Answer:
Step-by-step explanation:
Given
ID Card of 5 digits
Possibly Digits = {0,1...,9}
Required
Probability that a card has exact number 94213
First, we have o determine the total possible number of ID card numbers
Let the card number be represented by ABCDE
Given that repetition of digits is not allowed;
<em>A can be any of 10 digits</em>
<em>B can any of the remaining 9 digits</em>
<em>C can be any of the remaining 8 digits</em>
<em>D can be any of the remaining 7 digits</em>
<em>E can be any of the remaining 6 digits</em>
<em />
Total number of cards = 10 * 9 *8 * 7 * 6
Total = 30240
Provided that the card number is generated at random; each card number has the same probability of
Hence, the probability of having 94213 is
solved by a system of equations in two variables.
Answer:
1 .4x2-9= 2x+3,2x-3
2 .16x2-1=4x-1,4x+1
3 .16x2-4=4(2x+1)(2x-1)
4 .4x2-1=(2x+1)(2x-1)
Step-by-step explanation:
16x² − 1 = (4x − 1)(4x + 1) ; 16x² − 4 = 4(2x + 1)(2x − 1); 4x² − 1 = (2x + 1)(2x − 1) ;
4x² − 9 = (2x + 3)(2x − 3)
16x² − 1 is the difference of squares. This is because 16x² is a perfect square, as is 1. To find the factors of the difference of squares, take the square root of each square; one factor will be the sum of these and the other will be the difference.
The square root of 16x² is 4x and the square root of 1 is 1; this gives us (4x-1)(4x+1).
16x² − 4 is also the difference of squares. The difference of 16x² is 4x and the square root of 4 is 2; this gives us (4x-2)(4x+2). However, we can also factor a 2 out of each of these binomials; this gives us
2(2x-1)(2)(2x+1) = 2(2)(2x-1)(2x+1) = 4(2x-1)(2x+1)
4x² − 1 is also the difference of squares. The square root of 4x² is 2x and the square root of 1 is 1; this gives us (2x-1)(2x+1).
4x² − 9 is also the difference of squares. The square root of 4x² is 2x and the square root of 9 is 3; this gives us (2x-3)(2x+3).
Answer:
Step-by-step explanation:
y - 8 = -22(x - 8)
y - 8 = -22x + 176
y = -22x + 184
