Answer:
14)
21√2
15)
Leg: 7√3
Hypotenuse: 14
Step-by-step explanation:
The hypotenuse is √2 as long as each leg. That means the leg is 42/√2. Simplified to make 21√2.
The hypotenuse is always twice as long as the shortest leg on a 30-60-90 triangle. The longer leg is √3 as long as the shortest side.
Answer: second option y = 2(x + 7/2)^2 + 1/2
Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
Answer:
6x^2 +12x -1
Step-by-step explanation:
The perimeter is the sum of the two leg lengths and the base length:
P = 2(3x^2 +4x +2) +(4x -5)
= 6x^2 +8x +4 +4x -5
P = 6x^2 +12x -1
