Answer:
f(x) = (x +6)^3 +4
Step-by-step explanation:
f(x -h) +k is the function f(x) translated by (h, k). You want to translate the function by (-6, 4), so it will be ...
f(x +6) +4 = (x+6)^3 +4
The translated function is ...
f(x) = (x +6)^3 +4
f(x) = x^3 +18x^2 +108x +220 . . . . . . with parentheses eliminated
_____
The graph shows the two versions of the translated function. One is dashed so you can see the other has the same graph.
We are given this inequality,
We will follow these steps to solve it:
Step 1:
First let us bring 10 to the left side.
10 is in addition on right, so we apply opposite operation of addition that is subtracting 10 from left side, we get
Step 2:
Next we have to eliminate -4 which is in multiplication with x on the right side.
So applying opposite operation of multiplication that is dividing both sides by -4.
We have to consider here that when we divide or multiply with a negative the sign of inequality reverses, that is ≥ becomes ≤ and vice versa.
x≥4
Answer is last option x≥4.
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!