Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition
11th Edition
ISBN: 9781285464657
Author: Soo T. Tan
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5.4, Problem 17E
EXERCISE PROGRAM As part of her fitness program, Karen has taken up jogging. If she jogs 1 mi the first day and increases her daily run by
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(3) (4 points) Given three vectors a, b, and c, suppose:
|bx c = 2
|a|=√√8
• The angle between a and b xc is 0 = 135º.
.
Calculate the volume a (bxc) of the parallelepiped spanned by the three vectors.
Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE:
Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator.
1. If the denominator does not go to 0, you should be able to right down the answer immediately.
2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided.
3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing.
So, group your limits into these three forms and work with them one group at a time.
(a) lim
t-pi/2
sint-√ sin 2t+14cos ² t
7
2
2
2cos
t
(b) lim
sint + sin 2t+14cos
=
∞
t-pi/2
2
2cos t
(c) lim
cost-√sin 2t+14cos² t
=
t-pi/2
2cos t
(d) lim
t→pi/2
cost+√ sin t + 14cos
2cos ² t
=
∞
(e) lim
sint-v sin
2
t + 14cos
=
0
t-pi/2
(f) lim
t-pi/2
sin t +√ sin
2sin 2 t
2
t + 14cos
t
2sin t
cost-
(g)…
Think of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector a--b geometrically?
Chapter 5 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition
Ch. 5.1 - Explain the difference between simple interest and...Ch. 5.1 - Prob. 2CQCh. 5.1 - Prob. 3CQCh. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Find the accumulated amount at the end of 9months...Ch. 5.1 - Find the accumulated amount at the end of 8months...Ch. 5.1 - Prob. 5ECh. 5.1 - A bank deposit paying simple interest at the rate...Ch. 5.1 - Prob. 7E
Ch. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Determine the simple interest rate at which 1200...Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - In Exercises 21-24, find the effective rate...Ch. 5.1 - Prob. 22ECh. 5.1 - In Exercises 21-24, find the effective rate...Ch. 5.1 - In Exercises 21-24, find the effective rate...Ch. 5.1 - In Exercises 25-28, find the present value of...Ch. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Find the accumulated amount after 4years if 5000...Ch. 5.1 - Prob. 30ECh. 5.1 - CONSUMER DECISIONS Mitchell has been given the...Ch. 5.1 - COURT JUDGMENT Jennifer was awarded damages of...Ch. 5.1 - BRIDGE LOANS To help finance the purchase of a new...Ch. 5.1 - CORPORATE BONDS David owns 20,000 worth of 10-year...Ch. 5.1 - MUNICIPAL BONDS Maya paid 10,000 for a 7-year bond...Ch. 5.1 - TREASURY BILLS Isabella purchased 20,000 worth of...Ch. 5.1 - TREASURY BILLS Maxwell purchased 15,000 worth of...Ch. 5.1 - COMPARING INVESTMENT RETURNS The value of Marias...Ch. 5.1 - Prob. 39ECh. 5.1 - INVESTMENTS The value of Jacks investment...Ch. 5.1 - INVESTMENTS The value of Arabellas stock portfolio...Ch. 5.1 - Write Formula 1b in the slope intercept form, and...Ch. 5.1 - HOSPITAL COSTS If the cost of a semiprivate room...Ch. 5.1 - Prob. 44ECh. 5.1 - HOUSING APPRECIATION The Kwans are planning to buy...Ch. 5.1 - Prob. 46ECh. 5.1 - PENSION FUNDS The managers of a pension fund have...Ch. 5.1 - RETIREMENT FUNDS Five and a half years ago, Chris...Ch. 5.1 - MUTUAL FUNDS Jodie invested 15,000 in a mutual...Ch. 5.1 - TRUST FUNDS A young man is the beneficiary of a...Ch. 5.1 - INVESTMENT PLANNING Find how much money should be...Ch. 5.1 - PROMISSORY NOTES An individual purchased a 4-year,...Ch. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - COMPARING RATES OF RETURN In the last 5 years,...Ch. 5.1 - COMPARING RATES OF RETURN Fleet Street Savings...Ch. 5.1 - LOAN CONSOLIDATION The proprietors of The Coachmen...Ch. 5.1 - Prob. 58ECh. 5.1 - ZERO COUPON BONDS Juan is contemplating buying a...Ch. