Answer:
≈ 6 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = 
with (x₁, y₁ ) = F(2, 11) and (x₂, y₂ ) = G(5, 16)
d = 
= 
= 
= 
≈ 6 ( to the nearest whole number )
The easist way to find the vertex is to complete the square:
y=2x^2 +11x-6 => <span>y=2[ x^2 + (11/2)x + (11/2)^2 - (11/2)^2 ] - 6
This can be rewritten as
y = 2[(x+11/2)^2 ] -(121/4) - 24/4
y = 2 (x+11/2)^2 - 145/4
this is the equation in vertex form. The vertex is at (-11/2, -145/4).</span>
Answer:
14 divided by 9 = 1.5
The result of 14/9 is a non-terminating, repeating decimal.
Answer:
Around 5.5 square meters
Step-by-step explanation:
You can start by finding the area of the segment. Since the rest of the circle that is not in the segment is 240 degrees, the segment is 120 degrees or a third of the circle. You can therefore find the area of that segment with the formula 
square meters. Now, you need to find the area of the triangle inside the sector. This is more difficult than last time, because it is not a 90 degree angle. However, you can solve this by dividing this triangle into two 30-60-90 triangles, which you know how to find the ratio of sides for. In a 30-60-90 triangle, the hypotenuse is twice the length of the smallest leg, and the larger leg is 
times larger than the smaller leg. In this case, these dimensions are a base of 
for the smaller leg and 
for the larger leg, or the base. Using the triangle area formula and multiplying by 2 (because remember, we divided the big triangle in half), you get 
square meters. Subtracting this from the area of the segment, you get about 5.5 square meters. Hope this helps!
