First of all, let's recall the area of a triangle, knowing its base (b) and height (h):
The exercise is showing you that, if you inscribe a polynomial with more and more side, the area of the polynomial will approximate the area of the circle better and better (you can see youself that the polygon is "filling" the circle more and more as the number of sides increase).
Now, the second column tells you the area of each of the triangles the polygon is split into. So, we can see that the first polygon is split into 3 triangles, each of them having base 1.73 and height 0.5.
So, the area of each triangle is
There are three of these triangles, so the area of the whole polygon is
In the second case, you have six triangles, each with base 1 and height 0.87. So, the whole area is
Finally, in the last case you have 8 triangles, each with base 0.77 and height 0.92. So, the whole area is
Hello,
- 3&2/5=-17/5=-3.4
==>-3.4<n<-2.7
==>n=-3 (if -3 is an integer)
Answer:
B. (1,-8)
Step-by-step explanation:
Slope of the first one:
(-6-0)/(0--3) = -6/3 = -2
y = -2x - 6
3y + 30 = 6x
y + 10 = 2x
-2x - 6 + 10 = 2x
4 = 4x
x = 1
y = -2(1) - 6
y = -8
X = first venture, y = second venture, z = third venture
x + y + z = 15,000
x + z = y + 7000
3x + 2y + 2z = 39,000
these are ur equations.....
x + y + z = 15,000
x - y + z = 7000
--------------------add
2x + 2z = 22,000
x + y + z = 15,000....multiply by -2
3x + 2y + 2z = 39,000
-------------------
-2x - 2y - 2z = - 30,000 (result of multiplying by -2)
3x + 2y + 2z = 39,000
------------------add
x = 9,000
2x + 2z = 22,000
2(9000) + 2z = 22000
18,000 + 2z = 22000
2z = 22000 - 18000
2z = 4000
z = 4000/2
z = 2,000
x + y + z = 15,000
9000 + y + 2000 = 15,000
11,000 + y = 15,000
y = 15,000 - 11,000
y = 4,000
first venture (x) = 9,000 <==
second venture (y) = 4,000 <==
third venture (z) = 2,000 <==
Answer:
a) g(x) = f(x) + 3
So g(x) is a vertical translation of f(x), 3 units upwards
b) g(x) = 3x² - 1 + 3
g(x) = 3x² + 2
The graph has shifted 3 units upwards, so has the vertex.
The vertex of f is (0,-1)
Whereas the vertex of g is (0,2)
-1 + 3 = 2
