Answer:
Step-by-step explanation:
Question (1)
x² + 10x + 12
= x² + 2(5x) + 5² - 5² + 12
= [x² + 2(5x) + 5²] - 5² + 12
= (x + 5)² - 25 + 12 [Since, a² + 2ab + b² = (a + b)²]
= (x + 5)² - 13
Question (2)
y² - 6y - 15
= y² - 2(3y) - 15
= y² - 2(3y) + 3² - 3² - 15
= [y² - 2(3y) + 3²] - 3² - 15 [Since, a² - 2ab + b² = (a - b)²]
= (y - 3)² - 3²- 15
= (y - 3)² - 9 - 15
= (y - 3)² - 24
Answer:
5
Step-by-step explanation:
Well it really depends because there are four properties of addition; They are commutative, associative, additive identity, and distributive properties.
Answer: height of TV = 21"
Width of TV = 36.372"
Step-by-step explanation:
The TV is rectangular and the diagonal divides the rectangle into 2 equal right angle triangles. The diagonal represents the hypotenuse of the right angle triangle. If the diagonal forms a 30 degree angle with the base of the TV, then the height of the TV represents the opposite side of the right angle triangle and the width of the TV represents the adjacent side of the right angle triangle.
To determine the height, h of the TV, we would apply the Sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin 30 = h/42
h = 42Sin30 = = 42 × 0.5
h = 21"
To determine the width, w of the TV, we would apply the
the cosine trigonometric ratio.
Cos θ, = adjacent side/hypotenuse. Therefore,
Cos 30 = w/42
w = 42Cos30 = 42 × 0.866
w = 36.372"
