Which inequality represents all values of x for which the quotient below is defined? the problem is down below.

To make sure the stuff under the square root is not negative, we force the (x+2) expression to be 0 or positive. Meaning that we write which solves to when we subtract 2 from both sides

At the same time, the expression (5-x) under the other root is set to be greater than 0. We do not let (5-x) be equal to zero. Why not? Because this would cause a division by zero error. You cannot have the denominator be zero.

So, 5-x > 0 turns into 5 > x or x < 5 when we isolate x. This is after adding x to both sides.

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We have the two inequalities and x < 5 at the same time. So we're describing some number between -2 and 5, where we include -2 but exclude 5. Again we're making sure x=5 is not allowed to avoid division by zero errors.

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the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

move it to the other side

step-by-step explanation: