Question

What property does the statement show? (4x8)x3=(8x4)x3

Answer 1

Associative Property of Multiplication

Answer 2

1. commutative property states that : a + b = b + a 

2. 3x - 5 = 5x - 17 -- add 5 to both sides 
3x = 5x - 17 + 5 -- subtract 5x from both sides 
3x - 5x = -17 + 5 -- combine like terms 
-2x = -12 -- divide both sides by -2 
x = 6 

3. slope formula : slope = (y2 - y1) / (x2 - x1) 
(3,-1) x1 = 3 and y1 = -1 
(-2,-5) x2 = -2 and y2 = -5 
now we sub 
slope = ((-5 - (-1)) / (-2 -3) 
slope = (-5 + 1) / -5 
slope = -4/-5 
slope = 4/5 

4. x = first integer 
x + 2 = 2nd integer 
x + x + 2 = 80 -- combine like terms 
2x + 2 = 80 -- subtract 2 from both sides 
2x = 80 - 2 
2x = 78 -- divide both sides by 2 
x = 39 <== this is the smallest number 
x + 2 = 41 

5. p = 1/2g - 3 

6. The union of two sets is all the numbers in both sets, no need to copy the same number more then once. Answer is : (1,2,3,4,5,6,8,10) 

7. 2x + 3y <= 6 -- put in y = mx + b form 
3y <= -2x + 6 
y <= -2/3x + 2 
In y = mx + b form, the y intercept is in the b position. So the y intercept is (0,2) 
To find the x intercept, sub in 0 for y (change inequality sign to equal sign) 
2x + 3y = 6 
2x + 3(0) = 6 
2x = 6 
x = 3 
x intercept is (3,0) 
So plot your points (3,0) and (0,2) 
Connect the points with a solid line because there is an equal sign in there. 
Shade below the line because it is less then. 

8. 3x + 6y = 8 
6y = -3x + 8 
y = -1/2x + 4/3 

y = 2x - 8 

Perpendicular lines have negative reciprocal slope. All that means is " flip " the slope and change the sign. The slope in these equations are -1/2 and 2. These are negative reciprocals of each other. 

9. 7x + 3y - 2 + 6x + 1 + y^2 
y^2 + 3y + 13x - 1 

10. (0,6) x1 = 0 and y1 = 6 
(3,0) x2 = 3 and y2 = 0 
slope(m) = (y2 - y1) / (x2 - x1) 
slope(m) = (0 - 6) / (3 - 0) 
slope(m) = -6/3 
slope(m) = -2 

y = mx + b 
(0,6) x = 0 and y = 6 
6 = 0(-2) + b 
6 = b 

your equation is : y = -2x + 6 (slope intercept form) 
2x + y = 6 (standard form) 

11. x + y = 5 -- put this in y = mx + b form, and the m position is your slope 
y = -x + 5 (-x is the same as -1x) so your slope is -1 

12. 4y = 8x - 3 -- put in y = mx + b form, and the b stands for the y intercept 
y = 8/4x - 3/4 
y = 2x - 3/4 (the y intercept is -3/4 

13. |a| + b --- (a = -1.4 and b = -2.7) 
absolute values, whether they have a negative or not, they are always positive 
|a| + b 
|-1.4 | + (-2.7) 
1.4 - 2.7 = -1.3 <== your answer 

14. I cannot see the problem 

15. -4 < 2t <= 2 --- divide everything by 2 
-2 < t <= 1 
open circle on -2, closed circle on 1, shading in between 

16. x + 2y = -9 ---> x = -2y - 9 
now sub -2y - 9 in for x in the other equation 
4x - 2y = 14 
4(-2y - 9) - 2y = 14 -- distribute through the parenthesis 
-8y - 36 - 2y = 14 -- add 36 to both sides 
-8y - 2y = 14 + 36 combine like terms 
-10y = 50 -- divide by -10 
y = -5 
now sub -5 in for y in either of the original equations 
x + 2y = -9 
x + 2(-5) = -9 
x - 10 = -9 
x = -9 + 10 
x = 1 
answer : x = 1 and y = -5 or (1,-5) 


I was really bored so I thought I would just help out :)