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4 years ago

Which equation represents the linear relationship shown in the table?

Mathematics

2 answers:

Nastasia [14]4 years ago

7 0

Answer:

Step-by-step explanation:

The first expression represents the linear relationship shown in the table. We can demonstrate this just by replacing each value into the equation, and see if it returns the same values as the table shows.

For $x=0$ :

$y=3(0)+4=4$

For $x=2$ :

$y=3(2)+4=10$

For $x=4$ :

$y=3(4)+4=16$

For $x=5$ :

$y=3(6)+4=22$

As you can see, the first the expression is the only one that completely fits with the table. Therefore, the right answer is the first equation.

DochEvi [55]4 years ago

3 0

Plug your X values into the X spot in each equation and plug in the corresponding Y value into the Y spot in each equation. If the statement is true, then it is a linear relationship. If not, then it is not linear.

EXAMPLE:
y=3x+4
1. Plug it in
0=3(4)+4
2. Solve/Simplify
0=12+4
0=16
3.Is the statement true?
This statement is NOT true because 0 is not equal to 16
4. Answer
This is not a linear equation.

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Answer:

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Step-by-step explanation:

we want to solve the following trigonometric equation:

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back-substitute:

$\begin{cases} \cos( \theta) = \dfrac{1}{2} \\ \cos( \theta) = - 1 \end{cases} \theta \in[0,2\pi)$

take inverse trig in both sides

$\implies \begin{cases} \theta = \dfrac{\pi}{3} + 2n\pi\\\theta= \frac{5\pi}{3} + 2n\pi \\ \theta = \pi + 2n\pi\end{cases} \theta \in[0,2\pi) \\\\\implies\theta= \frac{\pi}{3}+\dfrac{2n\pi}{3},\theta\in [0,2\pi)\\\text{when n=0}\\ \implies \theta = \frac{\pi}{3} \\ \text{when n=1}\\ \theta= \pi\\ \text{when n=2}\\\theta=\frac{5\pi}{ 3}$

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$\displaystyle\theta = \frac{\pi}{3} , \pi, \frac{5\pi}{ 3}$

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