An irrational number is one that can’t be expressed as a simple fraction.
For instance, the first few digits of the square root of two is written as 1.414213562373095... The digits keep going and cannot be expressed as a fraction. But think of 0.33333... That can easily be written as one-third. The distinguishing feature is that there’s no pattern in the digits for the square root of two.
The first two options are integer fractions. We rule those out immediately. The square root of four is tempting, but realize that it is just equal to two. We come to π (pi).
Arguably the most famous irrational number is π, which starts off as 3.14159265358979... Here, there is again no pattern and the digits extend forever. This meets our definition of our irrational.
Answer:
Totalitarianism goes to C, Fascism goes to B, Communism goes to D, and Constitutional Monarchy goes to A
Step-by-step explanation:
Thats the way it works
Answer:
3) (2,-9)
4) (0,-5)
5) (1,-8)
Step-by-step explanation:
3)
The vertex will occur between you x-intercepts.
You already found that happens at x=2.
To find the corresponding y-coordinate, replace x in
f(x)=(x+1)(x-5) with 2:
f(2)=(2+1)(2-5)
f(2)=(3)(-3)
f(2)=-9
So the vertex is (2,-9).
4)
The y-intercept is when x=0.
So in f(x)=(x+1)(x-5) replace x with 0:
f(0)=(0+1)(0-5)
f(0)=(1)(-5)
f(0)=-5
So the y-intercept is (0,-5).
5)
To find another point just plug in anything besides any x already used.
We preferably want to use a value of x that will keep us on their grid however far up,down,left, or right their grid goes out. So I'm going to choose something close to the vertex which is at x=2. Let's go with x=1.
So replace x in f(x)=(x+1)(x-5) with x=1:
f(1)=(1+1)(1-5)
f(1)=(2)(-4)
f(1)=-8
So another point to graph is (1,-8).
Each pound of potato salad serves 6 people and the average number of pounds of potato salad that each person is served will be 
pound.
<u><em>Explanation</em></u>
At a party of 102 people, 17 pounds of potato salad is served.
<u>a.</u> Suppose, each pound of potato salad is served to 
number of people.
So, 17 pounds of salad is served to 
or 
number of people. That means......
So, each pound of potato salad is served to 6 people.
<u>b.</u> Suppose, the average number of pounds of potato salad that each person is served is 
So, the total number of pounds of salad, served to 102 people 
pounds 
pounds. That means .....
So, the average number of pounds of potato salad that each person is served will be pound.
I will give you everything I can do:
11)
Lets say Car A travels at x mph. That means Car B travels at x+2 mph.
Both of them are traveling towards each others, so we can say the total speed is 2x+2.
Now i takes 3 hrs and we know the distance.
Since R*T=D
Then 3(2x+2)=270
So 2x+2=90
2x=88
x=44
12)
To find perpendicular we want to find the opposite reciprocal of the original slope. Therefore the slope is 3/2.
Now we must find the equation of the line with the given variable.
First find b.
5=3/2*4+b
b = -1
So the equation of this line is:
y=3/2x-1
13) All work will be shown below.
6-3(-2-4x)=2(3(x-4)+7)
6+6+12x=2(3x-12+7)
12+12x=2(3x-5)
12+12x=6x-10
6x=-2
x = -1/3
14)
First we must find the amount each train traveled.
The speed of F train(Freight train)=x
The speed of P train(passenger train)=x+6
Their combined speed is 2x+6
It takes 2 hrs to cover 100 miles
So 2(2x+6)=100
2x+6=50
2x=44
x=22
So the freight train covered 44 miles and the passenger train covered 56 miles.
To find average speed you must do Total Distance/Total Time.
44/2 and 56/2
Which are 22 and 28.
The average speed of F train is 22 mph and average speed of P train is 28 mph.
15) Again opposite reciprocal.
3/5 -> -5/3
Work:
-4=-3*-5/3+b
-4=5+b
b=-9
y = -5/3x-9
16)
F=kx-kx0
First kx0 = 0
So F=kx
So x=F/k
