The answer Is C: SAS Congruence Postulate.
Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8
Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?
Let's check it out:
Even-numbered lists of odd numbers:
1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .
Amazing ! The sum is always the square of the number of items in the set !
For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.
I slogged through it on my calculator, and it's true.
I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).
Answer:
(x, g(x)) = {(-2, -2), (0, 0), (2, 2), (4, -3), (6, -3)}
Step-by-step explanation:
The first three values of x in the table are all less than or equal to 2, so the first part of the function definition applies. The y-value is equal to the x-value. The ordered pairs are ...
(-2, -2), (0, 0), (2, 2)
The last two values of x in the table are more than 2, so the last part of the function definition applies. For those values of x, the y-value is -3. The ordered pairs are ...
(4, -3), (6, -3)
Well, following the order of PEMDAS, I got choice B. 52
For instance, when you plug in 5 for x, you get F(5)=2(5)^2+2.
Moreover, following PEMDAS, you're supposed to solve what's inside the parenthesis, but since there is no operation going on inside the parenthesis, then you simple move on to the exponent.
In this case, you square the number 5, which gives you F(5)=2(25)+2
After that, you Multiply (letter M in PEMDAS). This results in F(5)=50+2.
Finally, you add them, which results in F=52.
By the way, I noticed a mistake in your work. When multiplying 2 by 5, the answer is 10, not 20.
Anyway, hope this helped! :-)
