Answer:
20 degrees
Step-by-step explanation:
If QS bisects Angle PQR, it would mean that Angle PQS and Angle RQS are equal
2x+6=5x
Subtract 2x on both sides
6=3x
Divide by 3 on both sides
x=2
Plug the value of x into either one of the angle measures equation
5x
5(2)=10
If they are equal to one another it would mean that the other angle would be the same measure and you would multiply it by 2
10(2)=20
Therefore 20 degrees is the answer for the measure of Angle PQR
Hope it helped :))
Step-by-step explanation:
4 miles / 27.8 min = 0.14388 miles per minute
26.2 / 0.143888 = 182.1 min
Answer:
Geometric sequence
Step-by-step explanation:
Since the accidents increase by 5% this represents that the number is increasing exponentially . So the sequence is geometric sequence. The geometric sequence can be represented by: a, ar, ar^2, ar^3...
Answer:
The first term is 3 and common difference is 8.
And
The formula for sequence is: ![a_n = -5+8n](https://tex.z-dn.net/?f=a_n%20%3D%20-5%2B8n)
Function is: ![f(n) = f(n-1)+8](https://tex.z-dn.net/?f=f%28n%29%20%3D%20f%28n-1%29%2B8)
Step-by-step explanation:
Given that
![a_4 = 27\\a_8 = 59](https://tex.z-dn.net/?f=a_4%20%3D%2027%5C%5Ca_8%20%3D%2059)
The general formula for arithmetic sequence is:
![a_n = a+(n-1)d](https://tex.z-dn.net/?f=a_n%20%3D%20a%2B%28n-1%29d)
Here
a is the first term
n is the term number
and d is the common difference
for 4th term
![a_4 = a+(4-1)d\\27 = a+3d\ \ \ Eqn\ 1](https://tex.z-dn.net/?f=a_4%20%3D%20a%2B%284-1%29d%5C%5C27%20%3D%20a%2B3d%5C%20%5C%20%5C%20Eqn%5C%201)
For 8th term
![59 = a+ (8-1)d\\59= a+7d\ \ \ \ \ Eqn\ 2](https://tex.z-dn.net/?f=59%20%3D%20a%2B%20%288-1%29d%5C%5C59%3D%20a%2B7d%5C%20%5C%20%5C%20%5C%20%5C%20Eqn%5C%202)
subtracting equation 1 from equation 2
![59-27 = a+7d-(a+3d)\\32 = a+7d-a-3d\\32 = 4d\\d =\frac{32}{4}\\d = 8](https://tex.z-dn.net/?f=59-27%20%3D%20a%2B7d-%28a%2B3d%29%5C%5C32%20%3D%20a%2B7d-a-3d%5C%5C32%20%3D%204d%5C%5Cd%20%3D%5Cfrac%7B32%7D%7B4%7D%5C%5Cd%20%3D%208)
Putting d = 8 in equation 1
![a+3d = 27\\a+3(8) = 27\\a+24=27\\a = 27-24\\a = 3](https://tex.z-dn.net/?f=a%2B3d%20%3D%2027%5C%5Ca%2B3%288%29%20%3D%2027%5C%5Ca%2B24%3D27%5C%5Ca%20%3D%2027-24%5C%5Ca%20%3D%203)
Now for the function
![a_n = a+(n-1)d\\a_n = 3+(n-1)(8)\\a_n = 3 + 8n-8\\a_n = -5+8n](https://tex.z-dn.net/?f=a_n%20%3D%20a%2B%28n-1%29d%5C%5Ca_n%20%3D%203%2B%28n-1%29%288%29%5C%5Ca_n%20%3D%203%20%2B%208n-8%5C%5Ca_n%20%3D%20-5%2B8n)
The sequence can also be expressed as a function as:
![f(n) = f(n-1) + 8](https://tex.z-dn.net/?f=f%28n%29%20%3D%20f%28n-1%29%20%2B%208)
Hence,
The first term is 3 and common difference is 8.
And
The formula for sequence is: ![a_n = -5+8n](https://tex.z-dn.net/?f=a_n%20%3D%20-5%2B8n)
Function is: ![f(n) = f(n-1)+8](https://tex.z-dn.net/?f=f%28n%29%20%3D%20f%28n-1%29%2B8)
Answer:
x = 5
Step-by-step explanation:
x + 1 = 6. subtract the given numbers
(5) + 1 = 6. find the solution (x)
x = 5