10. cos(theta)= 1/2
find one solution and then find the "general formula"

Solved

Show answers

Ответ:

hannahkharel2

25.12.2022

Mathematics

The correct option is (D) (3, -5).

Step-by-step explanation: We are given to find the correct ordered pair that is a solution to the following system of equations :

$x+3y=-12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=\dfrac{1}{3}x-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We will be using the method of SUBSTITUTION to solve the given system.

Substituting the value of y from equation (ii) in equation (i), we get

$x+3y=-12\\\\\Rightarrow x+3\left(\dfrac{1}{3}x-6\right)=-12\\\\\\\Rightarrow x+x-18=-12\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.$

From equation (ii), we get

$y=\dfrac{1}{3}\times3-6=1-6=-5.$

Thus, the required solution is (x, y) = (3, -5).

Option (D) is CORRECT.

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice

10. cos(theta)= 1/2 find one solution and then find the "general formula"