Which linear inequality represents the graph below?

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

6 0

Answer:

Step-by-step explanation:

1. We can clearly see that the "rise" is 5 and the "run" is 2, which cancels out both A. and D.

2. The line is dashed, which therefore cancels out both C. and D.

3. Just by canceling out those two can help you see that B fits what is seen in this figure because option A. has the wrong amount of "rise" over "run".

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If cos x=8/17, and 270° < x < 360° what is cos(2x)?

svp [43]

Answer: $\bold{-\dfrac{161}{289}}$

Step-by-step explanation:

Given: cos x = $\dfrac{8}{17}$ , x is in Quadrant 4

Use Pythagorean Theorem to find sin x:

8² + y² = 17²

y² = 17² - 8²

y² = 289 - 64

y² = 225

y = 15

→ sin x = $-\dfrac{15}{17}$

Use the double angle formula to find cos (2x):

$cos (2x) = cos^2 x - sin^2 x\\\\.\qquad=\bigg(\dfrac{8}{17}\bigg)^2-\bigg(-\dfrac{15}{17}\bigg)^2\\\\\\.\qquad=\dfrac{64}{289}-\dfrac{225}{289}\\\\\\.\qquad=-\dfrac{161}{289}$