If your directrix is a "y=" line, that means that the parabola opens either upwards or downwards (as opposed to the left or the right). Because it is in the character of a parabola to "hug" the focus, our parabola opens upwards. The vertex of a parabola sits exactly halfway between the directrix and the focus. Since our directrix is at y = -2 and the focus is at (1, 6) AND the parabola opens upward, the vertex is going to sit on the main transversal, which is also the "line" the focus sits on. The focus is on the line x = 1, so the vertex will also have that x coordinate. Halfway between the y points of the directrix and the focus, -2 and 6, respectively, is the y value of 2. So the vertex sits at (1, 2). The formula for this type of parabola is 
where h and k are the coordinates of the vertex and p is the DISTANCE that the focus is from the vertex. Our focus is 4 units from the vertex, so p = 4. Filling in our h, k, and p: 
. Simplifying a bit gives us 
. We can begin to isolate the y by dividing both sides by 16 to get 
. Then we can add 2 to both sides to get the final equation 
, choice 4 from above.
Answer:
48 Units
Step-by-step explanation:
Use the Pythagorean theorem to make two right triangles.
Ex= Base is cut in half to make two 9 unit bases
Then count the units from the half point.
Ex= 12 units long
Then use Pythagorean theorem to find one side of the 9-12 right triangle
Ex= 9^2+12^2=c^2
After finding that c=15 units, add all the sides back together
Ex= 18+15+15=48
The answer is 30%. It would be like 70% is what you have left of the 100.
So the image below shows what quadrants are. From the top-right square, the order of quadrants goes from 1-4 in a counter-clockwise matter.
Quadrant I: Top-right square
Quadrant II: Top-left square
Quadrant III: Bottom-left square
Quadrant IV: Bottom-right square.
Any points that are on the bolded vertical line are on the y-axis, and any points on the bolded horizontal line is on the x-axis.
Answer:
c = 13.2
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
# Side a is opposite to ∠A
# Side b is opposite to ∠B
# Side c is opposite to ∠C
- The sine rule is:
# 
* Lets solve the problem
- In Δ ABC
∵ m∠A = 16°
∵ m∠B = 49°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ 16° + 49° + m∠C = 180°
∴ 65° + m∠C = 180° ⇒ subtract 65° from both sides
∴ m∠C = 115°
- Lets use the sine rule to find c
∵ a = 4 and m∠A = 16°
∵ m∠C = 115°
∵ 
- By using cross multiplication
∴ c sin(16) = 4 sin(115) ⇒ divide both sides by sin(16)
∴ 
* c = 13.2
