Answer:
<u><em>-29/15</em></u>
Step-by-step explanation:
- <u><em>Multiply 2 and 3 to get 6</em></u>
- <u><em>-6+2/3 + 11/15</em></u>
- <u><em>Add 6 and 2 to get 8</em></u>
- <u><em>-8/3+11/15</em></u>
- <u><em>LCM of 3 and 15 is 15. Convert -8/3 and 11/15 to fractions with 15 as the denominator</em></u>
- <u><em>-40/15 + 11/15</em></u>
- <u><em>Since -40/15 and 11/15 have the same denominator, add them by adding the numerators</em></u>
- <u><em>-40+11 / 15</em></u>
- <u><em>Add -40 snd 11 to get -29</em></u>
- <u><em>-29/15</em></u>
Step-by-step explanation:
![= \sum \limits_{n = 1}^{7} ( - 2. {6}^{n - 1} )](https://tex.z-dn.net/?f=%20%3D%20%20%5Csum%20%5Climits_%7Bn%20%20%3D%201%7D%5E%7B7%7D%20%28%20-%202.%20%7B6%7D%5E%7Bn%20-%201%7D%20%29)
![= \sum \limits_ {n = 1}^{n_{ \text{max}}} (a_1. {r}^{n - 1} )](https://tex.z-dn.net/?f=%20%3D%20%20%5Csum%20%5Climits_%20%7Bn%20%3D%201%7D%5E%7Bn_%7B%20%5Ctext%7Bmax%7D%7D%7D%20%28a_1.%20%7Br%7D%5E%7Bn%20-%201%7D%20%29)
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
![a_1 = - 2](https://tex.z-dn.net/?f=a_1%20%3D%20%20-%202)
![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
![r = 6 \to r >1](https://tex.z-dn.net/?f=r%20%3D%206%20%5Cto%20r%20%20%3E1)
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
• Find S7.
![s_n = a_1.( \frac{ {r}^{n} - 1}{r - n} )](https://tex.z-dn.net/?f=s_n%20%3D%20%20a_1.%28%20%5Cfrac%7B%20%7Br%7D%5E%7Bn%7D%20%20-%201%7D%7Br%20-%20n%7D%20%29)
![s_7 = - 2.( \frac{ {6}^{7} - 1 }{6 - 1} )](https://tex.z-dn.net/?f=s_7%20%3D%20%20-%202.%28%20%5Cfrac%7B%20%7B6%7D%5E%7B7%7D%20-%201%20%7D%7B6%20-%201%7D%20%29)
![s_7 = - 2.( \frac{279.936 - 1}{5} )](https://tex.z-dn.net/?f=s_7%20%3D%20%20-%202.%28%20%5Cfrac%7B279.936%20-%201%7D%7B5%7D%20%29)
![s_7 = - 2.( \frac{279.935}{5} )](https://tex.z-dn.net/?f=s_7%20%3D%20%20-%202.%28%20%5Cfrac%7B279.935%7D%7B5%7D%20%29)
![s_7 = - 2 \: . \: 55.987](https://tex.z-dn.net/?f=s_7%20%3D%20%20-%202%20%5C%3A%20.%20%5C%3A%2055.987)
![s_7 = - 111.974](https://tex.z-dn.net/?f=s_7%20%3D%20%20-%20111.974)
The answer is B.
Answer:
5 mph.
Step-by-step explanation:
Let the runner travel at x miles an hour , then the cyclist travels at 5/ 3 * x
= 5/3 x miles an hour.
So we have the equation
5/3 x - x = 2 ( since the cyclist was travelling at 2 mph faster).,
2/3 x = 2
x = 3/2 * 2 = 3 mph.
So the cyclists speed was 3 * 5/3
= 5 mph.
Answer:
98.5 cm2
Step-by-step explanation:
1/2 × b × h = A
1/2 × b × 10 = 100
5b = 100
b = 100/5
b = 20
<span>The length of the base is 20 units.</span>