Answer:
see explanation
Step-by-step explanation:
(1)
5(x - 3y) + 4(4y - x) - 2(x - y) ← distribute all 3 parenthesis
= 5x - 15y + 16y - 4x - 2x + 2y ← collect like terms
= 3y - x
(2)
3 - 2(x + 2) = 6 ( subtract 3 from both sides )
- 2(x + 2) = 3 ( divide both sides by - 2 )
x + 2 = - 1.5 ( subtract 2 from both sides )
x = - 3.5
solution set = { - 3.5 }
(3)
The median is the middle value of the data in ascending order
1 4 4 7 8 ← in ascending order
↑ median = 4
The mean is the sum of the values divided by the count
mean = [tex]\frac{1+4+4+7+8}{5}[/tex] = [tex]\frac{24}{5}[/tex] = 4.8
The mode is the value which occurs most often
mode = 4
Thus the mode is equal to the median → C
(4)
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (A(1 - a, b + 1 ) and (x₂, y₂ ) = B(1 + a, 1 - b )
m = [tex]\frac{1-b-(b+1)}{1+a-(1-a)}[/tex]
= [tex]\frac{1-b-b-1}{1+a-1+a}[/tex]
= [tex]\frac{-2b}{2a}[/tex] ( cancel 2 on numerator/ denominator )
= [tex]\frac{-b}{a}[/tex] → d
