Question

Pls help!! I seriously don’t get anything

Answer 1

(1)

distribute parenthesis on both sides of the equation and simplify

10r - 30 = 4r + 52 - 10r - 50

10r - 30 = - 6r + 2 ( add 6r to both sides )

16r - 30 = 2 ( add 30 to both sides )

16r = 32 ( divide both sides by 16 )

r = 2

(2)

distribute parenthesis

- 0.5x + 5 < 12 ( subtract 5 from both sides )

- 0.5x < 7

divide both sides by - 0.5, remembering to reverse the inequality symbol as a consequence

x > - 14 → (C)

(3)

obtain the equation of the line in slope-intercept form

y = mx + c ( m is the slope and c the y-intercept )

calculate the slope using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, - 3 ) ← 2 points on the line

m = $\frac{-3-2}{3-0}$ = - $\frac{5}{3}$

the y-intercept = (0, 2 ) ⇒ c = 2

y = - $\frac{5}{3}$ + 2 ← equation of line

the shaded area ( the solution ) is below the line which is solid, thus

y ≤ - $\frac{5}{3}$ x + 2 → (B)

(4)

This data can only be a function if each value of x maps to exactly one value of y

The only values satisfying this criteria are B, C and D

as 0 → 1 and - 3 → - 1 so cannot map to other values of y