Is the point (1,-3) a solution to the system? show all your work y>x-1y >-x+2

Mathematics

1 answer:

vagabundo [1.1K]2 years ago

6 0

Answer:

To determine if the point is a solution, substitute the x value into the right side of the inequality and compare the result with the y value of the point.

- x + 2 = - 1 + 2 = 1

Now - 3 < 1

Thus (1, - 3) is not a solution

Step-by-step explanation:

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Trigonometric Identities.

To solve this problem, we need to keep in mind the following:

* The tangent function is negative in the quadrant II

* The cosine (and therefore the secant) function is negative in the quadrant II

* The tangent and the secant of any angle are related by the equation:

$\sec ^2\theta=\tan ^2\theta+1$

We are given:

$\text{tan}\theta=-\frac{\sqrt[]{14}}{4}$

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Substituting in the identity:

$\begin{gathered} \sec ^2\theta=(-\frac{\sqrt[]{14}}{4})^2+1 \\ \text{Operating:} \\ \sec ^2\theta=\frac{14}{16}+1 \\ \sec ^2\theta=\frac{14+16}{16} \\ \sec ^2\theta=\frac{30}{16} \end{gathered}$

Taking the square root and writing the negative sign for the secant: