Question

Given the equations Y = -2x + 34, y = -|3x|, y = -x/3 - 10, and y = (x - 2)^2, which equation satisfies the condition where the input is 6, and the output is 15? a) Y = -2x + 34 b) y = -|3x| c) y = -x/3 - 10 d) y = (x - 2)^2

Answer 1

The only equation that satisfies the condition where the input is 6 and the output is 15 is d) y = (x - 2)^2.

Step-by-step explanation:

To determine which equation satisfies the condition where the input is 6 and the output is 15, we can substitute x = 6 into each equation and evaluate the resulting expression.

a) Y = -2x + 34

Substituting x = 6, we get:

Y = -2(6) + 34

Y = -12 + 34

Y = 22

b) y = -|3x|

Since the absolute value of any number is its non-negative distance from zero, |-3x| is always non-negative. Therefore, -|3x| will always be non-positive. Substituting x = 6, we get:

y = -|3(6)|

y = -|18|

y = -18

c) y = -x/3 - 10

Substituting x = 6, we get:

y = -(6)/3 - 10

y = -2 - 10

y = -12

d) y = (x - 2)^2

Substituting x = 6, we get:

y = (6 - 2)^2

y = (4)^2

y = 16

Therefore, the only equation that satisfies the condition where the input is 6 and the output is 15 is d) y = (x - 2)^2.