5x^2 − 24 = 26
APPROXIMATE ANSWERS X= OR X=
THE EXACT SOLUTIONS ARE OR X=

Approximation = 3 < x < 4 or -4 < x < -3

Exact Solution = 3.162 or -3.162

Step-by-step explanation:

5x^2 - 24 = 26

First add 24 to both sides....

5x^2 = 50

Divide by 5...

x^2 = 10

Square root of 10 is exactly 3.162 or -3.162

Since 10 is not a perfect square, we can approximate it's square root by analyzing the perfect squares it is in between.

These perfect squares are 9 and 16

It looks like this:

We know that the square roots of these numbers are 3 and 4 so that leaves us with this...

Since we are dealing with square roots and perfect squares, we can also consider this as an option...

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

sorry, i can't understand your question. will later if you describe more clearly!

: )