Answer:
110
Step-by-step explanation:
lets assume y is the angle next to x which should complete to form a 360.
50 + 25 + 35 + y = 360
y = 250
x + y = 360
x + 250 = 360
x = 110
26^2 = 18.8^2 + H^2
H^2 = 322.56
H = 17.96 inches
Answer:
<h3>
f(x) = - 3(x + 8)² + 2</h3>
Step-by-step explanation:
f(x) = a(x - h)² + k - the vertex form of the quadratic function with vertex (h, k)
the<u> axis of symmetry</u> at<u> x = -8</u> means h = -8
the <u>maximum height of 2</u> means k = 2
So:
f(x) = a(x - (-8))² + 2
f(x) = a(x + 8)² + 2 - the vertex form of the quadratic function with vertex (-8, 2)
The parabola passing through the point (-7, -1) means that if x = -7 then f(x) = -1
so:
-1 = a(-7 + 8)² + 2
-1 -2 = a(1)² + 2 -2
-3 = a
Threfore:
The vertex form of the parabola which has an axis of symmetry at x = -8, a maximum height of 2, and passes through the point (-7, -1) is:
<u>f(x) = -3(x + 8)² + 2</u>
We can answer the first part of the question not taking intersecting function into account. The domain of 
is all the numbers, x∈(-∞, +∞) and the range is y∈(-∞, 36]. We can observe these results with the help of a graph, as well. Since we are talking about the rainbow, the values above the ground level will make sense. In this case, we will take into account the range as it changes between 0 and 36, included and the domain between -6 and 6. Here (0;36) is the y-intercept and (-6;0) and (6;0) are the x-intercepts of the parabola.
Since in our problem, the linear function that intersects parabola is not given, we have to provide it by ourselves according to the conditions of the problem. It could be any line intersecting parabola in two points. One important point is that the y-intercept has to be no more than 36. Considering these conditions, we can set our linear function to be 
. We can observe the points that we included in the table (they have been given with orange dots in the graph and the table is attached below). We can see that the values of the function (values of y) are positive. Indeed, we are discussing the part of the rainbow above the ground level.
The system of equations with linear and quadratic functions has got two solutions and we can observe that result from the graph. The solutions are (-5.823; 2.088) and (5.323; 7.662). The solutions are the intersection points.
Answer:
1
Step-by-step explanation:
First find f(0) and g(0). These are the values where x=0 in each function.
f(0) = 1+0 = 1
g(0) = 1^2 - 1 = 1-1 = 0
So f(0) = 1 and g(0) = 0.
Now substitute f(0) = 1 into g(t).
g(1) = 1^2 -1 = 1-1 = 0.
So g(f(0)) = 0.
Now substitute g(0) = 0 into f(t).
f(0) = 1 + 0 = 1.
So f(g(0)) = 1.
Add the values 0 and 1 to get 0+1 = 1.
