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  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 :)

The required property is the commutative property of multiplication.

Given:

The given statement is \((4\times 8)\times 3=(8\times 4)\times 3\).

To find:

The correct property for the given statement.

Explanation:

In the given statement \((4\times 8)\) is written as \((8\times 4)\) and the remaining part remains the same.

According to the commutative property of multiplication \(a\times b=b\times a\).

Therefore, the commutative property of multiplication shows the given statement.

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https://brainly.com/question/778086

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