Answer:
50
Step-by-step explanation:
For this case we have the following quadratic equation:
![s (t) = - 16t ^ 2 + 35t + 3 ](https://tex.z-dn.net/?f=s%20%28t%29%20%3D%20-%2016t%20%5E%202%20%2B%2035t%20%2B%203%0A)
Where,
t: time
s: height of the ball
By the time the height is 20 feet we have:
![-16t ^ 2 + 35t + 3 = 20 ](https://tex.z-dn.net/?f=-16t%20%5E%202%20%2B%2035t%20%2B%203%20%3D%2020%0A)
Rewriting the polynomial we have:
![-16t ^ 2 + 35t + 3-20 = 0 -16t ^ 2 + 35t-17 = 0](https://tex.z-dn.net/?f=-16t%20%5E%202%20%2B%2035t%20%2B%203-20%20%3D%200%0A%0A-16t%20%5E%202%20%2B%2035t-17%20%3D%200)
Using the quadratic formula we have:
![t = \frac{-b+/- \sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B-b%2B%2F-%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D%20)
Substituting values we have:
![t = \frac{-35+/- \sqrt{35^2 - 4(-16)(-17)}}{2(-16)}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-35%2B%2F-%20%5Csqrt%7B35%5E2%20-%204%28-16%29%28-17%29%7D%7D%7B2%28-16%29%7D%20)
Doing the calculations we have the roots are:
Answer:
the time when the football will be 20ft above the ground is:
B) 0.73 seconds or 1.46 seconds
Answer:
see explanation
Step-by-step explanation:
The opposite sides of a parallelogram are congruent, then
19x - 9 = 13x + 15 ( subtract 13x from both sides )
6x - 9 = 15 ( add 9 to both sides )
6x = 24 ( divide both sides by 6 )
x = 4
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Consecutive angles are supplementary, sum to 180° , that is
10y - 37 + 4y + 7 = 180
14y - 30 = 180 ( add 30 to both sides )
14y = 210 ( divide both sides by 14 )
y = 15
Then
∠ R = 10y - 37 = 10(15) - 37 = 150 - 37 = 113°
Then
∠ P = 113° ( opposite angles are congruent )