Answer:
Solution
p = {-3, 1}
Step-by-step explanation:
Simplifying
p2 + 2p + -3 = 0
Reorder the terms:
-3 + 2p + p2 = 0
Solving
-3 + 2p + p2 = 0
Solving for variable 'p'.
Factor a trinomial.
(-3 + -1p)(1 + -1p) = 0
Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve:
Simplifying
-3 + -1p = 0
Solving
-3 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '3' to each side of the equation.
-3 + 3 + -1p = 0 + 3
Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3
Combine like terms: 0 + 3 = 3
-1p = 3
Divide each side by '-1'.
p = -3
Simplifying
p = -3
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:
Simplifying
1 + -1p = 0
Solving
1 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1p = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1p = 0 + -1
-1p = 0 + -1
Combine like terms: 0 + -1 = -1
-1p = -1
Divide each side by '-1'.
p = 1
Simplifying
p = 1
Solution
p = {-3, 1}
The square root of 32 is 5.65685
Step-by-step explanation:
the answer is in the above image
Answer:
Polynomial equations that can be solved with the quadratic formula have the following properties, assuming all like terms have been simplified.
1. degree = 2 (i.e. the highest power equals exactly two)
2. the linear term (e.g. 4x, or -5x...) and constant term (e.g. 5, -30, pi, etc.) may or may not be present.
Now let's simplify and examine the given equations, and see if each can be solved with the quadratic formula:
A.
The degree (highest power) is three, so it is not "exactly two". NO.
B.
The degree (highest power) is two, so it is "exactly two". YES.
C.
The degree (highest power) is one, so it is not "exactly two". NO.
D.
The degree (highest power) is two, so it is "exactly two". YES.
Note that it is very important to simplify the equations before checking the degree.
Step-by-step explanation:
1-A. About fifty people because the odds are 1/2 and half of 100 is fifty.
B. They would raise 3,000 cents if 100 people played the game because of half didn't win you would have 2,500 cents from what they paid and if half did win you would have 500 cents from having to pay for the prizes leaving only 10 cent from each person who won.
C. I do not think it is an effective game for raising money at a school party because even though the chance is 50:50 it does necessarily mean that half of the people will win and half will lose. Also if not a lot of people come to play your game it won't raise as much money.
2-A. If you flipped a coin 75 times you would expect to get heads 37 to 38 times. Because that is around half.
B. If you flipped a coin 75 you would expect to get heads 37 to 38 times because that is also around half.
C. No, you cannot conclude that the coin is not a fair coin. You have a fifty:fifty chance of getting it heads or tails. Just because the coin landed on heads more that tails does not necessarily make it unfair because every time you flip it it still has that fifty: fifty chance.
I hope this helps.
