Answer:
260 degrees.
Step-by-step explanation:
Attached is the work to your problem.
Please see the attachment, it includes explanations and the algebraic process.
I hope this helps.
Given:
Three numbers in an AP, all positive.
Sum is 21.
Sum of squares is 155.
Common difference is positive.
We do not know what x and y stand for. Will just solve for the three numbers in the AP.
Let m=middle number, then since sum=21, m=21/3=7
Let d=common difference.
Sum of squares
(7-d)^2+7^2+(7+d)^2=155
Expand left-hand side
3*7^2-2d^2=155
d^2=(155-147)/2=4
d=+2 or -2
=+2 (common difference is positive)
Therefore the three numbers of the AP are
{7-2,7,7+2}, or
{5,7,9}
Answer:
The answer just so happens to be 6!
Ok, so you know that AB + BC = AC, so you can identify the equation by identifying all of the segment values, as shown below,
AB= 2x-8 AB + BC = AC, therefore
BC= x+17 2x-8 + x+17 = 39
AC=39
So, simply solve the equation algebraically, first by combining all of the like terms, and you should get 3x + 9 = 39
You can subtract both sides by 9, leaving you with 3x=30
Now you can isolate "x" by dividing both sides by 3, leaving "x" to equal 10.
Now that you know the "x" value (10), you can now plug in all of the "x" terms with 10, like so:
AB= 2(10)-8 = 12
BC= 10+17 = 27
Adding both 12 and 27 will give you 39, confirming both the "x" value being 10 and the correct length of the segments AB and BC.
If you have anymore questions, please let me know.