Answer:
π + 2
Step-by-step explanation:
x² + y² - 4x - 4y + 4 = 0
(x² - 4x + 4) + (y² - 4y + 4) + 4 - 4 - 4 = 0
(x - 2)² + (y - 2)² = 4
So the radius of the circle = 2, center C(2, 2)
Are a of AMNB = area of semi-circle - area of segment AB
= area of semi-circle - (area of quarter circle ABC - area of triangle ABC)
= area of quarter circle ABC + area of triangle ABC
= π(2)²/4 + 2*2/2
= π + 2
Answer:
b. 3/8
Step-by-step explanation:
There are 8 total outcomes on what the coin will land on. If you look at the image, you'll see that there are 3 outcomes for the coin landing on 2 heads and 1 tail.
HHT
HTH
THH
Hey there! I'm happy to help!
Let's think of this as the equation y=mx+b, where m represents the slope and b equals the y-intercept.
The y-intercept is where the line hits the y-axis. As we can see, it hits it at the y-value of zero. Therefore, our equation is just left as y=mx now because b is 0.
We want to find the slope now. This is known as the rise/run, or the y/x. This is basically saying how far up it goes for every one step to the right. If we go to the x-value of one, we see that the y-value is at a little bit less than one. We want to keep on moving to the right until the y-value is at a nice integer value (number without fractions).
If we keep on moving to the right, we see that at the x-value of 3, the y is at 2. This means that the slope is 2/3. And it makes sense! When we were looking at that value of 1, the y-value was less than one and looked like it was at about 2/3, or 0.666....
This will apply to all points on the line. Our y will always be 2/3 of what x is.
Therefore, the equation is y=2/3x
I hope that this helps! Have a wonderful day!
Answer:
y = (1/4)(x - 6)² + 8
Step-by-step explanation:
x² - 4y - 12x + 68 = 0
put in standard form
-4y = -x² + 12x - 68
4y = x² - 12x + 68
y = (1/4)(x² - 12x + 68)
use 1/2 the x coefficent, (-12/2 = -6), as the complete the square term
y = (1/4)(x - 6)² + 68/4 - (1/4)(-6)²
y = (1/4)(x - 6)² + 17 -9
y = (1/4)(x - 6)² + 8