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Prob. 64ECh. 5.1 - SAVING FOR COLLEGE Having received a large...Ch. 5.1 - Prob. 66ECh. 5.1 - REAL ESTATE INVESTMENT An investor purchased a...Ch. 5.1 - Prob. 68ECh. 5.1 - Prob. 69ECh. 5.1 - Prob. 70ECh. 5.1 - Prob. 71ECh. 5.1 - Prob. 72ECh. 5.1 - Prob. 73ECh. 5.1 - Prob. 74ECh. 5.1 - Prob. 75ECh. 5.1 - Prob. 76ECh. 5.1 - Prob. 77ECh. 5.1 - Prob. 78ECh. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.1 - Prob. 81ECh. 5.1 - Prob. 82ECh. 5.1 - Prob. 83ECh. 5.1 - Prob. 84ECh. 5.1 - Optional In Exercises 7986, use logarithms to...Ch. 5.1 - Prob. 86ECh. 5.1 - Prob. 1TECh. 5.1 - Prob. 2TECh. 5.1 - Prob. 3TECh. 5.1 - Prob. 4TECh. 5.1 - Prob. 5TECh. 5.1 - Prob. 6TECh. 5.1 - Prob. 7TECh. 5.1 - Prob. 8TECh. 5.1 - Prob. 9TECh. 5.1 - Prob. 10TECh. 5.1 - Prob. 11TECh. 5.1 - Prob. 12TECh. 5.2 - Is the term of an ordinary annuity fixed or...Ch. 5.2 - Prob. 2CQCh. 5.2 - Prob. 3CQCh. 5.2 - Prob. 4CQCh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 2ECh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 4ECh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 6ECh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - In Exercises 9-14, find the present value of each...Ch. 5.2 - Prob. 14ECh. 5.2 - IRAs If a merchant deposits 1500 at the end of...Ch. 5.2 - SAVINGS ACCOUNTS If Jackson deposits 100 at the...Ch. 5.2 - SAVINGS ACCOUNTS Linda has joined a Christmas Fund...Ch. 5.2 - KEOGH ACCOUNTS Robin, who is self-employed,...Ch. 5.2 - INVESTMENT ANALYSIS Karen has been depositing 150...Ch. 5.2 - RETIREMENT PLANNING As a fringe benefit for the...Ch. 5.2 - INVESTMENT ANALYSIS Luis has 150,000 in his...Ch. 5.2 - AUTO LEASING The Betzes have leased an auto for 2...Ch. 5.2 - SAVINGS ACCOUNTS The Pirerras are planning to go...Ch. 5.2 - INSTALLMENT PLANS Mikes Sporting Goods sells...Ch. 5.2 - Prob. 25ECh. 5.2 - LOTTERY PAYOUTS A state lottery commission pays...Ch. 5.2 - PURCHASING A HOME The Johnsons have accumulated a...Ch. 5.2 - PURCHASING A HOME Refer to Exercise 27. If local...Ch. 5.2 - Prob. 29ECh. 5.2 - SAVINGS PLAN Lauren plans to deposit 5000 into a...Ch. 5.2 - FINANCIAL PLANNING Joe plans to deposit 200 at the...Ch. 5.2 - INVESTMENT ANALYSIS From age 25 to age 40, Jessica...Ch. 5.2 - ROTH IRAS Suppose that Jacob deposits 3000/year...Ch. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 1TECh. 5.2 - Prob. 2TECh. 5.2 - Prob. 3TECh. 5.2 - Prob. 4TECh. 5.2 - Prob. 5TECh. 5.2 - Prob. 6TECh. 5.2 - Prob. 7TECh. 5.2 - Prob. 8TECh. 5.3 - Write the amortization formula. a. If P and i are...Ch. 5.3 - Prob. 2CQCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - In Exercises 1-8, find the periodic payment R...Ch. 5.3 - Prob. 4ECh. 5.3 - In Exercises 1-8, find the periodic payment R...Ch. 5.3 - Prob. 6ECh. 5.3 - In Exercises 1-8, find the periodic payment R...Ch. 5.3 - Prob. 8ECh. 5.3 - In Exercises 9-14, find the periodic payment R...Ch. 5.3 - Prob. 10ECh. 5.3 - In Exercises 9-14, find the periodic payment R...Ch. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Suppose payments were made at the end of each...Ch. 5.3 - Suppose payments will be made for 612 years at the...Ch. 5.3 - Suppose payments will be made for 914 years at the...Ch. 5.3 - LOAN AMORTIZATION A sum of 100,000 is to be repaid...Ch. 5.3 - Prob. 20ECh. 5.3 - HOME MORTAGES Complete the following table which...Ch. 5.3 - FINANCING A HOME The Flemings secured a bank loan...Ch. 5.3 - FINANCING A CAR The price of a new car is 20,000....Ch. 5.3 - FINANCIAL ANALYSIS A group of private investors...Ch. 5.3 - FINANCING A HOME The Taylors have purchased a...Ch. 5.3 - FINANCIAL PLANNING Jessica wants to accumulate...Ch. 5.3 - SINKING FUNDS A city has 2.5 million worth of...Ch. 5.3 - TRUST FUNDS Carl is the beneficiary of a 20,000...Ch. 5.3 - SINKING FUNDS Lowell Corporation wishes to...Ch. 5.3 - SINKING FUNDS The management of Gibraltar...Ch. 5.3 - RETIREMENT ACCOUNTS Andrea, a self-employed...Ch. 5.3 - STUDENT LOANS Joe Secure a loan of 12000 3years...Ch. 5.3 - RETIREMENT ACCOUNTS Robin wishes to accumulate...Ch. 5.3 - FINANCING COLLEGE EXPENSES Yumis grandparents...Ch. 5.3 - IRAs Martin has deposited 375 in his IRA at the...Ch. 5.3 - RETIREMENT PLANNING Jennifer is the owner of a...Ch. 5.3 - Prob. 37ECh. 5.3 - FINANCING A CAR Darla purchased a new car during a...Ch. 5.3 - AUTO FINANCING Dan is contemplating trading in his...Ch. 5.3 - AUTO FINANCING Paula is considering the purchase...Ch. 5.3 - FINANCING A HOME Eight years ago, Kim secured a...Ch. 5.3 - FINANCING A HOME Sarah secured a bank loan of...Ch. 5.3 - PERSONAL LOANS Two years ago, Paul borrowed 10,000...Ch. 5.3 - INVESTMENT ANALYSIS Since he was 22 years old, Ben...Ch. 5.3 - BALLOON PAYMENT MORTGAGES Emilio is securing a...Ch. 5.3 - BALLOON PAYMENT MORTGAGES Olivia plans to secure a...Ch. 5.3 - HOME REFINANCING Four years ago, Emily secured a...Ch. 5.3 - HOME REFINANCING Five years ago, Diane secured a...Ch. 5.3 - REFINANCING A HOME The Sandersons are planning to...Ch. 5.3 - REFINANCING A HOME Josh purchased a condominium 5...Ch. 5.3 - Prob. 51ECh. 5.3 - ADJUSTABLE-RATE MORTGAGES George secured an...Ch. 5.3 - Prob. 53ECh. 5.3 - REFINANCING A HOME: The Martinezes are planning to...Ch. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - HOME AFFORDABILITY: Suppose that the Carlsons have...Ch. 5.3 - Prob. 58ECh. 5.3 - Prob. 1TECh. 5.3 - Prob. 2TECh. 5.3 - Prob. 3TECh. 5.3 - Prob. 4TECh. 5.3 - Prob. 5TECh. 5.3 - Prob. 6TECh. 5.3 - Prob. 7TECh. 5.3 - Prob. 8TECh. 5.3 - Prob. 9TECh. 5.3 - Prob. 10TECh. 5.4 - Suppose an arithmetic progression has first term a...Ch. 5.4 - Prob. 2CQCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Find the sum of first 15 terms of the arithmetic...Ch. 5.4 - Prob. 10ECh. 5.4 - Find the sum of odd integers between 14 and 58.Ch. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - SALES GROWTH Moderne Furniture Company had sales...Ch. 5.4 - EXERCISE PROGRAM As part of her fitness program,...Ch. 5.4 - COST OF DRILLING A 100-ft oil well is to be...Ch. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - SUM-OF-THE-YEARS-DIGITS METHOD OF DEPRECIATION One...Ch. 5.4 - SUM-OF-THE-YEARS-DIGITS METHOD OF DEPRECIATION The...Ch. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - Prob. 25ECh. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - DOUBLE DECLINING-BALANCE METHOD OF DEPRECIATION...Ch. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.CRQ - Fill in the blanks. a. Simple interest is computed...Ch. 5.CRQ - Prob. 2CRQCh. 5.CRQ - Prob. 3CRQCh. 5.CRQ - Prob. 4CRQCh. 5.CRQ - Prob. 5CRQCh. 5.CRQ - Prob. 6CRQCh. 5.CRQ - Prob. 7CRQCh. 5.CRQ - Prob. 8CRQCh. 5.CRE - Prob. 1CRECh. 5.CRE - Prob. 2CRECh. 5.CRE - Find the effective rate of interest corresponding...Ch. 5.CRE - Prob. 4CRECh. 5.CRE - Prob. 5CRECh. 5.CRE - Prob. 6CRECh. 5.CRE - Prob. 7CRECh. 5.CRE - Prob. 8CRECh. 5.CRE - Prob. 9CRECh. 5.CRE - Prob. 10CRECh. 5.CRE - Prob. 11CRECh. 5.CRE - Prob. 12CRECh. 5.CRE - Prob. 13CRECh. 5.CRE - Prob. 14CRECh. 5.CRE - Prob. 15CRECh. 5.CRE - Prob. 16CRECh. 5.CRE - Prob. 17CRECh. 5.CRE - Prob. 18CRECh. 5.CRE - Prob. 19CRECh. 5.CRE - Prob. 20CRECh. 5.CRE - Prob. 21CRECh. 5.CRE - Prob. 22CRECh. 5.CRE - MUTUAL FUNDS Juan invested 24.000 in a mutual fund...Ch. 5.CRE - COLLEGE SAVINGS PROGRAM The Blakes have decided to...Ch. 5.CRE - RETIREMENT ACCOUNTS Mai Lee has contributed 200 at...Ch. 5.CRE - Prob. 26CRECh. 5.CRE - INSTALLMENT FINANCING Peggy made a down payment of...Ch. 5.CRE - HOME FINANCING The Turners have purchased a house...Ch. 5.CRE - Prob. 29CRECh. 5.CRE - Prob. 30CRECh. 5.CRE - SINKING FUNDS The management of a condominium...Ch. 5.CRE - CREDIT CARD PAYMENTS The outstanding balance on...Ch. 5.CRE - Prob. 33CRECh. 