Answer:
The correct statements are options 1 (E F + F G > E G), 2 (E G + F G > E F), and 5 (E G + E F < F G).
Step-by-step explanation:
We have triangle EFG.
For any triangle with sides a, b, and c, these inequalities hold:
Specifically for triangle EFG:
Thus, the true statements are options 1, 2, and 5.
Statements 3 and 4 are incorrect.
Solution:
We know, g(x) = f(x) + k --------(1)
It is given that f(x) = (x+2)
and g(x) = (x+5)
Substituting f(x) and g(x) into equation (1):
→ (x+5) =
(x+2) + k
→ = k
→ k =
Thus, the value of k is 1.
Explanation:
Step-by-step clarification:
Referring to step 6
(b² — 4ac) / 4a² = (x + b/2a)²
The mistake in the question is that it should be (x + b/2a)²
According to step 7
±√(b² —4ac) /2a = x + b/2a
The error in the question is that it should be divided by 2a, not 1a.
1. The transition from step 6 to step 7 involves taking the square roots of both sides
(b² — 4ac) / 4a² = (x + b/2a)²
Taking the square of both sides
√(b²—4ac) / √4a² = √(x + b/2a)²
√(b²—4ac) / 2a = x + b/2a
This forms step 7 correctly.
Next, subtracting b/2a from both sides
√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a
√(b²—4ac) / 2a — b/2a = x
(√(b²—4ac) — b)/2a = x
x = [—b ± √(b²—4ac)] / 2a
This gives the desired formula.
The discriminant is D = b²—4ac.
