Linear Algebra

If i understand correctly, 2 numbers add to 115 and these 2 numbers have a difference of 45. If so 80 and 35

Example:

When deciding about the purchase of a new warehouse for the storage of merchandise and tools, a company faces the option to incur in payment of two types of mortgages, one with fixed-rate and other with variable-rate. The decision will depend on the study of the equations (graphs) that represent each of them and the time they plan to hold the investment.

Variable mortgage:

Y=50/3 X + 600

Fixed mortgage:

Y=700

Y=50/3 X + 600

Y=700

SOLUTION:

700= 50/3 X + 600 (substitution)

50/3 X = 100

X= 100 x 3 / 50

X=6

SOLUTION: (6,700)

When graphing both equations we find out that the intersection (solution of the system) occurs at (6,700), what represents that?

1) the variable graph is under the fixed one from the year 0 to year 6.

2) the fixed graph is under the variable one after the year 6.

3) both graphs intersect each other at the solution of the system, the pair (6,700).

For the business analysis, it is recommendable to take a variable mortgage if the investment is to be hold for less than 6 years, because it will represent less expenses for the mortgage.

On the other side, if the investment is to be hold for more than 6 years, for example 20 years or more, the fixed mortgage is more suitable for the organization since it will expend less money than taking the variable one.

If it is between 6 years and other specific time, the amount finally paid with the variable mortgage and the fixed one can be compared studying the areas involved between the graphs with the specific time selected.

y = x - 4 × 2 + 12

y = x - 8 + 12

y = x - 20

That is the simplest form of the equation, as you can only solve completely by having only 1 variable to solve.

Bisymmetry is the state or quality of being bisymmetric - symmetric around both of the main diagonals of a square matrix.

represent x > 6 and x <=18

enter the compound inequality without using and

Neither the 'x' nor the 'y' component should have any exponents (squared, cubed, square root, etc.) and therefore it should be a one-to-one ratio (each 'x' has one 'y' value and vice versa).

independent is the money

depdendent is the satisfaction

It is a point where two sides of the shape meet.

(10x + 3)(x - 1)

5 = -2x + 110x - 1,000

5 = 108x - 1,000

1,005 = 108x

335/36 = x

44

67% of 22 = 22*67/100 = 14.74 = 15 (rounded)

Technically,no. A radical equation has a radical (Square root) in it, and has two solutions because the square root can be positive or negative.

36 hours

Presumably the question concerned a PAIR of linear equations!

The answer is two straight lines intersecting at the point whose coordinates are the unique solution.

y = ax + b

It comes from the Law of Cosines.

* * * * *

For any two vectors A and B, the projection of A onto B, that is, the component of A along B, is ab.cos(x) where x is the angle between the two vectors. By symmetry, this is also the projectoin of B onto A.

It solves a system of equations.

Think of the 2X2 case of having X+Y=1 and 3X+2Y=6.

3x/(5-x)/3=4

3x/(5-x)=4X3

3x=12(5-x)

3x=60-12x

3x+12x=60

x=4

Example system: 4x + 2y = 20 and 5y + 4 = 8x

First, pick one equation and solve for one variable as far as possible (we will solve for the y variable).

4x + 2y = 20 (divide everything by 2)

2x + y = 10 (subtract 2x from each side)

y = 10 - 2x (stop when you have a variable all on its own)

Then, plug this new equation into the other one for the variable you solved for (we solved for the y variable earlier, so now we will solve for the x variable).

5y + 4 = 8x

5 (10 - 2x) + 4 = 8x (substitution)

50 - 10x + 4 = 8x (distribute/simplify)

54 - 10x = 8x (simplify)

54 = 18x (add 10x to both sides)

x = 3 (divide both sides by 18, stop here)

Then, plug x = 3 back into either equation to solve for the value of y (before we solved for y, but it stayed in the form of an equation).

4x + 2y = 20

4(3) + 2y = 20 (substitute)

12 + 2y = 20 (simplify)

6 + y = 10 (divide both sides by 2)

y = 4 (subtract 6 from both sides, stop here)

Now, you know that x = 3 and y = 4. This means that this is the intersection point of these two equations if you were to graph them (3, 4). If solve the system using the method above but end up with an answer that doesn't make sense (such as 3=7), the lines do not intersect and there is therefore no answer.

54.3 squared

obtained value/actual value * 100

when it is in its most reduced form.

y=7/3x-13

speed = distance ÷ time