You probably mean either
![8\cdot2^x + 3 = 48](https://tex.z-dn.net/?f=8%5Ccdot2%5Ex%20%2B%203%20%3D%2048)
or
![8\cdot2^{x+3} = 48](https://tex.z-dn.net/?f=8%5Ccdot2%5E%7Bx%2B3%7D%20%3D%2048)
Write 8 = 2³, so that in the first interpretation,
![8\cdot2^x = 2^3 \cdot 2^x = 2^{x + 3}](https://tex.z-dn.net/?f=8%5Ccdot2%5Ex%20%3D%202%5E3%20%5Ccdot%202%5Ex%20%3D%202%5E%7Bx%20%2B%203%7D)
and in the second,
![8\cdot2^{x+3} = 2^3 \cdot 2^{x+3} = 2^{x + 6}](https://tex.z-dn.net/?f=8%5Ccdot2%5E%7Bx%2B3%7D%20%3D%202%5E3%20%5Ccdot%202%5E%7Bx%2B3%7D%20%3D%202%5E%7Bx%20%2B%206%7D)
Then in the first interpretation, we have
![2^{x + 3} + 3 = 48 \implies 2^{x + 3} = 45 \implies x + 3 = \log_2(45) \implies x = \log_2(45) - 3 \approx \boxed{2.492}](https://tex.z-dn.net/?f=2%5E%7Bx%20%2B%203%7D%20%2B%203%20%3D%2048%20%5Cimplies%202%5E%7Bx%20%2B%203%7D%20%3D%2045%20%5Cimplies%20x%20%2B%203%20%3D%20%5Clog_2%2845%29%20%5Cimplies%20x%20%3D%20%5Clog_2%2845%29%20-%203%20%5Capprox%20%5Cboxed%7B2.492%7D)
Otherwise, the second interpretation gives
![2^{x + 6} = 48 \implies x + 6 = \log_2(48) \implies x = \log_2(48) - 6 \approx -0.415](https://tex.z-dn.net/?f=2%5E%7Bx%20%2B%206%7D%20%3D%2048%20%5Cimplies%20x%20%2B%206%20%3D%20%5Clog_2%2848%29%20%5Cimplies%20x%20%3D%20%5Clog_2%2848%29%20-%206%20%5Capprox%20-0.415)
Answer:
![1 \frac{2}{3} - 2\frac{2}{3} = -1](https://tex.z-dn.net/?f=1%20%5Cfrac%7B2%7D%7B3%7D%20-%202%5Cfrac%7B2%7D%7B3%7D%20%20%3D%20-1)
Step-by-step explanation:
![1\frac{2}{3} - 2 \frac{2}{3\\} \\\\\frac{5}{3} - \frac{8}{3} = \frac{-3}{3} \\ \\\frac{-3}{3} = -1](https://tex.z-dn.net/?f=1%5Cfrac%7B2%7D%7B3%7D%20-%202%20%5Cfrac%7B2%7D%7B3%5C%5C%7D%20%5C%5C%5C%5C%5Cfrac%7B5%7D%7B3%7D%20-%20%5Cfrac%7B8%7D%7B3%7D%20%3D%20%5Cfrac%7B-3%7D%7B3%7D%20%5C%5C%20%5C%5C%5Cfrac%7B-3%7D%7B3%7D%20%3D%20-1)
Hope this helps! :)
Answer:
80 square feet
Step-by-step explanation:
You can split it into a rectangle and a triangle. The area of the rectangle would be 2 * 16 = 32 square feet.
Next, you need to find the height of the triangle. To do this, you can split the triangle into two right triangles and use the pythagorean theorem to find the height. The dimensions of one of the right triangle is 8 for one of the legs and 10 for the hypotenuse. Using the pythagorean theorem, 8^2 + b^2 = 10^2, which is 64 + b^2 = 100, so b^2 = 36 and b = 6. This means that the height is 6. Now, you find the area of the triangle and you get 16 * 6 / 2 = 48.
Adding the area of the rectangle and the triangle: 32 + 48 = 80
Not sure why that's not an answer choice, I'm fairly confident it's right.
Answer: 9.2•10^7 kilometers
Step-by-step explanation:
5.8•10^7=58,000,000
1.5•10^8=150,000,000
150,000,000-58,000,000=92,000,000
92,000,000=9.2•10^7
Answer:
2.) undefined slope 3.) zero slope (i'm not sure what 1 and 4 are, sorry!)
Step-by-step explanation:
undefined slope has the same x-coordinate and the denominator becomes 0. it also is a vertical line. for a zero slope, it has the same y-coordinate and the numerator is 0. this is a horizontal line. *this is my first response so if i am wrong, that is embarrassing*