higgsb

Oops, I made a typo when I was submitting the problem (sorry!). 

"AX = 3 CX = 12" should actually be AX = 3CX = 12. 

28.3 x 14.9 = 421.67

sqrt(2056) = sqrt(2^3*257) = 2*sqrt(514)

25+-2 = 25-2 = 23

1. 0,1

2. -1, 0, 1

3. -1, 0, 1 

4. sqrt (2), 1/3, -1/6 

1/2*1/9+2 = 1/18+2 =1/18 + 36/18 = 38/18 = 19/9 

Plan 1: 22*3 = 66, so she can afford plan 1.

Plan 2: 29.26+23.99+23.74 = 76.99, so she can not afford plan 2. 

Question 1: The associtative property of addition (when adding 3 numbers, it doesn't matter which numbers you add first: (a+b)+c = a+(b+c). 

Question 2: The maximum amount of money she can spend, which is $75. 

1. 8 + (9t + 4)  --> combine like terms

12+9t

2. 9(2x)  --> multiply 

18x

3. (4 + 105x) + 5  --> combine like terms

105x+9

4. 10p(11)  --> multiply

110p

5. (12r)13  --> multiply 

156r

6. (2+3x)+9  --> combine like terms

11+3x

7. 4(x6.3) --> multiply

25.2x

8. 1.1 + (7d + 0.1)  --> combine like terms

7d+1.2

9. 56ab/b  --> combine like terms

56a

10. 1.5mn/m  --> combine like terms

1.5n

11. 13p/pq --> combine like terms

13/q

12. 33xy/3x  --> combine like terms

11y

When multiplying two negatives together, you multiply the numbers like you usually do, but the negative signs cancel each other out, so the product ends up being possitive. 

In this case, -2*-2 = 4. 

Alright, thanks for clarifying!

3. (x² - 3x - 2) - (2x² - x + 6)  --> remove parenthesis

x^2 - 3x - 2 - 2x^2 + x - 6      --> combine like terms

-x^2 - 2x - 8

3x-9 = -x+7  --> add x to both sides

4x-9 = 7       --> add 9 to both sides

4x = 16        --> divide both sides by 4

x = 4

I don't understand what you are asking for in question 3, so I'm going to skip it for now...

4.(x² + 1) - (3x² + 4x - 1)    --> remove parenthesis

x^2 + 1 - 3x^2 - 4x + 1       --> combine like terms

-2x^2 - 4x + 2

2. (a² + a - 1) - (3a² - 2a + 5)  --> remove parenthesis 

a^2 + a - 1 - 3a^2 + 2a - 5      --> combine like terms

3a - 2a^2 - 6                           --> rewrite into standard form for a quadratic (ax^2 + bx + c)

-2a^2 + 3a - 6

1. (3x² + 2xy + 7) - (6x² - 4xy + 3) --> remove parenthesis

3x^2 + 2xy + 7 - 6x^2 + 4xy - 3     --> combine like terms

6xy - 3x^2 + 4                               --> rewrite in standard form of a quadratic (ax^2+bx+c)

-3x^2 + 6yx + 4

Since you are multiplying 86 by 97 right after you are dividing 86 by 97, and multiplication and division are opposite opertations, they cancel each other out, and your answer is 86. 

The domain of a function f(x) is the values that x can be. 

If you want to know how to find the domain of a function, this website gives some examples: 

http://www.coolmath.com/algebra/15-functions/06-finding-the-domain-01

p = perimiter

h = height

w = width

You have the inequality p<200, and the equation 2w+2h = p.

You can subsitute 2w+2h for p, so you get a new inequatlity of 2w+2h<200.

Since we know that w is 36, we can plug that value in: 2*36+2h<200  -->  72+2h<200.

Now we can solve this inequality for h: 

72+2h<200  -->  subtract 72 from both sides

2h<128        --> divide both sides by 2

h<64            --> Our answer is that the height of the frame must be less than 64 inches. 

−10 + 7𝑥 + 24 − 2  ---> combine like terms (add the numbers)

7x + 12 

If you have a set of numbers, the range is the difference between the largest number and the smallest number.

(Example - If your set was {3, 2, 7, 11, 12}, your range would be the largest number (12) - the smallest number (2).

[12-2 = 10, which is the range.]

1.05-z=1.65  --> subtract 1.05 from both sides

-z = 0.6 --> multiple both sides by -1

z = -0.6