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3 years ago

A functionf(x) is graphed on the coordinate plane.

Mathematics

2 answers:

ollegr [7]3 years ago

8 0

Answer:

y = -1/2x +1

Step-by-step explanation:

The y intercept is 1 (this is where it crosses the y intercept)

(0,1) and (2,0) are two points on the line

The slope is given by

m = (y2-y1)/(x2-x1)

= (0-1)/(2-0)

= -1/2

The slope is -1/2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = -1/2x +1

fgiga [73]3 years ago

4 0

Answer:

$-0.5x+1$

I took the test, I hope this helps anyone in the future!

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Find values of  that satisfy the equation for 0º    360º and 0  θ  2 . Give answers in degrees and radians.

suter [353]

Answer:

$\theta = 30^\circ, 330^\circ$

$\theta = \frac{\pi}{6}, \frac{11\pi}{6}$

Step-by-step explanation:

Given [Missing from the question]

Equation:

$cos\theta = \frac{\sqrt 3}{2}$

Interval:

$0 \le \theta \le 360$

$0 \le \theta \le 2\pi$

Required

Determine the values of $\theta$

The given expression:

$cos\theta = \frac{\sqrt 3}{2}$

... shows that the value of $\theta$ is positive

The cosine of an angle has positive values in the first and the fourth quadrants.

So, we have:

$cos\theta = \frac{\sqrt 3}{2}$

Take arccos of both sides

$\theta = cos^{-1}(\frac{\sqrt 3}{2})$

$\theta = 30$ --- In the first quadrant

In the fourth quadrant, the value is:

$\theta = 360 -30$

$\theta = 330$

So, the values of $\theta$ in degrees are:

$\theta = 30^\circ, 330^\circ$

Convert to radians (Multiply both angles by $\pi/180$ )

So, we have:

$\theta = \frac{30 * \pi}{180}, \frac{330 * \pi}{180}$

$\theta = \frac{\pi}{6}, \frac{33 * \pi}{18}$

$\theta = \frac{\pi}{6}, \frac{11 * \pi}{6}$

$\theta = \frac{\pi}{6}, \frac{11\pi}{6}$

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