Answer:
y = (1/3)x +4
Step-by-step explanation:
The line intercepts the y-axis at y=4. It has a "rise" of 1 unit for each "run" of 3 units, so its slope is rise/run = 1/3.
The slope-intercept form of the equation of a line is ...
y = mx + b . . . . . where m is the slope and b is the y-intercept.
When we put the proper numbers in the equation, we have ...
y = (1/3)x + 4
Answer:
![Recursive\ formula\ a_n=3a_{n-1}-8,\ a_1=7](https://tex.z-dn.net/?f=Recursive%5C%20formula%5C%20a_n%3D3a_%7Bn-1%7D-8%2C%5C%20a_1%3D7)
Step-by-step explanation:
Recursive Formula: The formula that defines the every term of sequence using previous terms.
![a_n=3^n+4\\\\a_1=3^1+4\\\\a_1=3+4\\\\a_1=7](https://tex.z-dn.net/?f=a_n%3D3%5En%2B4%5C%5C%5C%5Ca_1%3D3%5E1%2B4%5C%5C%5C%5Ca_1%3D3%2B4%5C%5C%5C%5Ca_1%3D7)
![a_n=3^n+4...................................(1)\\\\a_{n-1}=3^{n-1}+4..........................(2)\\\\Multiply\ by\ 3\ both\ the\ sides\\\\3a_{n-1}=3\times (3^{n-1}+4)\\\\3a_{n-1}=3\times 3^{n-1}+3\times 4\\\\3a_{n-1}=3^{n}+12\\\\3a_{n-1}==3^n+4+8\\\\From\ eq(1)\ 3^n+4=a_n\\\\3a_{n-1}=a_n+8\\\\Subtract\ 8\ from\ the\ both\ sides\\\\3a_{n-1}-8=a_n+8-8\\\\a_n=3a_{n-1}-8](https://tex.z-dn.net/?f=a_n%3D3%5En%2B4...................................%281%29%5C%5C%5C%5Ca_%7Bn-1%7D%3D3%5E%7Bn-1%7D%2B4..........................%282%29%5C%5C%5C%5CMultiply%5C%20by%5C%203%5C%20both%5C%20the%5C%20sides%5C%5C%5C%5C3a_%7Bn-1%7D%3D3%5Ctimes%20%283%5E%7Bn-1%7D%2B4%29%5C%5C%5C%5C3a_%7Bn-1%7D%3D3%5Ctimes%203%5E%7Bn-1%7D%2B3%5Ctimes%204%5C%5C%5C%5C3a_%7Bn-1%7D%3D3%5E%7Bn%7D%2B12%5C%5C%5C%5C3a_%7Bn-1%7D%3D%3D3%5En%2B4%2B8%5C%5C%5C%5CFrom%5C%20eq%281%29%5C%203%5En%2B4%3Da_n%5C%5C%5C%5C3a_%7Bn-1%7D%3Da_n%2B8%5C%5C%5C%5CSubtract%5C%208%5C%20from%5C%20the%5C%20both%5C%20sides%5C%5C%5C%5C3a_%7Bn-1%7D-8%3Da_n%2B8-8%5C%5C%5C%5Ca_n%3D3a_%7Bn-1%7D-8)
![Recursive\ formula\ a_n=3a_{n-1}-8,\ a_1=7](https://tex.z-dn.net/?f=Recursive%5C%20formula%5C%20a_n%3D3a_%7Bn-1%7D-8%2C%5C%20a_1%3D7)
Answer:
23
Step-by-step explanation:
Answer:
m∠3 = 24°
Step-by-step explanation:
By the theorem,
"Intercepted arc measures the double of the inscribed angle formed by two chords meeting at one point of the circle."
In the given picture,
∠3 is the inscribed angle subtended by the arc ED and is the intercepted arc.
Therefore, m∠3 = ![\frac{1}{2}m(\text{arc}ED)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dm%28%5Ctext%7Barc%7DED%29)
m∠3 = ![\frac{1}{2}(48)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2848%29)
= 24°
Measure of angle 3 is 24 degrees.
Answer:
10/30 multiplied by 9/29 equals 90/870
P(two yellow cards) = 3/29