Course: MATH 1414 Master 2017/2018

pls answer all

chapter 1

1. Evaluate the given expression if x = - 2 and y = 3. 3x + 5y 3+ 4y 3x + 5y (Type an integer or a simplified fraction.) 3+4y12. Divide as indicated. x2 - 9 x2 +6x+9 3x - 3 x2+ 2x - 3 Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) x- - 9 x2+ 6x+9 O A. X# 3x - 3 x4 + 2x - 3 x2 - 9 x2 + 6x+9 OB. = , no numbers must be excluded. 3x - 3 x+ 2x - 316. Solve and check the following linear equation. 16 = 3(x - 1) - (x - 5) What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is O B. The solution set is {x | x is a real number). O C. The solution set is .20. The accompanying bar graph shows the percentage of adults in a certain city who smoked cigarettes for selected 50- years from 1970 through 2010. 40- The mathematical model p + 2 =29 describes the 30% 30- 25% percentage who smoke percentage, p. of adults who smoked cigarettes x years 21% 20- 16% after 1970. Use this information to answer questions (a) and 11% (b) below. 10- 1970 1980 1990 2000 2010 year (a) Does the mathematical model underestimate or overestimate the percentage of adults who smoked cigarettes in 2010? By how much? Select the correct choice below and fill in the corresponding answer box to complete your choice. O A. The model underestimates the actual value by %. O B. The model overestimates the actual value by %. (b) Use the model to project the year when only 7% of adults in this city will smoke cigarettes. The year predicted is24. Solve the equation using the quadratic formula. x2 - 6x + 34 =0 The solution set is { (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)28. Solve the following equation by making an appropriate substitution. 2: - 9x1 '2 + 9 = 0 Make an appropriate substitution and rewrite the equation in quadratic form. Let u = . then the quadratic equation in u is Solve the equation. Select the correct choice below and. it necessary. ll in the answer box to complete your choice. {31' A- The solution set is { H'- {Simplily your answer. Use a comma to separate answers as needed] C? B. The solution set is the empty set. 4. Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between seven times a number and two more than two times the number. What is the algebraic expression? (Do not simplify.) What is the simplified expression?8. Factor the difference of two squares. 4x - 25 Select the correct choice below and fill in any answer boxes within your choice. O A. 4X2 - 25= O B. The polynomial is prime.1. Find values for the variables so that the following matrices are equal. X 6y 10 18 Z 3 8 3 X= (Simplify your answer.) y= (Simplify your answer.) Z= (Simplify your answer.)12. Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution. 2w + 3x + 4y - 2z = 12 w+ x+ y- z= 3 3w + x -3y - 2z= - 10 -w+ 3x + 3y - 3z= 1 The solution set is . (Simplify your answers.) O B. There are infinitely many solutions. The solution set is z) }, where z is any real number. (Type expressions using z as the variable.Use integers or fractions for any numbers in the expression.) O C. There is no solution. The solution set is O.20. Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. x + 4y + 52 = 6 y - 42 = 0 Select the correct choice below and fill in any answer boxes within your choice. O A. There is one solution. The solution set is (Simplify your answers.) O B. There are infinitely many solutions. The solution set is z) }. where z is any real number. (Type expressions using z as the variable. Use integers or fractions for any numbers in the expressions.) O C. There is no solution. The solution set is O.24. Find the products AB and BA to determine whether B is the multiplicative inverse 01A. E E 3 15 5 3 568 1 1 A=589 B= - 0 3 3 593 _1 1-1 3 3 AB: EA: Is B the multiplicative inverse of A? ._ No 1:;- Yes 28. Write the system below in the form AX = B. Then solve the system by entering A and B into a graphing utility and computing A " B. 5x - y + 3z = 17 2x + 2y + 32 = -1 2x - 3y + 3z = 19 Write the system in the form AX = B. (Type an integer or a simplified fraction for each matrix element.) The solution set, {(x.y.z)}, is . (Type integers or fractions.)4. Find (if possible) a. AB and b. BA -9 -9 3 A= B = 9 3 9 a. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. AB = (Simplify your answers.) O B. This matrix operation is not possible. b. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. BA = (Simplify your answers.) O B. This matrix operation is not possible.8. Write the augmented matrix for the system of equations 5x - 5y + 2z = -9 to the right. 7x - 9y = 5 5x - 5z = -6 Enter each element. (Do not simplify.)