Answer:
D
Step-by-step explanation:
Since this is a compound interest, we will use this formula: A = P(1+r/n)^n*t
P = $1000 --> the amount that we start with
r = 8% --> this is the rate
n = 4 --> This is because it is compounded quarterly.
t = 5 --> the amount of years
A = 1,000.00(1 + 0.02)^(20)
So our final value after inserting those numbers in the equation is: $1,485.95.
Answer:
D)4x + 6/(x + 1)(x - 1)
Step-by-step explanation:
A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle

where
is the perimeter
is the length
is the width
We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so
and
.
Replacing values:


Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula
where
is the first term and
is the second term. We can infer that
and
. So,
. Replacing that:


We can see that the common denominator of our fractions is
. Now we can simplify our fraction using the common denominator:




We can conclude that the perimeter of the field is D)4x + 6/(x + 1)(x - 1).
Answer:
t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Step-by-step explanation:
To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.
h(t) = -16t² + 96t
= -16(t² - 6t)
= -16(t² - 6t + 9) - (-16) * 9
= -16(t - 3)² + 144
Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".