3x – 4y = 12
1 answer:
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Answer:
There are 35 different sets of 3 books Joe could choose
Step-by-step explanation:
* Lets explain how to solve the problem
- Combination is a collection of the objects where the order doesn't
matter
- The formula for the number of possible combinations of r objects from
a set of n objects is nCr = n!/r!(n-r)!
- n! = n(n - 1)(n - 2)................. × 1
Lets solve the problem
- Joe has one book each for algebra, geometry, history, psychology,
Spanish, English and Physics in his locker
∴ He has <em>seven</em> books in the locker
- He wants to chose <em>three</em> of them
∵ The order is not important when he chose the books
∴ We will use the combination <em>nCr</em> to find how many different sets
of three books he can choose
- The total number of books is 7
∴ n = 7
∵ He chooses 3 of them
∴ r = 3
∵ 7C3 = 7!/3!(7 - 3)! = 7!/3!(4!)
∴
∴ 7C3 = 35
* There are 35 different sets of 3 books Joe could choose
Answer:
x = 30 and x = 3 both solve the equation correctly. See work below.
Step-by-step explanation:
The very first step is to realize that p(x) is in hundreds of dollars and that the given number is not. 60000 is not in hundreds of dollars. It is in dollars. 60000 dollars = 60000/100 = 600 hundreds of dollars.
Make the polynomial = 600
-x^3+3x^2+900x-2100 = 600 Subtract 600 from both sides
-x^3+3x^2+900x-2100 - 600 = 0 Combine
-x^3+3x^2+900x- 2700 = 0 Group the first and second term and the Thrid and fourth terms.
(-x^2 + 3x^2) + (900x - 2700) = 0 Bring out the common factors from both groups.
-x^2(x - 3) + 900(x - 3) = 0 Factor out x - 3 on both sides of the plus sign
(- x^2 + 900)(x - 3) = 0 Reverse -x^2 + 900 to 900 - x^2
(900 - x^2)(x - 3) = 0 factor (900 - x^2) using the difference of squares
(30 - x)(30 + x) (x - 3) = 0
The two answers that work are
30 - x = 0 Solve
- x = - 30 Divide by - 1
-x/-1 = -30/-1 Combine
x = 30
============
x - 3 = 0
x = 3
===========
There are two values that will work to give p(x) = 600. There is no way to account for why both values work.
The graph below confirms both answers.
