3
The period is the amount it time it takes to make one complete cycle. If we start at 0 for simplicity sake, the graph is at its maximum point. It reaches its maximum point again at 3, this is one complete cycle and thus the period is 3.
If x=4, rewrite the equation which would be 5(4)+6
First you multiply 4 by 5 which would give you 20
Now put in the 6 in the equation
20+6
20+6=26
Therefore for the expression given the value of x would make your answer be 26
24×1/6 =24/6 = 4
Marco drew 4 pictures
Let's set it up like this:
![0.513=\frac{\left(2x\right)^2}{\left(0.05-x\right)}](https://tex.z-dn.net/?f=0.513%3D%5Cfrac%7B%5Cleft%282x%5Cright%29%5E2%7D%7B%5Cleft%280.05-x%5Cright%29%7D)
Multiply both sides by
![0.05-x](https://tex.z-dn.net/?f=0.05-x)
![0.513\left(0.05-x\right)=\frac{\left(2x\right)^2}{0.05-x}\left(0.05-x\right)](https://tex.z-dn.net/?f=0.513%5Cleft%280.05-x%5Cright%29%3D%5Cfrac%7B%5Cleft%282x%5Cright%29%5E2%7D%7B0.05-x%7D%5Cleft%280.05-x%5Cright%29)
![0.513\left(0.05-x\right)=4x^2](https://tex.z-dn.net/?f=0.513%5Cleft%280.05-x%5Cright%29%3D4x%5E2)
We are then going to use the distributive property. Since we also know that the opposite of an number that is squared is the square root, we can also apply that. We would be left with something like this:
![x=-\frac{0.513+\sqrt{0.673569}}{8},\:x=\frac{\sqrt{0.673569}-0.513}{8}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B0.513%2B%5Csqrt%7B0.673569%7D%7D%7B8%7D%2C%5C%3Ax%3D%5Cfrac%7B%5Csqrt%7B0.673569%7D-0.513%7D%7B8%7D)
The variable
![x](https://tex.z-dn.net/?f=x)
can be both positive or negative.
We have found successfully our answer.
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish<span />
Given:
• AD = 3
,
• DC = 27
,
• BD = x + 3
Let's solve for x.
To solve for x, apply the altitude formula:
![\frac{AD}{BD}=\frac{BD}{DC}](https://tex.z-dn.net/?f=%5Cfrac%7BAD%7D%7BBD%7D%3D%5Cfrac%7BBD%7D%7BDC%7D)
Where BD is the altitude.
Cross multiply:
![BD^2=AD*DC](https://tex.z-dn.net/?f=BD%5E2%3DAD%2ADC)
Plug in the values and solve for x:
![\begin{gathered} (x+3)^2=3*27 \\ \\ (x+3)^2=81 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28x%2B3%29%5E2%3D3%2A27%20%5C%5C%20%20%5C%5C%20%28x%2B3%29%5E2%3D81%20%5Cend%7Bgathered%7D)
Take the square root of both sides:
![\begin{gathered} \sqrt{(x+3)^2}=\sqrt{81} \\ \\ x+3=9 \\ \\ \text{ Subtract 3 from both sides:} \\ x+3-3=9-3 \\ \\ x=6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csqrt%7B%28x%2B3%29%5E2%7D%3D%5Csqrt%7B81%7D%20%5C%5C%20%20%5C%5C%20x%2B3%3D9%20%5C%5C%20%20%5C%5C%20%5Ctext%7B%20Subtract%203%20from%20both%20sides%3A%7D%20%5C%5C%20x%2B3-3%3D9-3%20%5C%5C%20%20%5C%5C%20x%3D6%20%5Cend%7Bgathered%7D)
Therefore, the value of x is 6 .
ANSWER:
d. 6