Common Pythagorean triples include
(3, 4, 5)
(5, 12, 13)
(7, 24, 25)
(9, 40, 41)
The only Pythagorean triple that is an arithmetic sequence is (3, 4, 5), so any arithmetic sequence that is a Pythagorean triple must be a multiple of that, such as (9, 12, 15) or (15, 20, 25).
The arithmetic sequences of selections B and D are unrelated to the (3, 4, 5) triple, so cannot be Pythagorean triples. For selection A, we know that 9² + 11² = 81 + 121 = 202 > 14², so that is not a right triangle.
The appropriate selection is ...
C. 7, 24, 25
g(x) = -(x + 1)^2 - 3
Let's simplify this equation
g(x) = -(x^2 + 2x + 1) - 3
Distribute the negative sign
g(x) = -x^2 - 2x + 1 - 3
Combine like terms
g(x) = -x^2 - 2x - 2
The value of a = -2 and this value is LESS THAN 0
The answer would be 0 solutions.
Here, we see <em>|</em><em />x+6<em>|</em><em /> = 2.
Oh wow! A foreign object!
|x+6|... two lines... what is that?
That is called absolute value. Whatever is inside the two lines, must have a positive answer!
Let's pretend we have a machine that has this absolute value function activated.
What we put in, we must get a positive answer out.
Let's put in -6.
-6 ==> BEEP BEEP ==> 6
Let's try 3.
3 ==> BEEP BEEP ==>3
Whatever we put in, if it is negative or positive, what comes out is always positive.
So, for how many values <em>x</em> is |x+6|=-2 true?
None, because the answer <em>must</em><em /> be positive!
-2 is not positive, <em>2</em><em /> is.
Answer:
42.86
Step-by-step explanation:
