The sum of the two <em>rational</em> equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).
<h3>How to simplify the addition between two rational equations</h3>
In this question we must use <em>algebra</em> definitions and theorems to simplify the addition of two <em>rational</em> equations into a <em>single rational</em> equation. Now we proceed to show the procedure of solution in detail:
- (n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given
- (n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)
- 1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse
- [3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator
- (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / Result
To learn more on rational equations: brainly.com/question/20850120
#SPJ1
Answer:
x = 17
Step-by-step explanation:
77° + (6x + 1)° = 180° (angels on a straight line)
Solve for x
77 + 6x + 1 = 180
Add like terms
6x + 78 = 180
6x + 78 - 78 = 180 - 78
6x = 102
6x/6 = 102/6
x = 17
Answer:
The correct answer is D) areas, probability, and relative frequencies
Step-by-step explanation:
This is because each of these terms refers to an amount of space surrounding the mean on the normal distribution curve. Each of them let's us know how likely a spot is to have a value within it.
The z-score would not fit this as it identifies the value and how far away a single spot on the graph would be.
<u>ANSWER </u>
and 
<u>EXPLANATION</u>
Given;
and
The augmented matrix of the two linear equation is given by;
![\left[\begin{array}{ccc}4&-12|&-1\\6\:&\:\:\:4|&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-12%7C%26-1%5C%5C6%5C%3A%26%5C%3A%5C%3A%5C%3A4%7C%264%5Cend%7Barray%7D%5Cright%5D)
We now perform row operations;
.
This gives us
![\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\6\:&\:\:\:4|&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-3%7C%26%5Cfrac%7B-1%7D%7B4%7D%5C%5C6%5C%3A%26%5C%3A%5C%3A%5C%3A4%7C%264%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:22|&\frac{11}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-3%7C%26%5Cfrac%7B-1%7D%7B4%7D%5C%5C0%5C%3A%26%5C%3A%5C%3A%5C%3A22%7C%26%5Cfrac%7B11%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-3%7C%26%5Cfrac%7B-1%7D%7B4%7D%5C%5C0%5C%3A%26%5C%3A%5C%3A%5C%3A1%7C%26%5Cfrac%7B1%7D%7B4%7D%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}1&0|&\frac{1}{2}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%7C%26%5Cfrac%7B1%7D%7B2%7D%5C%5C0%5C%3A%26%5C%3A%5C%3A%5C%3A1%7C%26%5Cfrac%7B1%7D%7B4%7D%5Cend%7Barray%7D%5Cright%5D)
Hence and
Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:
a-) -√2 / 2.
<h3>What is implicit differentiation?</h3>
Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.
In this problem, the function is:
xcos(y) = 2.
The derivative is relative to t, applying the product rule, as follows:
Since dx/dt=−2, we have that:
When y = π/4, x is given by:
xcos(y) = 2.
Hence:
Since cot(pi/4) = 1, we have that:
Which means that option a is correct.
More can be learned about implicit differentiation at brainly.com/question/25608353
#SPJ1
