nameizmel

If Bill is 3 years older than his brother but 5 years younger than his sister, assuming Bills age is x, the sum of their ages would be be represented as the following

Evaluate the algebraic expression for the given value or values of the variable(s).

x2 - 3(x - y);x = 6 and y = 2

Compute the discriminant. Then determine the number and type of solutions for the given equation.

x2 - 4x + 3 = 0

0; one real solution

-28; no real solution

4; one real solution

4; two unequal real solutions

x2 - 4x + 3 = 0

a. 0; one real solution

b. -28; no real solution

c. 4; one real solution

d. 4; two unequal real solutions

Multiply or divide as indicated.

(x^2+7x+10)/(x^2+4x+4)

*

(x^2+10x+6)/(x^2+13x+40)

Find all numbers that must be excluded from the domain of the rational expression.

(x-9)/(x^2+4x-45)

Find all numbers that must be excluded from the domain of the rational expression.

8/x+4

Factor and simplify the algebraic expression

(x + 7)^(-1/3) - (x + 7) ^(-2/3)

Multiply or divide as indicated.

(9x^2+58x-35)/(7x-35)

*

(x2-5x)/(81x^2-25)

÷

(5x+33)/(3x^3)

Evaluate the exponential expression. 4^3 * 4^9

A department store is having a clearance sale. The price on a television is reduced by 21%. That sale price is then reduced by another 21%. If x is the television's original price, the sale price can be represented by (x - 0.21x) - 0.21(x - 0.21x). With these two reductions, at what percentage of the original price is the television being sold? Use the factored, simplified form of the expression to answer the question.

Multiply or divide as indicated.

(9x^2+58x-35)/(7x-35)*(x2-5x)/(81x^2-25)÷(5x+35)/(3x^3)

Kelsey has a collection of 40 coins, consisting of dimes and quarters, worth $7.60. How many coins of each kind does she have?

Create systems of linear equations with each possible number of solutions.

y=x+3, y=-2x-2; y=x+4, y=x+4; y=2x-6, y=2x+3

Explain the equations, and if there is other ways to write them. Is

it possible for the equations to look completely different but the solution

set still be "infinitely many"?

My answered questions:

i. How many solutions of a system of two linear equations in two unknowns can exist?

There can be 0 solutions, 1 solution, or infinite solutions.

0 if the two equations can be graphed as parallel lines

1 if the two equations can be graphed as two intersecting lines

Infinite if the two equations represent the SAME line.

ii. How would each possible number of solutions appear graphically?

The solution(s) of a system of equations are visually represented by the intersection(s) between the lines.

2 intersecting lines

2 lines on top of each other (the same line)

2 parallel lines

iii. Create systems of linear equations with each possible number of solutions.

y=x+3, y=-2x-2; y=x+4, y=x+4; y=2x-6, y=2x+3

Professor's feedback:

You did a good job and also provided some examples in part (iii) but you

did not clearly state which one is which. I understand though and I think

you followed the order mentioned in part (ii). Is that right? Also, the third

and the fourth lines look exactly the same. I am assuming that it was for

the "Infinite" number of solutions. Is that the only possibility though? Is

it possible for the equations to look completely different but the solution

set still be "infinitely many"?

I am not exactly sure what he's saying or asking here? Can anyone give me some feedback how to answer his questions??

Explain how to apply substitution in solving a system of equations.

Explain how to apply elimination in solving a system of equations.

Explain how to apply elimination in solving a system of equations.

1. Explain how to apply elimination in solving a system of equations.

2. Explain how to apply substitution in solving a system of equations.

3. Demonstrate each technique in solving the system

1. 3x + 9y = 12

2. 5x - 4y = 3

1. How many solutions of a system of two linear equations in two unknowns can exist?

2. How would each possible number of solutions appear graphically?

3. Create systems of linear equations with each possible number of solutions.

Using the slope formula

m = y2 – y1

x2 – x1

find the slope of the line determined by this pair of points:

(-2, 5) and (1, -5)

One number is five more than the second number. The sum of the numbers is -1. What are the numbers?