Which inequality represents the values of x that ensure triangle ABC exists? a triangle with side lengths of 6.5 units, 3.5 units, and 2.5 + x units A. 0.5 < x < 7.5 B. 3.0 < x < 7.5 C. -0.5 < x < 7.5 D. -3.0 < x < 7.5

D. -3.0 < x < 7.5

Step-by-step explanation:

Given the side lengths of a triangle: 6.5 units, 3.5 units, and 2.5 + x units

For the triangle to exist:

Therefore, the third side length

x+2.5>0

x>-2.5

x must be greater than -2.5 and less than or equal to 6.5 units.

The correct option is D which satisfies this condition.

D. -3.0 < x < 7.5

a

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.