Answer:
w = -10,6
Step-by-step explanation:
w(4+w)=60
4w + w^2 -60 = 0
w^2 +4w -60 = 0
w^2 +10w -6w -60 = 0
w(w+10) -6(w+10) = 0
w = -10, 6
Answer: Conjecture: There is no triangle with side lengths N, 2N, and 3N (where N is a positive real number)
Proof:
We prove this by contradiction: Suppose there was an N for which we can construct a triangle with side lengths N, 2N, and 3N. We then apply the triangle inequalities tests. It must hold that:
N + 2N > 3N
3N > 3N
3 > 3
which is False, for any value of N. This means that the original choice of N is not possible. Since the inequality is False for any value of N, there cannot be any triangle with the given side lengths, thus proving our conjecture.
Answer:
4
Step-by-step explanation:
Divide the coefficient of the x term by 2, then square the result. This number will be added to both sides of the equation. For the quadratic equation x2+4x=96, the coefficient of the x term is 4.
1 13/24 is the answer
1 5/6 - 3 3/8 = 1 13/24