MATH 095 Lecture Notes - Lecture 2: Solution Set

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emeraldbuffalo21

30 May 2018

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Math 95

Conceptual Notes

1/22/18

11:00 am – 12:20 pm

Sole the euation and then ite it’s solution set.

1. X = 3 → {3}

2. 2 = Y → {2}

3. X – 7 = 2 → {9}

Addition property of Equality:

If you add the same quantity to both sides of the equation or subtract the same quantity from both side

of an equation. The euation’s solution set does not change.

Example:

X – 7 = 2 →

X – 7 + 7 = 2 + 7 →

X + 0 = 9 →

X = 9 →

{9}

Example:

W + 7 = -12 →

W + 7 – 7 = -12 – 7 →

W = -19 →

{-19}

Example:

3x – 11 = 2x +15 →

3x – 11 – 2x = 2x + 15 – 2x →

X – 11 = 15 →

X – 11 + 11 = 15 + 11 →

X = 26

{26}

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Document Summary

Sol(cid:448)e the e(cid:395)uation and then (cid:449)(cid:396)ite it"s solution set: x = 3 {3, 2 = y {2, x 7 = 2 {9} If you add the same quantity to both sides of the equation or subtract the same quantity from both side of an equation. X 7 + 7 = 2 + 7 . W + 7 7 = -12 7 . 3x 11 2x = 2x + 15 2x . X 11 + 11 = 15 + 11 . To simplify this, i have to get rid of the parentheses. The distributive property says to multiply the outside number onto everything inside the parentheses. 16x 20 = 15x + 219 . 16x 20 + 20 = 15 x + 219 + 20 . Check: in the equation you are checking, replace x with the number you came up with and work the equation. Example: (cid:1876)(cid:889)=(cid:891)(cid:890) (cid:889)(cid:4672)(cid:1876)(cid:889)(cid:4673)=(cid:889)(cid:4666)(cid:891)(cid:890)(cid:4667) (cid:1876)=(cid:888)(cid:890)(cid:888) (cid:883)(cid:887)(cid:884)(cid:890)(cid:1877)=(cid:884)(cid:887)(cid:884)(cid:883) (cid:884)(cid:890)(cid:883)(cid:887)((cid:883)(cid:887)(cid:884)(cid:890)(cid:1877))=(cid:884)(cid:890)(cid:883)(cid:887)((cid:884)(cid:887)(cid:884)(cid:883)) (cid:884)(cid:890)(cid:883)(cid:887) (cid:883)(cid:887)(cid:884)(cid:890) (cid:1877)=(cid:884)(cid:890)(cid:883)(cid:887) (cid:884)(cid:887)(cid:884)(cid:883) (cid:1877)=(cid:884)(cid:882)(cid:891)

Related Questions

I need help with problems 7-17, showing all work, Thank you

For the best rating please complete by answering all thequestions in one post so I could rate you once you post.

Answers must be correct in order to get best rating.

1. Factor out the GCF from thepolynomial.
20m^9 + 6m^7 + 20m^5

2(10m^9 + 3m^7 +10m^5)
No common factor
m^5 (20m^4 + 6m^2 +20)
2m^5 (10m^4 + 3m^2 +10)

2. Find the solution to the system by addition(elimination) method.
4x + 15y = 15
8x - 3y = -3

(1, 0)
(0, 0)
(0, 1)
(1, 1)

3. (11p + 4)(11p - 4)

p^2 - 16
121p^2 + 88p - 16
121p^2 - 16
121p^2 - 88p -16

4. Find the solution to the system by addition(elimination) method.
2x + 15y = -91
9x + 5y = 28

(-5, 7)
(7, -7)
(9, -9)
(-7, 7)

5. Factor by grouping.
18x^3 + 15x^2 + 12x + 10

(3x^2 + 2)(6x + 5)
(18x^2 - 2)(x - 5)
(3x^2 - 2)(6x - 5)
x(18x + 2)(x +5)

6. (x + 3y)(x + 5y)

x^2 + 5xy + 15y^2
x^2 + 8xy + 8y^2
x^2 + 8xy + 15y^2
x + 8xy + 15y

7. 6x^7 (9x^7 + 12x^2 - 7)

54x^7 + 72x^2 - 42
54x^14 + 72x^9
54x^14 + 72x^9 -42x^7
54x^14 + 12x^2 -7

8. 15x^2 - 12x + 10x - 8

(15x + 2)(x - 4)
(15x - 2)(x + 4)
(3x - 2)(5x + 4)
(3x + 2)(5x -4)

