Answer:
Step-by-step explanation:
You have 3 unknowns: a, b, and c. It's our job to find them algebraically. I'm going to start with the point where x = 0 and y = 7. You'll see why in a minute. Filling in the standard form of a quadratic
using (0, 7):
gives you that c = 7. We will use that value now when we write the next 2 equations. Now the point (-2, 19):
and
so
12 = 4a - 2b
Now for the next point (-1, 12):
and
so
5 = a - b
Now we have a system of equations (the 2 bold font equations) that we will solve by elimination:
12 = 4a - 2b
5 = a - b
Multiply the bottom equation by -4 to get a new system:
12 = 4a - 2b
-20 = -4a + 4b
Add those together to get rid of the a terms and end up with
-8 = 2b so
b = -4
Now we can sub in -4 for b to solve for a. I'm using the second bold type equation to do this:
5 = a - (-4) and
5 = a + 4 so
a = 1 and the equation for the quadratic function is
Answer:
Step-by-step explanation:
We are given a circle with a partially shaded region. First, we need to determine the area of the whole circle. To do this, we need the measurement of the radius of the circle:
Use the Pythagorean theorem to solve for the other leg of the right triangle inside the circle:
5^2 = 3^2 + x^2
x = 4
The radius is 4 + 1 cm = 5 cm
So the area of the circle is A = pi*r^2
A = 3.14 * (5)^2
A = 25pi cm^2
To solve for the area of the shaded region:
Ashaded = Acircle - Atriangles
we need to solve for the area of the triangles:
A = 1/2 *b*h
A = 1/2 *6 * 5
A = 15 cm^2
Atriangles = 2 * 15
Atriangles = 30 cm^2
Ashaded = 25pi - 30
Answer: 0.1840
Step-by-step explanation:
The binomial probability formula :-
, here n is the number total of trials , p is the probability of getting success in each trial and P(x) is the probability of getting success in x trial.
Given : The probability of the community favored building a police substation in their neighborhood = 0.64
If 14 citizens are chosen, then the probability that exactly 8 of them favor the building of the police substation will be :-
Hence, the probability that exactly 8 of them favor the building of the police substation = 0.1840
Everything that is not in B.
8. 15. 13
2/3, 5/6, 4/7....common denominator is 42
2/3 = 28/42
5/6 = 35/42
4/7 = 24/42
least to greatest : 2/3, 5/6, 4/7
3/4, 7/12, 4/5....common denominator is 60
3/4 = 45/60
7/12 = 35/60
4/5 = 48/60
least to greatest : 7/12, 3/4, 4/5
7/10, 8/15, 11/20.....common denominator is 60
7/10 = 42/60
8/15 = 32/60
11/20 = 33/60
least to greatest : 8/15, 11/20, 7/10
