Answer:
x^4 * (1/y^2)
Step-by-step explanation:
A negative exponent is just the reciprocal of the positive version of the exponent.
f(x) = x² + 2x + 1
f(x + h) = (x + h)² + 2(x + h) + 1
f(x + h) = (x + h)(x + h) + 2(x) + 2(h) + 1
f(x + h) = (x(x + h) + h(x + h)) + 2x + 2h + 1
f(x + h) = (x(x) + x(h) + h(x) + h(h)) + 2x + 2h + 1
f(x + h) = (x² + hx + hx + h²) + 2x + 2h + 1
f(x + h) = (x² + 2hx + h²) + 2x + 2h + 1
f(x + h) = x² + 2x + 2hx + h² + 2h + 1
Answer:
Step-by-step explanation:
The figure shown here consists of two pieces:
- A hemicircle
- A triangle
So, the total area of the figure is the sum of the areas of the two parts.
The area of the hemicircle is given by:
where
r = 4 in. is the radius (half the diameter, which is 8 inches)
Therefore,
The area of the triangle is given by
where
b is the base
h is the height
Here we have:
h = 8 in. is the height
The base is the total length (16 in.) minus the radius of the circle, so
So the area of the triangle is
So the total area of the figure is
Given:
The pair of expressions in the options.
To find:
The two expressions are equivalent for any value of y.
Solution:
Two expressions are equivalent for any value of y, iff they are equivalent.
Clearly, is not equivalent to or . So, options A and B are incorrect.
The expression is not equivalent to . So, option C is incorrect.
The expression is equivalent to .
Therefore, the correct option is D.