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# Coll Alg Bus MATH 1090

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This 8 page Class Notes was uploaded by Miss Noel Mertz on Monday October 26, 2015. The Class Notes belongs to MATH 1090 at University of Utah taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/229945/math-1090-university-of-utah in Mathematics (M) at University of Utah.

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Date Created: 10/26/15

MATH 1090 Sea 5 Section 15 Solutions of Systems of Linear Equations of solutions 0 l 00 Graph Equations Solving systems of equations 4ziy3 Exll 12 Solve the system of equatlons 21 By 19 ll Substitution method 2 Elimination method 3 Equating two equations can use only if both equations are given in the form of either y or I z 2y 3 Exi2 16 Solve the system of equatlons 31 6y 6 6x 7 4y 16 Ex 22 Solve the system of equatlons 91 7 6y 24 Three equations in three variables Leftto right elimination method will be discussed When we study Chapter 3 Substitution method I 7 3y 7 2 0 EXA 32 Solve the system of equations 1 7 2y 2 8 2x 7 6y 2 6 Application problems Ex 37 One safe investment pays 10 per year7 and a more risky investment pays 18 per year A woman Who has 145600 to invest would like to have an income of 20000 per year from her investmentsi How much should she invest at each rate Exi6 44 A biologist has a 40 solution and a 10 solution of the same plant nutrienti How many cubic centimeters of each solution should be mixed to obtain 25 cc of a 28 solution MATH 1090 Sec 5 Section 65 Loans and Amortization De nition The process of repaying the loan by making all payments of equal size is called amortiza tion Formula If the debt of 14 With interest at a rate ofi per period is amortized by n equal periodic payments at the end of each period the size of each payment is An39l l Exl 4 A loan of 10000 is to be amortized With 10 equal quarterly payments If the interest rate is 6 compounded quarterly What is the periodic payment De nition An amortization schedule is the summary of all the information regarding the amortization of a loan See the table on page 452 De nition An unpaid balance of a loan or payoff amount and outstanding principal of the loan is the present value needed to generate all the remaining payment Formula For a loan of n payments of R per period at interest rate 239 per period the unpaid balance after k payments is the present value of an ordinary annuity With n 7 k payments and 1 7 1 239 WM Unpaid balance 14746 R 2 Ex 14 A debt of 8000 is to be amortized With 8 equal semiannual payments of 128829 If the interest rate is 12 compounded semiannually nd the unpaid balance immediately after the fth payments MATH 1090 Sec 5 Section 05 Operations With Algebraic Expressions De nitions 1 Variables letters that represent7 in general7 real numbers eg7 m a m 2 Algebraic expression an expression obtained by performing operation 7 7 x or extraction of roots with one or more real numbers or variables We usually deal with real numbers eg7 1 2 3 3 Term Real number Variables coef cient 4 Polynomial in z anx an1x 1 mm a0 Where each coef cient ai is a real number for 239 01 ni If an y 07 the degree of the polyno mial is n7 and an is the leading coef cient a0 is the constant termi eigi7 Note 1 If there are more than one variables7 the degree of each term is the sum of the exponents of all the variables eigi7 2 The degree of the polynomial With more than one variables is the degree of the term in the polynomial having the highest degree eigi7 5 Types of polynomials Operations with Algebraic Expressions Ex1 14 Compute 3x3 4z2y2 3m2y2 7 7 Steps 1 Solution 1 Get rid of parentheses 2 Combine like terms77 3 Compute focusing on the coefficients Ex2 16 Compute 4m 7 2723 7 11732 7 11732 7 2m 4723 Ex3 Multiply 8my32m3y73zy2 Steps Solution 1 Combine numbers and same variables 2 Use exponential rule to combine Ex4 Divide 715m2y3 7 3my5 Steps Solution 1 Write as a fraction 2 Simplify with cancellation and and exponential rule Ex5 Find the product 74ab3a2b 4ab2 7 1 Distributive law EX6 Multiply 3m 22m 5 EX7 Multiply 4m2 3mg 4m2z 7 3y miazazzia2 EX8 54 Multiply 3m 43 EX9 Divide 4x3 7 13m 7 22 by m 7 37 where z 7 3 Steps Solution

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