, 61, 57, 52, 61, 57 51.2 55.78 56.89 582 points Question 82 Find the mean of the following set of data. Round your answer to two decimal places.48, 65, 57, 54, 61, 57, 52, 61, 57 51.2 55.78 56.89 582 points Question 83 What is the standard deviation of the following data? If necessary, round your answer to two decimal places.46, 53, 38, 67, 46, 57, 61, 42, 63, 55, 46 8.45 8.87 9.12 9.32 points Question 84 What is the standard deviation of the following data? If necessary, round your answer to two decimal places.13, 11, 4, 5, 6, 9, 10, 12, 15, 16 3.91 6.27 4.52 5.782 points Question 85 What sampling method was used in the following scenario?For a survey being taken at the school, an alphabetized list of the students, by their last name, is taken and every fifth student is questioned. Simple Random Sampling Systematic Sampling2 points Question 86 The Greek letter sigma, σ, is use to represent what statistical quantity? mean standard deviation variance range2 points Question 87 What percentage of the data falls outside 1 standard deviation of the mean? 0% 1% 5% 32%2 points Question 88 Suppose you have a normally distributed set of data pertaining to a standardized test. The meanscore is 500 and the standard deviation is 100. What is the z-score of 450 point score? 1.5 1 0.5 -0.52 points Question 89 Suppose you did a survey of male shoes size and the mean of that survey was size 10 with a standard deviation of 1.5. What is the z-score of a size of 12? 1.33 1 0.67 0.332 points Question 90 The following sequence is arithmetic.3, 1, 5, 2, 6, 4…. TRUE FALSE2 points Question 91 What is the d value of the following arithmetic sequence?-16, -9, -2, 5, 12, 19…. 7 -7 -8 82 points Question 92 Find the 2nd term of an arithmetic sequence if t1 = 0 and t5 = 16? 8 6 4 22 points Question 93 Find the 3rd term of an arithmetic sequence with t5 = 3 and t7 = 7. 2 -1 -5 -32 points Question 94 Find S11 for 5 + 1 + (-3) + (-7) +… -165 -173 -187 -1912 points Question 95 The following is a geometric sequence. TRUE FALSE2 points Question 96 What is the r value of the following geometric sequence?4, 7, 12.25, 21.4375 … 1.25 1.5 1.75 1.8252 points Question 97 Find the 6th term of a geometric sequence with t1=5 and r = 2 points Question 98 Find the 8th term in the geometric sequence with t4 = 48 and t6 = 192. 768 1922 points Question 99 Find S7 for the geometric series 2 + -6 + 18 + -54 +… 162 -486 1094 -43742 points Question 100 Find the sum of the following infinite geometric series, if it exists.4 + 3 + 2.25 + 1.6875 +… Does not exist 12 14 162 points

hello i need help with math and it discussion please see the file below thank you for your help