Answer:
x = -8/2
Step-by-step explanation:
To make the equation easier to work with, our first step will be to make all of our fractions have a common denominator. Both 2 and 4 are factors of 8, so that will be our common denominator.
Old Equation: 1/4x - 1/8 = 7/8 + 1/2x
New Equation (with common denominators): 2/8x - 1/8 = 7/8 + 4/8x
Now, we're going to begin to isolate the x variable. First, we're going to subtract 2/8x from both sides, eliminating the first variable term on one side completely.
2/8x - 1/8 = 7/8 + 4/8x
-2/8x -2/8x
__________________
-1/8 = 7/8 + 2/8x
We're one step closer to our x variable being isolated. Next, we're going to move the constants to the left side of the equation. To do this, we must subtract by 7/8 on both sides.
-1/8 = 7/8 + 2/8x
- 7/8 -7/8
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-1 = 2/8x
Our last step is to multiply 2/8x by its reciprocal in order to get the x coefficient to be 1. This means multiply both sides by 8/2.
(8/2) -1 = 2/8x (8/2)
The 2/8 and 8/2 cancel out, and you're left with:
-8/2 = x
I hope this helps!

we know all it's doing is adding 6 over again to each term to get the next one, so then

now for the explicit one
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=7\\ d=6 \end{cases} \\\\\\ a_n=7+(n-1)6\implies a_n=7+6n-6\implies \stackrel{\textit{Explicit Formula}}{\stackrel{f(n)}{a_n}=6n+1} \\\\\\ therefore\qquad \qquad f(10)=6(10)+1\implies f(10)=61](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%20%5C%5C%5C%5C%20a_n%3Da_1%2B%28n-1%29d%5Cqquad%20%5Cbegin%7Bcases%7D%20n%3Dn%5E%7Bth%7D%5C%20term%5C%5C%20a_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%20d%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a_1%3D7%5C%5C%20d%3D6%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20a_n%3D7%2B%28n-1%296%5Cimplies%20a_n%3D7%2B6n-6%5Cimplies%20%5Cstackrel%7B%5Ctextit%7BExplicit%20Formula%7D%7D%7B%5Cstackrel%7Bf%28n%29%7D%7Ba_n%7D%3D6n%2B1%7D%20%5C%5C%5C%5C%5C%5C%20therefore%5Cqquad%20%5Cqquad%20f%2810%29%3D6%2810%29%2B1%5Cimplies%20f%2810%29%3D61)
Given:
In triangle OPQ, o = 700 cm, p = 840 cm and q=620 cm.
To find:
The measure of angle P.
Solution:
According to the Law of Cosines:

Using Law of Cosines in triangle OPQ, we get




On further simplification, we get




Therefore, the measure of angle P is 79 degrees.
Answer:
A.true
Step-by-step explanation:
The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:

Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.