6. The variable x and y vary directly, and y = 40 when x = 5. Which equation relates the variables? A.) y = 1/8 x
B.) y = 4x
C.) y= 40x
D.) y = 8x
E.) none of these

The equation relates the variables is y = 8x ⇒ D

Step-by-step explanation:

If x and y vary directly (y ∝ x), then y = k x, where

∵ The variable x and y vary directly

∴ y ∝ x

→ By using the rule above

∴ y = k x

∵ y = 40 when x = 5

∴ The initial values of x and y are x = 5 and y = 40

→ Substitute them in the equation above to find k

∵ 40 = k(5)

∴ 40 = 5k

→ Divide both sides by 5

∵ =

∴ 8 = k

→ Substitute the value of k in the equation above

∴ y = 8x

∴ The equation relates the variables is y = 8x

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)