# Algebra of Rational and Irrational

0.123 as a percentage

6.8% as a decimal

rational-irrational

17x

-75. 12

2.32

Commutative property

associative property

additive Identity Property

additive Inverse Property

7+ (8+y) = (8+y) + 7

(8+a) + 5 = 8 + (a+5)

4+0=4

Solve for u

194-u=292

Solve for x

-5/7x=15

Solve for t

2t + 11 = 51

Solve for w

2w-8= -4

-13u -5 =8

Find the value of u + 4 given that -13u -5 =8

Simplify your answer as much as possible u+4=

Solve for x

6(x-4) -8x = -22

Solve for x

3x + 33 = -5 (x-5)

The surface area s of the right prism is given by

s= 2B + Ph

where B is the base, P is the perimeter of the base and h is the height of the prism Solve for P

P =

The length of the rectangle is four times its width. If the area of the rectangle is 144in^2, find its perimeter

m=

The perimeter of a rectangular painting is 304 centimeters. If the length of the painting is 89 centimeters, what is it's width

centimeters =

plot (-1,5)

Give an ordered pair (xy) of numbers that satisfy the equation 4x +y = 5

(xy) =

Graph 2x + 5y = 10

Graph y = 5x -2

Graph line with slop -1 passing through the point (3,1)

Find the slop of the line graphed

(-6, 6) (4, -7)

Find x intercept and y intercept of the line given by the equation

8x - 3y + 14 = 0

x=

y=

Find the slop of the line 4y - 5x - 3 = 0

Write an equation of the line below

(0,2) (-6, 2)

A line passes through the point (x,y) = (-7, 1) and has a slope of -4. Write an equation for this line.

Find an equation of the line (-2,2) (-5,7)

Write an equations for the vertical and the horizontal lines passing through the point (-8, -1) in (xy) coordinates

Vertical line-

Horizontal line-

Classify system Consistent dependent..Consistent independent...Inconsistent and solution

y= -2x -2

y= 2x -2

y= 1/3x -4

-x + 3y = -12

y= 2x -3

y= 2x

Find the values of x & y that solve the following systems of equations

2x -5y = 11

8x -9y = -11

Find 2 numbers sum is 39 and whose difference is 7

x=

y= ?

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#### Solution Preview

Please find the solutions/explanations attached herewith.

Solve and solutions

0.123 as a percentage = 12.3%

6.8% as a decimal = 6.8/100 = 0.068

rational-irrational: Please resend these questions, NOT CLEAR

17x

-75. 12

2.32

Commutative property

associative property

additive Identity Property

additive Inverse Property

7+ (8+y) = (8+y) + 7: Commutative property

(8+a) + 5 = 8 + (a+5): associative property

4+0=4: additive Identity Property

Solve for u

194 - u=292

-u = 292 - 194

-u = 98

=> u = -98

Solve for x

-5/7x=15

Multiply each side by -7/5, we will get

x = 15*(-7/5) = -21

Answer: x = -21

Solve for t

2t + 11 = 51

Subtract 11 from each side, we will get

2t = 51 - 11

2t = 40

⇨ t = 20

Answer: t = 20

Solve for w

2w-8= -4

add 8 to each side

2w = 4

⇨ w = 4/2 = 2

Answer: w = 2

-13u -5 =8

Add 5 to each side

-13u = 13

u = -1

Find the value of u + 4 given that -13u -5 =8

Simplify your answer as much as possible u+4= -1 + 4 = 3

Solve for x ...

#### Solution Summary

This solution covers examples of a variety of topics, including solving equations, surface area, properties, decimals and percentages, and graphing.

Rational Numbers - 1. Classify the given numbers as real and rational, real and irrational, or complex. ...

2. a) Select any irrational number, and turn it into a rational number by using addition, subtraction, multiplication, division, or exponentiation. ...

[See the attached questions file.]

Assignment 1: Irrational, Real, and Complex Numbers

1. Classify the given numbers as real and rational, real and irrational, or complex.

a. (4)1/2 + 2

b. 6+0i

c. 30007.413

d. 3i

e. 2-(-9)_ i

f. (80)1/5

g. 1

h. (16)1/4

Rational Number Irrational Number Complex Number

2. a) Select any irrational number, and turn it into a rational number by using addition, subtraction, multiplication, division, or exponentiation.

b) Select any imaginary number (of the form "a + bi" where a and b are non-zero real numbers), and turn it into a real number by using addition, subtraction, multiplication, division, or exponentiation.

Assignment 2: Discussion Questions

1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1.

2. Using FOIL, simplify the expression "(3x + 2)(3x - 2)". Show that a particular factoring formula leads to the same answer.

3. If a fourth-degree polynomial is multiplied by a third-degree polynomial, what is the degree of the product? Explain your reasoning and provide examples to support your explanation.

4. Think of a condition under which the product of any two binomials is a binomial. You can support your answer with the help of one of the identities of factorization of polynomials.

5. (i) Is "12.5555..." a rational or irrational number? Explain.

(ii) Is "2.1273685..." a rational or irrational number? Explain.

(iii) Is "548/799" a rational or irrational number? Explain.

(iv) Simplify "(5 + 3i)(5 - 3i)". Is the result real, complex, or both? Explain.

[See the attached questions file.]

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