Answer:
the object is in the air on the time interval (0.24 sec, 6.51 sec)
Step-by-step explanation:
The object is 'in the air' for all t such that h> 0. We need to find the roots of h = -16t^2 + 108t - 25 = 0. From the graph we see that both t values are positive. Once we find them, we subtract the smaller t from the larger t, which results in the length of time the object is in the air.
Use the quadratic formula to find the roots of h(t). The coefficients of t are {-16, 108, -25}, and so the discriminant b^2 - 4ac is
108² - 4(-16)(-25) = 11664 - 1600 = 10064, whose square root is 100.32.
Then the quadratic formula x = (-b ± √[b² - 4ac)/(2a) becomes
-108 ± 100.32 108 ± 100.32
t = ---------------------- = --------------------- = 3.375 ± 3.135
2(-16) 32
or t = 6.51 or t = 0.24 (both times expressed in seconds).
So, again, the object is in the air on the time interval (0.24 sec, 6.51 sec)
Answer:−21x−8
Step-by-step explanation: All sides have the same measure in a square, therefore all sides are 3x-8. Area is equal to 3x-8 times 3x-8 which is −21x−8
Answer:
(x, y) → (1.5x, 1.5y)
Step-by-step explanation:
Each of the image coordinates is 1.5 times the corresponding pre-image coordinate. The transformation is a dilation by a factor of 1.5 about the origin.
Some authors use a notation like D(1.5,O) to indicate the transformation. I like the one shown above, or ...
(x, y) → 1.5(x, y)
<span>The fully covered premium amounts to $4,668. Next, we calculate the partially covered premium using:
25% * 9,264 = 2,316
Now, the total annual premium paid by Mr. Henderson's employer is equivalent to the sum of the completely covered premium and partially covered premium. This is:
4,668 + 2,316
= $6,984 of the Henderson family's annual premium is covered by Mr. Henderson's employer</span>
If you split a circle in to 4, and color in 3 of the 4 pieces you will find that 3/4 are bigger than 2/3