9. For the polynomial, state the degree andwhether or not the polynomial is a monomial, a binomial, or atrinomial.
5x^3y^4 - 8x^5y^6 + 8

Binomial, degree 7
Trinomial, degree 3
Trinomial, degree18
Trinomial, degree11

10. (3x^8 + 2x^7 - 4x^6 + 8) + (7x^8 - 4x^7 +8x^6 + 1)

10x^8 - 2x^7 + 4x^6 +9
12x^42 + 9
10x^26 - 2x^14 + 4x^12 +9
4x^8 + 4x^7 + 4x^6 +9

11. (2n^5 - 3n^3 - 6) - (5n^5 - 14n^3 -3)

-3n^5 + 2n^3 - 9
-3n^5 + 11n^3 - 3
5n^8
-3n^5 + 11n^3 -9

12. Use the substitution method to solve thesystem.
x - 4y = -13
7x - 5y = -22

(1, 4)
(-2, 4)
(-1, 3)
No solution

13. Use the substitution method to solve thesystem.
8x - 6y = 32
2x - 2y = 8

(3, 1)
(4, 1)
(4, 0)
No solution

14. Terms in a polynomial are separated byaddition or subtraction.

True
False

15. A polynomial is an algebraic expression ofone or more terms.

True
False

16. A solution of two linear equations in twovariables is an ordered pair that is a solution to eachequation.

True
False

17. The greatest common factor will always begreater than the largest factor of each term of theexpression.

True
False

18. A system of equations in two variables mayhave infinite solutions.

True
False

19. When two or more algebraic expressions aremultiplied, each expression is called a term.

True
False

20. Factoring is multiplication inreverse.

True
False

pucesalmon393

1. One of the tables below contains (x,y) values that weregenerated by a linear function. Determine which table, and thenwrite the equation of the linear function represented by the

Table #1 x 2 5 8 11 14 17 20 y 1 3 7 13 21 31 43

Table #2 x 1 2 3 4 5 6 7 y 10 13 18 21 26 29 34

Table #3 x 2 4 6 8 10 12 14 y 1 6 11 16 21 26 31

2. Give an example of each of the following:

A function whosedomain is [2, infinity)

An arithmeticsequence

A system of equationswith no solutions

3. For f(x) =1/x^2-3, find:

f(3)
f(2+h)

4. For f(x) = 1/x-5and g(x) = x^2+2, find:

1. (fog)(x)

2. (gof)(6)

5. For the sequencegiven by a (subscript n) = 4n+5 an=4n+5, answer the following:

Find the first fiveterms

Find the sum of thefirst 25 terms.

Is this an arithmeticsequence? If so, how can you tell? If not, why not?

6. Graph the areabound by y<1/2x+6, x+3y>=12, x>=0, and x<=12

7. For the functiondefined by:

f(x)= {x^2,x<=1}

{2x+1,x>1}

a. evaluate f(0)

b. graph f(x)

8. Solve thefollowing system of equations algebraically. Verify your solutioneither graphically or by using matrices.

3x-y=0

5x+2y=22

9. Solve thefollowing system of equations algebraically. Verify your solutioneither graphically or by using matrices

8x-2y=5

-12x+3y=7

10.Given matricesA, B, and C below, perform the indicatedoperations if possible. If the operation is not possible, explainwhy.

A (3x3) [1st 2, -1,0] [2nd 0, 5, 0.3] [3rd 1, 4, 10]

B (3x3) [1st 5, 0, 2][2nd 1, -3, 9] [3rd2, 0, 4]

C (1x1) [1, 3, 5]

1.3A+B

2. B+C

3. CA

11. Given the tablebelow, evaluate the following:

x	-3	-2	-1	0	1	2	3	4	5
f(x)	10	20	30	40	50	60	70	80	90
g(x)	-1	-2	-3	-4	-5	-6	-7	-8	-9

a.(3f+2g(1) b. (fog)(-1)

12.Express the following function, F(x) as a composition of twofunctions f and g

f(x)= x^2/(x^2+4)

13.You have a coupon for your favorite clothing store for $25 off anypurchase of more than $50. The store is also running a 20%-off saleon its entire inventory. Let x be the original price, f(x)be the price with the $25 coupon applied, and g(x) be the pricewith the 20% discount applied.

a.Write an expression for f(x)

b.Write an expression for g(x)

c.What would the expression (fog)(x) represent?

d.What would the expression (gof)(x) represent?

e.If the store allows you to apply both the 20% discount and the$25-off coupon, does it matter which you apply first? How do youknow?

MATH 095 Lecture Notes - Lecture 2: Solution Set

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