Answer:
$16.99
Step-by-step explanation:
The first step into solving this requires you to find out what 15% of $19.99 is. In order to do that, you must multiply the number (19.99) by the decimal form of the percentile (15%). To find a decimal form of a percent sign, you must simply move the decimal two spots to the left, to change the denominator to 100. A number always has a denominator, even if it isn't shown. in this case, it is 15/1, and we have to convert it to 15/100 so all you have to do is divide 15 by 100, or move the decimal to the left 2 spots. The answer you should get is 0.15
I normally don't round until I have the <em>final</em> answer, just so the numbers aren't off. So then, what you need to do, is multiply 19.99 by your newly found decimal. You should get 2.9985. Now, the question asks for how much the cartridge would cost if it were 15% off, so therefore you must subtract your answer from the original number (19.99), and should get 16.9915. Now is the time you should simplify to the nearest hundredth, and should get $16.99 as your final answer.
Answer:
![2x^2+32=0\\2x^2=-32\\x^2=-16\\x=16i \\x=-16i](https://tex.z-dn.net/?f=2x%5E2%2B32%3D0%5C%5C2x%5E2%3D-32%5C%5Cx%5E2%3D-16%5C%5Cx%3D16i%20%5C%5Cx%3D-16i)
are you completely sure you don't mean 2x^2-32? that would have real roots
Answer:
![Area = 5.84in^2](https://tex.z-dn.net/?f=Area%20%3D%205.84in%5E2)
Step-by-step explanation:
Given
![Circles = 3](https://tex.z-dn.net/?f=Circles%20%3D%203)
--- The radius of each
Required
The area between them
See attachment for illustration of the question. (figure 1)
First, calculate the height of the equilateral triangle formed by the 3 radii (See figure 2)
Using Pythagoras theorem, we have:
![12^2 = h^2 + 6^2](https://tex.z-dn.net/?f=12%5E2%20%3D%20h%5E2%20%2B%206%5E2)
![144 = h^2 + 36](https://tex.z-dn.net/?f=144%20%3D%20h%5E2%20%2B%2036)
Collect like terms
![h^2 = 144 - 36](https://tex.z-dn.net/?f=h%5E2%20%3D%20144%20-%2036)
![h^2 = 108](https://tex.z-dn.net/?f=h%5E2%20%3D%20108)
Take square roots
![h = \sqrt{108](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%7B108)
Expand
![h = \sqrt{36 * 3](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%7B36%20%2A%203)
Split
![h = \sqrt{36} * \sqrt{3](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%7B36%7D%20%2A%20%5Csqrt%7B3)
![h = 6\sqrt{3](https://tex.z-dn.net/?f=h%20%3D%206%5Csqrt%7B3)
Now, the area of the equilateral triangle can be calculated using:
![A = \frac{1}{2}bh](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7Dbh)
Where
![h = 6\sqrt{3](https://tex.z-dn.net/?f=h%20%3D%206%5Csqrt%7B3)
![b = 2r = 2 * 6 = 12](https://tex.z-dn.net/?f=b%20%3D%202r%20%3D%202%20%2A%206%20%3D%2012)
![A = \frac{1}{2} * 12 * 6\sqrt 3](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%2012%20%2A%206%5Csqrt%203)
![A = 6 * 6\sqrt 3](https://tex.z-dn.net/?f=A%20%3D%206%20%2A%206%5Csqrt%203)
![A_1 = 36\sqrt 3](https://tex.z-dn.net/?f=A_1%20%3D%2036%5Csqrt%203)
Next, is to calculate the area of the sector formed by 2 radii in each circle (figure 3).
Since the radii formed an equilateral triangle, then the central angle will be 60. So:
![A = \frac{\theta}{360} * \pi r^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B%5Ctheta%7D%7B360%7D%20%2A%20%5Cpi%20r%5E2)
![A = \frac{60}{360} * \pi 6^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B60%7D%7B360%7D%20%2A%20%5Cpi%206%5E2)
![A = \frac{60}{360} * \pi * 36](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B60%7D%7B360%7D%20%2A%20%5Cpi%20%2A%2036)
![A = \frac{60}{10} * \pi](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B60%7D%7B10%7D%20%2A%20%5Cpi)
![A = 6\pi](https://tex.z-dn.net/?f=A%20%3D%206%5Cpi)
For the three circles, the area is:
![A_2 = 3 * 6\pi](https://tex.z-dn.net/?f=A_2%20%3D%203%20%2A%206%5Cpi)
![A_2 = 18\pi](https://tex.z-dn.net/?f=A_2%20%3D%2018%5Cpi)
Subtract the areas of the sectors (A2) from the area of the equilateral triangle (A1), to get the area between them.
![A = A_1 - A_2](https://tex.z-dn.net/?f=A%20%3D%20A_1%20-%20A_2)
![A = 36\sqrt 3 - 18\pi](https://tex.z-dn.net/?f=A%20%3D%2036%5Csqrt%203%20-%2018%5Cpi)
![A = 36*1.7321 - 18 * 3.14](https://tex.z-dn.net/?f=A%20%3D%2036%2A1.7321%20-%2018%20%2A%203.14)
![A = 5.8356](https://tex.z-dn.net/?f=A%20%3D%205.8356)
Approximate
![A = 5.84in^2](https://tex.z-dn.net/?f=A%20%3D%205.84in%5E2)
Answer: I’m pretty sure it’s graph A
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The explicit formula for a geometric sequence is
= a![(r)^{n-1}](https://tex.z-dn.net/?f=%28r%29%5E%7Bn-1%7D)
where a is the first term and r the common ratio
From the recursive formula
= - 9![a_{n-1}](https://tex.z-dn.net/?f=a_%7Bn-1%7D)
The common ratio r = - 9 and with a = 300, then
= 300
→ C