Here's our equation.
![h=-16t+64t+3](https://tex.z-dn.net/?f=h%3D-16t%2B64t%2B3)
We want to find out when it returns to ground level (h = 0)
To find this out, we can plug in 0 and solve for t.
![0 = -16t+64t+3 \\ 16t-64t-3=0 \\ use\ the\ quadratic\ formula\ \frac{-b\±\sqrt{b^2-4ac}}{2a} \\ \frac{-(-64)\±\sqrt{(-64)^2-4(16)(-3)}}{2*16} = \frac{64\±\sqrt{4096+192}}{32}](https://tex.z-dn.net/?f=0%20%3D%20-16t%2B64t%2B3%20%5C%5C%2016t-64t-3%3D0%20%5C%5C%20use%5C%20the%5C%20quadratic%5C%20formula%5C%20%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%20%5C%5C%20%5Cfrac%7B-%28-64%29%5C%C2%B1%5Csqrt%7B%28-64%29%5E2-4%2816%29%28-3%29%7D%7D%7B2%2A16%7D%20%20%3D%20%5Cfrac%7B64%5C%C2%B1%5Csqrt%7B4096%2B192%7D%7D%7B32%7D)
![= \frac{64\±\sqrt{4288}}{32} = \frac{64\±8\sqrt{67}}{32} = \frac{8\±\sqrt{67}}{4} = \boxed{\frac{8+\sqrt{67}}{4}\ or\ 2-\frac{\sqrt{67}}{4}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B64%5C%C2%B1%5Csqrt%7B4288%7D%7D%7B32%7D%20%3D%20%5Cfrac%7B64%5C%C2%B18%5Csqrt%7B67%7D%7D%7B32%7D%20%3D%20%5Cfrac%7B8%5C%C2%B1%5Csqrt%7B67%7D%7D%7B4%7D%20%3D%20%5Cboxed%7B%5Cfrac%7B8%2B%5Csqrt%7B67%7D%7D%7B4%7D%5C%20or%5C%202-%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%7D)
So the ball will return to the ground at the positive value of
![\boxed{\frac{8+\sqrt{67}}{4}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cfrac%7B8%2B%5Csqrt%7B67%7D%7D%7B4%7D%7D)
seconds.
What about the vertex? Simple! Since all parabolas are symmetrical, we can just take the average between our two answers from above to find t at the vertex and then plug it in to find h!
![\frac{1}2(\frac{8+\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(2+\frac{\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(4) = 2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D2%28%5Cfrac%7B8%2B%5Csqrt%7B67%7D%7D%7B4%7D%2B2-%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%29%20%3D%20%5Cfrac%7B1%7D2%282%2B%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%2B2-%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%29%20%3D%20%5Cfrac%7B1%7D2%284%29%20%3D%202)
Linear because x moves up by 3 and y moves up by 7
Answer:
By thinking logically,here's hint: there are only 4 equal sections and 4 colors,all of them equal to=
![\frac{4}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B4%7D%20)
no matter what color you take,for example green is 1/4,red is 1/4 as well.Eventually the answer is:the probability of orange color is 1/4 too.
Answer:
it 20 chews 5 over 20 chews 10
= 20! / (20-5)! times 5! over 20! / (20-10)! times 10!
=15504/ 184756= .08 or 8%
Step-by-step explanation:
have a good day/night
may i please have a branllliest
sorry if wrong :(
The value of x is
1. x= -37/48
2. x=0
3. x = 33/4
4. x= -20/7
<h3>What is equation?</h3>
A mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
1. 6(8 x + 6) + = - 1
48x + 36 = -1
x= -37/48
2. 9x/7 + 6 = 6
9x/7= 6-6
9x/7 =0
x= 0*7/9
x= 0
3. 2x/11 (11 - 7) = 6
x * 4= 6*11/2
4x= 33
x = 33/4
4. 11x/4 (4 - 2) = 9x + 10
11x/4 * 2 = 9x +10
11/2*x = 9x +10
-7/2x = 10
x= -20/7
Learn more about equation here:
brainly.com/question/10413253
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