PLEASE GUYS, I NEED HELP

Q1. What is the simplified form of 5(x-3y)+4(4y-x)-2(x-y)?


Q2. What is the solution set of 3-2[x+2]=6?


Q3. Which of the following is true about the row data given below 4, 7, 8, 4 and 1?

A. The median is 6
B. The mean is equal to the median
C. The mode is equal to the median
D. The range is 8

Q4. Which of the following is the slope of the line passing through the points A(1-a,b+1) and B(1+a,1-b)?

[tex] a. \: \frac{1 - b}{1 + a} \\ \\ b. \: \: \frac{b + 2}{a - 2} \\ \\ c. \: \: \: \frac{b}{a} \\ \\ d. \: \frac{ - b}{a } [/tex]



Respuesta :

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

Answer:

d

Step-by-step explanation:

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