Given a circle described by the equation:

and a function g(x) given by the table

The function g(x) describes a straight line with the equation:

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.

When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0
Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).
The formula for the light bend would be n1*sin i= n2 * sin r
If you use "sin (90-x)= cos x" principle, you can change the sin in the equation into
n1*sin i= n2 * sin r
n1 * cos a= n2 * cos b
n2/n1= cos a/ cos b
Assuming the n constant is the ratio of the glass compared to water then the answer would be: cos a/ cos b
To find your answer you would need to add both colors(blue and green)
to do this you need to make the denominators the same :
24 is a number we can get 8 and 6 to :
1×4=4
6×4=24
5×3=15
8×3=24
your new fractions are 4/24 and 15/24, now we can add them :
4+15=19
and 24 stays the same
your answer is 19/24 (you can not simplify this)
hope this helped
Let's solve your equation step-by-step.<span><span><span>−18</span>−<span>6k</span></span>=<span>6<span>(<span>1+<span>3k</span></span>)
</span></span></span>Step 1: Simplify both sides of the equation.
<span><span><span>−18</span>−<span>6k</span></span>=<span>6<span>(<span>1+<span>3k</span></span>)
</span></span></span><span>Simplify: (Show steps)</span><span><span><span>−<span>6k</span></span>−18</span>=<span><span>18k</span>+6
</span></span>Step 2: Subtract 18k from both sides.<span><span><span><span>−<span>6k</span></span>−18</span>−<span>18k</span></span>=<span><span><span>18k</span>+6</span>−<span>18k</span></span></span><span><span><span>−<span>24k</span></span>−18</span>=6
</span>Step 3: Add 18 to both sides.<span><span><span><span>−<span>24k</span></span>−18</span>+18</span>=<span>6+18</span></span><span><span>−<span>24k</span></span>=24
</span>Step 4: Divide both sides by -24.<span><span><span>−<span>24k</span></span><span>−24</span></span>=<span>24<span>−24</span></span></span><span>k=<span>−1
</span></span>Answer:<span>k=<span>−<span>1</span></span></span>