Answer:
infinitely many
Step-by-step explanation:
Rewrite these equations as
y = (1/2)x + 1
2y = x + 2
and then solve the second for y: y = (1/2)x + 1. Note that these end results are identical. The two lines coincide; that is, one lies right on top of the other. Thus, there are infinitely many solutions.
Answer:
D = 32
Step-by-step explanation:
A+ B + E = 180 since they form a triangle
14+ 45 + E = 180
E = 180 -14-45
E =121
E on either triangle is the same since they are vertical angles
C+D+E = 180 since they form a triangle
27+ D + 121 = 180
D = 180-121-27
D =32
Answer:
-1
Step-by-step explanation:
First we combine like terms, so y2 - 5y = - 3y
Now we get - 3y = 3
Then we divide both sides by - 3
Now we get y =-1
Answer:
x > - 13
Step-by-step explanation:
Given
- 2(x + 3) < 20 ← distribute parenthesis on left side
- 2x - 6 < 20 ( add 6 to both sides )
- 2x < 26
Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
x > - 13
solution set is { x | x > - 13 }
Answer:
There are 5,827,360 different outcomes.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
In each party:
The order in which the people are selected is important(first is chair, second vice chair), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:

Reds:
Two from a set of 44. So

Blues:
Two from a set of 56. So

How many different outcomes are there for the chair and vice chair elections of both parties?
Considering both, by the fundamental counting principle:
1892*3080 = 5827360
There are 5,827,360 different outcomes.