The system of equations have no solution.
Explanation:
The equations are
and ![2r+\frac{1}{4} s=8](https://tex.z-dn.net/?f=2r%2B%5Cfrac%7B1%7D%7B4%7D%20s%3D8)
To find the two numbers, let us solve the equations using substitution method.
From the equation
, let us determine the value of r,
![$\begin{aligned} 2 r+\frac{1}{4} s &=8 \\ 2 r &=8-\frac{1}{4} s \\ r &=\frac{1}{2}\left(8-\frac{1}{4} s\right) \\ r &=4-\frac{1}{8} s \end{aligned}$](https://tex.z-dn.net/?f=%24%5Cbegin%7Baligned%7D%202%20r%2B%5Cfrac%7B1%7D%7B4%7D%20s%20%26%3D8%20%5C%5C%202%20r%20%26%3D8-%5Cfrac%7B1%7D%7B4%7D%20s%20%5C%5C%20r%20%26%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%288-%5Cfrac%7B1%7D%7B4%7D%20s%5Cright%29%20%5C%5C%20r%20%26%3D4-%5Cfrac%7B1%7D%7B8%7D%20s%20%5Cend%7Baligned%7D%24)
Let us substitute the value of r in
, we get,
![$\begin{aligned} 4\left(4-\frac{1}{8} s\right)+\frac{1}{2} s &=12 \\ 16-\frac{1}{2} s+\frac{1}{2} s &=12 \\ 16 &=12 \end{aligned}$](https://tex.z-dn.net/?f=%24%5Cbegin%7Baligned%7D%204%5Cleft%284-%5Cfrac%7B1%7D%7B8%7D%20s%5Cright%29%2B%5Cfrac%7B1%7D%7B2%7D%20s%20%26%3D12%20%5C%5C%2016-%5Cfrac%7B1%7D%7B2%7D%20s%2B%5Cfrac%7B1%7D%7B2%7D%20s%20%26%3D12%20%5C%5C%2016%20%26%3D12%20%5Cend%7Baligned%7D%24)
which is not possible.
This means that the system has no solution.
To solve the problem shown above, you must follow the proccedure shown below:
1. By definition, Completary angles are those angles whose sum is 90 degrees and Suplementary angles are those angles whose sum is 180 degrees.
2. Keeping the information above on mind, you have:
<span>
(a) An angle measures 43 . What is the measure of its complement?
=90°-43°
=47°
(b) An angle measures 81 . What is the measure of its supplement?
</span>
=180°-81°
=99°
The answers are:
a) 47°
b) 99°
<h2>Answer:</h2><h2>good to know</h2><h2 /><h2>thx :)</h2>
we know that
In the right triangle ABC
∠
∠
------> by complementary angles
so
Step ![1](https://tex.z-dn.net/?f=%201%20)
Find the measure of angle B
we know that
![tan\ B=\frac{opposite\ side\ angle\ B}{adjacent\ side\ angle\ B}](https://tex.z-dn.net/?f=%20tan%5C%20%20B%3D%5Cfrac%7Bopposite%5C%20%20side%5C%20%20angle%5C%20%20B%7D%7Badjacent%5C%20%20side%5C%20%20angle%5C%20%20B%7D%20%20)
in this problem
![opposite\ side\ angle\ B=7in\\ adjacent\ side\ angle\ B=5in](https://tex.z-dn.net/?f=%20opposite%5C%20%20side%5C%20%20angle%5C%20%20B%3D7in%5C%5C%20adjacent%5C%20%20side%5C%20%20angle%5C%20%20B%3D5in%20)
so
![tan\ B=\frac{7}{5} \\ \\ B=arc\ tan\frac{7}{5} \\ \\ B=54.5\ degrees](https://tex.z-dn.net/?f=%20tan%5C%20%20B%3D%5Cfrac%7B7%7D%7B5%7D%20%5C%5C%20%5C%5C%20B%3Darc%5C%20tan%5Cfrac%7B7%7D%7B5%7D%20%5C%5C%20%5C%5C%20B%3D54.5%5C%20degrees%20)
Step ![2](https://tex.z-dn.net/?f=%202%20)
Find the measure of angle A
![A+B=90\\ A=90-B\\ A=90-54.5\\ A=35.5\ degrees](https://tex.z-dn.net/?f=%20A%2BB%3D90%5C%5C%20A%3D90-B%5C%5C%20A%3D90-54.5%5C%5C%20A%3D35.5%5C%20degrees%20)
therefore
the answer is the option
35.5° and 54.5°