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Linear Algebra

Systems of Equations Word Problems

In a family there are two cars. In a given week, the first car gets an average of 40 miles per gallon, and the second car gets 25 miles per gallon. The two cars combined drive a total of 1775 miles in that week, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Systems of Equations Word Problems: Tickets Sold

A total of 200 tickets were sold for the carnival to adults and children. Children tickets were $6 and adult tickets were $8. If the total revenue for the carnival is $550 dollars, then how many tickets of each type were sold?

Find the linear equation.

56. If you earned an average of $25,000 over your working life and you retire after 2005 at age 62, 63, or 64, then your annual Social Security benefit will be $7,000, $7500, or $8000 respectively (www.ssa.gov). There is a linear equation that gives the annual benefit b in terms of age a for these three years. Find the equation.

Systems of Linear Inequalities

1) What conditions need to be satisfied for a solution of a system of linear inequalities to have it's solution in the first quadrant? Create an example of such a system. 2) Can you give a real world example when the solution of a system of inequalities must be in the first quadrant? 3) Suppose, wheat and sugar are two b

Show that every tree is central or bicentral.

1.- A tree is central if its center is K1 and bicentral if its center is K2. Show that every tree is central or bicentral. ( Kn is call complete graph and it if every two of its vertices are adjacent and every vertex has degree n) 2.- Prove taht a tree with Delta(T)=k ( Delta means maximum degree) has at least k vertices of d

Probs in Linear Algebra

1 3 11. Consider (A) = 2 1 (a) Find the eigenvalue and corresponding eigenvectors of A. (b) Determine matrices B and C such that B A C is diagonal. (c) Show the eigenvectors of (A) are linearly independent. (d) Repre

Solve each system by the substitution method.

Solve each system by the substitution method. Indicate whether each system is INDEPENDENT, INCONSISTENT or DEPENDENT 1. x+3(y-1)= 11 2(x-y)+8y+28 2. 1/3x-1/6y+1/3 1/6x+1/4y=0 Solve each compound inequity. State the solution set using interval notation and graph it. 3. x <=0 and x+6>3 and 1/4x>3 4. 1/3x>

linear equations and inequality

Complete each problem show work and ad graphs as needed John spent 1/3 of his inheritance on loose women, 1/5 on expensive cigars, and 3/10 on liquor. He invested the rest in lottery tickets. What percent of his inheritance went to lottery tickets? Evaluate the expression: -(2 - 3)4 Fred and Ethel are florists. They a

Solving Linear Systems of Equations

1. INDEPENDENT LINEAR SYSTEM a. a system with exactly one solution b. an equation that is satisfied by every real number c. equations that are identical d. a system of lines 2. DEPENDENT SYSTEM a. a system that is independent b. a system that depends on a variable c. a system that has no soluti

Solving Systems of Linear Equations by the Echelon Method

4. solve by gauss jordan method. 28.6x + 94.5y + 16.0z - 2 .94w = 198.3 16.7x + 44.3y - 27.3z + 8.9w = 254.7 12.5x - 38.7y +92.5z +22.4w =562.7 40.1x - 28.3y + 17.5z - 10.2w = 375.4 5. Solve by echelon method 4x - y + 3z = -2 3x + 5y - Z =15 -2x+y + 4z = 14 6. Solve the system of equation...let z be the

Exact and appropriate solutions

Find exact and appropriate solutions to the problem. Find two positive real numbers that differ by 1 and have a product of 1.

Level Curves

Sketch the graph: z= f(x,y) where f(x,y)= x^2 + xy ; c=0,1,2,3,-1,-2,-3 Please show/describe all steps AND explain why it is a hyperbola. Also, sketch the graph: z=f(x,y) where f(x,y)= x/y ; c= 0,1,2,3,-1,-2,-3 Please show/describe all steps.

Probability and Solving Systems of Equations

1. A coin is tossed and a die is rolled. What is the probability that the coin shows heads and the die shows a 1 OR a 2? I tried this one and came up with 1/6 but the OR part is kicking my tail. Maybe I am just over thinking this one. 2. A technician is designing a new portable CD player that requires ten batteries fo

Systems of Linear Equations and Inequalities

1. Solve by substitution: x + y = 6 2x - 4y = 0 2. Does the shaded region of the graph of the system of equations x < 3, x + 7< 4 include the point (2, 3)? How do you know? 3. Explain what it means for a system of equations to be inconsistent and how you can tell whether a system is inconsistent usin

Linear Congruences : Chinese Remainder Theorem

The idea of this problem is to investigate solutions to x2&#8801;1(mod pq) where p and q are distinct odd primes. (a) Show that if p is an odd prime, then there are exactly two solutions modulo p to x2&#8801;1(mod p). (b) Find all pairs (a,b) &#1028; Zp x Zq such that a2&#8801;1(mod p) and b2&#8801;1(mod q). (c) Let p=17 an

Solving Systems of Linear Equations by Substitution

4x+y=12 (1) x-y=8(2) 4x+y=12 x-y=8 5x/5 = 20/5 X=4 4(4) =y - 12 16+y = 12 Y =4 I think this would be an example of elimination method for solving a system of equations however I am unsure how it would transfer to substitution method thus I am needing assistance. I am needing this to be illustrated if you wi

Solving Systems of Equations Word Problems and Gaussian Elimination

1. Jim wants to plan a meal with 169 grams of carbs and 1330 calories. If green beans have 7 grams of carbs and 30 calories per half cup serving and if french fried shrimp have 9 grams of carbs and 190 calories per three ounce serving how many servings of green beens and shrimp should be used? 2. Solve the system of equation

Simple questions

(See attached file for full problem description) --- Section 8.1 Solve each of the following systems by graphing each of the following. 10. 2x - y = 4 2x - y = 6 12. x-2y = 8 3x - 2y = 12 20. 3x - 6y = 9 X - 2y = 3 26. Find values for m and b in the following system so that the solution

Slope, y intercept

What are the slope, y-intercept, and equation of the line passing through the points (-1,1.2) and (3,-2)? a. slope = -0.8, y-intercept = 0.4, y = -0.8x+0.4 b. slope = 0.8, y-intercept = 0.4, y = 0.8x+0.4 c. slope = -0.8, y-intercept = 1.5, y = -0.8x+1.5 d. slope = -1.25, y-intercept = 0.05, y = -1.25x+0.05

Linear equations

1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function and

Rates and Investments : Systems of Equations Problem

I would like to know if I am on the right track to writin this as a "systems of equations" using the substitution process. How much further do I have to go if this is right so far? A family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the in