Answer & Step-by-step explanation:
(2/5 + 3/4) * [ 3 - (1/4 : 1/5)]
When you see this sign, : , it usually means to divide the numbers because they represent some form of a ratio. So, we will divide 1/4 by 1/5.
First, do all of the operations in the parentheses ().
(2/5 + 3/4)*[ 3 - (1/4 : 1/5)]
(23/20) * [ 3 - (5/4)]
(23/20) * (7/4)
Now, we multiply 23/20 by 7/4.
(23/20) * (7/4)
161/80
This number can not be simplified so we will keep it as it is.
So, the answer to this expression is 161/80
Answer: 45z + 11
Explanation:
-9(-5z - 2) - 7
= 45z + 18 - 7
= 45z + 11
A right angle is 90 degrees so 90 plus 20 would equal 110
Answer: 110 degrees
Answer:
A w is less than 7
A x is greater then or equal to -1
Step-by-step explanation:
Answer: 8.73 ft/s
Step-by-step explanation:
We have the following equation that models the motion of the rock:
![h(t)=-16t^{2}+64t+180](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E%7B2%7D%2B64t%2B180)
Where
is the height of the rock at a time
.
Now, if
we can find
and then the velocity of the rock at that height:
![48=-16t^{2}+64t+180](https://tex.z-dn.net/?f=48%3D-16t%5E%7B2%7D%2B64t%2B180)
Rearranging the equation:
![-16t^{2}+64t+132=0](https://tex.z-dn.net/?f=-16t%5E%7B2%7D%2B64t%2B132%3D0)
Multiplying the equation by -1:
![16t^{2}-64t-132=0](https://tex.z-dn.net/?f=16t%5E%7B2%7D-64t-132%3D0)
Solving with the quadratic formula
, where
,
,
.
![t=\frac{-(-64)\pm\sqrt{(-64)^{2}-4(16)(-132)}}{2(16)}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-%28-64%29%5Cpm%5Csqrt%7B%28-64%29%5E%7B2%7D-4%2816%29%28-132%29%7D%7D%7B2%2816%29%7D)
Choosing the positive result of the equation:
Since velocity
is defined as the traveled distance
in a given time
, we have:
![V=\frac{h(t)}{t}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7Bh%28t%29%7D%7Bt%7D)
![V=\frac{48 ft}{5.5 s}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B48%20ft%7D%7B5.5%20s%7D)
This is the velocity of the rock at the height of 48 feet