Answer:
![y = \frac{1}{4} \times {2}^{x} - 1](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5Ctimes%20%20%7B2%7D%5E%7Bx%7D%20%20-%201)
Step-by-step explanation:
Assuming the given logarithmic equation is
![y = \log_{2}( {4}{x } - 4)](https://tex.z-dn.net/?f=y%20%3D%20%20%20%5Clog_%7B2%7D%28%20%7B4%7D%7Bx%20%7D%20%20-%204%29%20)
We interchange x and y to get:
![x= \log_{2}( {4}{y} - 4)](https://tex.z-dn.net/?f=x%3D%20%20%20%5Clog_%7B2%7D%28%20%7B4%7D%7By%7D%20-%204%29%20)
We solve for y now:
![{2}^{x} = {4}{y} - 4](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bx%7D%20%20%3D%20%20%7B4%7D%7By%7D%20%20%20-%204)
We add 4 to both sides to get;
![{2}^{x} + 4 = 4y](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bx%7D%20%20%2B%204%20%3D%204y)
Divide through by 4:
![y = \frac{1}{4} \times {2}^{x} - 1](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5Ctimes%20%20%7B2%7D%5E%7Bx%7D%20%20-%201)
Answer:
The answer is 2.
Step-by-step explanation:
1- Suppose we have following array of ten integers: 5 3 8 9 1 7 0 2 6 4.
2- Before the last merge, the left half and the right half must be sorted. So it should be
1 3 5 8 9 0 2 4 6 7
Therefore the solution is 2.
The given equation is
where h is the height, in feet, of a ball and t is the time, in seconds.
<u>Part a: The height of the ball when t = 2 seconds:</u>
The height of the ball above the ground 2 seconds after it is released can be determined by substituting t= 2 in the equation
, we get;
![h(2)=-16(2)^2+80(2)+4](https://tex.z-dn.net/?f=h%282%29%3D-16%282%29%5E2%2B80%282%29%2B4)
Simplifying the terms, we get;
![h(2)=-64+160+4](https://tex.z-dn.net/?f=h%282%29%3D-64%2B160%2B4)
![h(2)=100](https://tex.z-dn.net/?f=h%282%29%3D100)
Thus, the height of the ball after 2 seconds is 100 feet.
<u>Part b: The height of the ball when t = 4 seconds:</u>
The height of the ball above the ground 4 seconds after it is released can be determined by substituting t = 4 in the equation
, we get;
![h(4)=-16(4)^2+80(4)+4](https://tex.z-dn.net/?f=h%284%29%3D-16%284%29%5E2%2B80%284%29%2B4)
Simplifying the terms, we get;
![h(4)=-256+320+4](https://tex.z-dn.net/?f=h%284%29%3D-256%2B320%2B4)
![h(4)=68](https://tex.z-dn.net/?f=h%284%29%3D68)
Thus, the height of the ball after 4 seconds is 68 feet.
<span>Scale drawings make it easy to see large things on paper, like a house or road</span>
You bought a magazine for $5 and four erasers. you spent a total of $25.
Magazine cost: 5$ each
Eraser cost: X$ each
Total cost is the number of items (1 magazine) times the cost of each item (5$). We don't know the cost of each eraser, so we represent that using a variable, X.
1(5) + 4(X) = 25
5 + 4X = 25
subtract 5 from both sides
4X = 25 - 5
4X = 20
divide both sides by 4
X = 20/4
X = 5
Each eraser cost 5$