Given two positive even integers, it turns out that the square of the largest minus 10 times the smaller is 76. What is the sum
of the integers?
Please help....
Please help....
1 answer:
Answer:
26
Step-by-step explanation:
Even integers will only have a square ending in 6 if they end in 4 or 6.
The square will only have a value greater than 76 if the number is greater than 8, that is, 14 or 16, 24 or 26, and so on.
The "smaller" integer will only be smaller if the "larger" integer is less than 16.
So, the two integers are ...
14 and (14^2 -76)/10 = 12
The sum of 14 and 12 is 26.
_____
In the graph, we let x represent the "larger" integer and y the "smaller". The shaded area is where x > y, and the curve is the constraint on their values. The two vertical lines are the even numbers whose squares end in 6, resulting in integer values for y.
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Hey there,
Let's remember that a (inequality symbol) is things like (<), (>), (≤),(≥), (≠).
So, I believe that (-3x+7) and (-10-2) are separate. So we will find that out :)
Let's first do (-3x+7). As simplifying this expression here, we take that "x" of for a while and just stick to (-3+7).
-3
+ 7
______
4
Let's bring that "x" back, and the answer would be 4x for a while.
So far, 4x is the answer.
_____________________________________________________________
Now, Let's work on the other side.
We are talking about (<span>-10-2)
-10
- 2
_______
</span> -12
So, by solving the answer to (-10-2), we got -12.
So, let's determine what is greater . . . . .
-12 or 4.
-12 is on the negative side, and the number 4 is positive. This would conclude that 4 is great than -12.
Your correct answer would look like . . .
<span>(-3x+7) > (-10-2)
</span>
I really hope this helps you alot.
~Jurgen
Let's remember that a (inequality symbol) is things like (<), (>), (≤),(≥), (≠).
So, I believe that (-3x+7) and (-10-2) are separate. So we will find that out :)
Let's first do (-3x+7). As simplifying this expression here, we take that "x" of for a while and just stick to (-3+7).
-3
+ 7
______
4
Let's bring that "x" back, and the answer would be 4x for a while.
So far, 4x is the answer.
_____________________________________________________________
Now, Let's work on the other side.
We are talking about (<span>-10-2)
-10
- 2
_______
</span> -12
So, by solving the answer to (-10-2), we got -12.
So, let's determine what is greater . . . . .
-12 or 4.
-12 is on the negative side, and the number 4 is positive. This would conclude that 4 is great than -12.
Your correct answer would look like . . .
<span>(-3x+7) > (-10-2)
</span>
I really hope this helps you alot.
~Jurgen