5.BMO - Find the accumulated amount at the end of 3 years...Ch. 5.BMO - Prob. 2BMOCh. 5.BMO - Prob. 3BMOCh. 5.BMO - Prob. 4BMOCh. 5.BMO - Prob. 5BMOCh. 5.BMO - a. Find the sum of the first ten terms of the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Given: AABE ~ ACDE. Prove: AC bisects BD. Note: quadrilateral properties are not permitted in this proof. Step Statement Reason AABE ACDE Given 2 ZDEC ZAEB Vertical angles are congruent try Type of Statement A E B D Carrow_forward10-2 Let A = 02-4 and b = 4 Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}. -4 6 5 - 35 a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. ○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3. B. No, b is not in (a1, a2, a3} since b is not equal to a₁, a2, or a3. C. Yes, b is in (a1, a2, a3} since b = a (Type a whole number.) D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear combination of them. In particular, b = + + ☐ az. (Simplify your answers.)arrow_forward(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1). (a) (4 points) Using the dot product determine the angle between a and b. (b) (2 points) Determine the cross product vector axb. (c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify your answer. 1arrow_forward
- (d) (4 points) Think of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector ab geometrically? d be .dx adjarrow_forward2) Based on the given information and the diagram, a. Which congruence statements can be proven? Select all that apply.Given: Overline OR is congruent to overline OQ, angle N is congruent to angle PProve: angle 3 is congruent to angle 5A. Overline ON is congruent to overline OPB. Angle 1 is congruent to angle 2C. Overline ON is congruent to overline OR and overline OP is congruent to overine OQD. angle 1 is congruent to angle 3 and angle 2 is congruent to angle 5There are more than one correct answerarrow_forward(2) (4 points) Find all vectors v having length 1 that are perpendicular to both =(2,0,2) and j = (0,1,0). Show all work. a=arrow_forward
- No chatgpt pls will upvotearrow_forwardTitle: Analyzing Customer Satisfaction for UnileverAs a member of Unilever's Customer Experience Management team, you are responsible forevaluating customer satisfaction levels and monitoring competitive moves. This case studyinvolves analyzing satisfaction data to test two key hypotheses about Unilever's performancerelative to its main competitor, Procter & Gamble (P&G).Unilever’s leadership team has emphasized the importance of customer satisfaction inmaintaining competitive advantage and market leadership. As part of this initiative, yourteam regularly monitors satisfaction scores and benchmarks them against competitors likeP&G.You are tasked with analyzing the provided dataset to answer the following questions:1. Does Unilever’s average customer satisfaction score meet the minimum threshold of2. 75%?Is there no significant difference between Unilever’s overall average satisfaction scoreand P&G’s average satisfaction score?arrow_forwardPlease help me first one graphically and the other in matrixarrow_forward
- Please help me with this in matrix pleasearrow_forwardPlease solve the differential geometry problem No chatgpt pls will upvote.arrow_forwardQ1. A group of five applicants for a pair of identical jobs consists of three men and two women. The employer is to select two of the five applicants for the jobs. Let S denote the set of all possible outcomes for the employer's selection. Let A denote the subset of outcomes corresponding to the selection of two men and B the subset corresponding to the selection of at least one woman. List the outcomes in A, B, AUB, AN B, and An B. (Denote the different men and women by M₁, M2, M3 and W₁, W2, respectively.)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY