Answer:
Third option
Step-by-step explanation:
We can't factor this so we need to use the quadratic formula which states that when ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / 2a. However, we notice that b (which is 6) is even, so we can use the special quadratic formula which states that when ax² + bx + c = 0 and b is even, x = (-b' ± √(b'² - ac)) / a where b' = b / 2. In this case, a = 1, b' = 3 and c = 7 so:
x = (-3 ± √(3² - 1 * 7)) / 1 = -3 ± √2
Answer: x
=
−
30 7
Decimal Form :
x
=
−
4.
¯¯¯¯¯¯¯¯¯¯¯¯
285714
Mixed Number Form :
x
=
−
4
2
7
Step-by-step explanation:
From one vertex of an octagon you can draw 5 diagonals.
There are 8 vertices in an octagon, and we are choosing one as our starting vertex. There are then 7 vertices left to draw a line to, but 2 of the vertices are already connected to our main vertex (because they are connected along the side of the octagon). That leaves 5 vertices to draw a diagonal to from our original vertex.
Let

be an integer. Suppose there is a triangle with legs of length 16 and

. Then by the Pythagorean theorem, the length of the hypotenuse should be

The formulas for Pythagorean triples say that if the legs are integers, then so must be the hypotenuse, because if

and

are integers, then so are

,

, and

.
However,

is not a perfect square trinomial, which means for any integer

, the length of the hypotenuse is not an integer, so such a triangle doesn't exist.
30 divided by 2.5
so 12 hours until he catches 30 bad guys