ANSWER
EXPLANATION
We were given that,
This implies that,
We use the Pythagorean identity
to get,
We were also given that,
This means that,
This is because,
This angles are in the first quadrant so we pick the positive values.
The correct answer is D
We can answer this question by solving each equation for one variable, and then substituting.
3x + y = 11 Given
y = -3x + 11 Subtract 3x from both sides
This equation is now solved for y. Now, let's do the other equation. Make sure to solve it for the same variable.
-2x + y = 1 Given
y = 2x + 1 Add 2x to both sides
Now, let's set both equations equal to each other, since they both equal y.
2x + 1 = -3x + 11 Set both equations equal to each other
1 = -5x + 11 Subtract 2x from both sides
-10 = -5x Subtract 11 from both sides
2 = x Divide both sides by -5
Now, let's substitute x in for one of the equations we found earlier, so that we can find y.
y = 2x + 1 Given
y = (2)(2) + 1 Substitute the x-value, 2
y = 4 + 1 Multiply
y = 5 Add
So, x = 2 and y = 5.
Hope this helps!
Rearrange first
2x+y=10
x+y=6
Since there is one y in both equations, you can eliminate them by subtracting.
2x+y=10
- x+y=6 subtract the two equations
-------------------
x=4
Substitute x in one of them
2(4)+y=10
y=10-8
y=2
Area of a circle = PI x R^2
r = 1/2 diameter
r = 21.5/2
r = 10.75
Area of circle = 3.14 x 10.75^2 = 3.14 x 115.5625 = 362.86625 square units.
A semicircle is half a circle:
Area of semicircle = 362.86625 / 2 = 181.433125 square units (round the answer as needed).