Answer:
144°
Step-by-step explanation:
First, find the area of the circle, with the formula A = r²
Plug in 10 as the radius, and solve
A = r²
A = (10²)
A = 100
Using this, create a proportion that relates the area of the sector to the degree measure of the arc.
Let x represent the degree measure of the arc of the sector:
=
Cross multiply and solve for x:
100x = 14400
x = 144
So, the degree measure of the sector arc is 144°
Answer:
The probability of rolling a number that is even and a multiple of 3 is
Step-by-step explanation:
The total possible outcomes of cube = { 1, 2, 3 , 4 , 5 , 6}
Now, let E: Event of getting an even number and a multiple of 3
So, out of all the outcomes, {6) is the ONLY possible favorable outcome.
or,
Hence, the probability of rolling a number that is even and a multiple of 3 is
So the formula to workout the area of a rectangle is height X width
so 11/3 x 5/8
which is 55/24 ft if they want a mixed number then... 2
hope this helps
Answer:
Step-by-step explanation:
Let the quadratic equation of the function by the points in the given equation is,
f(x) = ax² + bx + c
If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),
For (0, 8),
f(0) = a(0)² + b(0) + c
8 = c
For a point (-3, -10),
f(-3) = a(-3)² + b(-3) + 8
-10 = 9a - 3b + 8
9a - 3b = -18
3a - b = -6 --------(1)
For (-4, -8),
f(-4) = a(-4)² + b(-4) + 8
-8 = 16a - 4b + 8
-16 = 16a - 4b
4a - b = -4 ------(2)
Subtract equation (1) from equation (2)
(4a - b) - (3a - b) = -4 + 6
a = 2
From equation (1),
6 - b = -6
b = 12
Function will be,
f(x) = 2x² + 12x + 8
= 2(x² + 6x) + 8
= 2(x² + 6x + 9 - 9) + 8
= 2(x² + 6x + 9) - 18 + 8
= 2(x + 3)² - 10
By comparing this function with the vertex form of the function,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the function 'f' will be (-3, -10)
And axis of symmetry will be,
x = -3
From the given graph, axis of the symmetry of the function 'g' is; x = -3
Therefore, both the functions will have the same axis of symmetry.
y-intercept of the function 'f' → y = 8 Or (0, 8)
y-intercept of the function 'g' → y = -2 Or (0, -2)
Therefore, y-intercept of 'f' is greater than 'g'
Average rate of change of function 'f' = in the interval [a, b]
=
=
= -6
Average rate of change of function 'g' =
=
=
= 3
Therefore, Average rate of change of function 'f' is less than 'g'.