There are 10 letters in the set {a, b, c, d, e, f, g, h, i, j} which is the pool of letters to choose from when making these three letter codes.
We have 10 choices for slot 1
Then 9 choices for slot 2. This is because we can't reuse the choice for slot 1
Then 8 choices for slot 3
Overall, there are 10*9*8 = 90*8 = 720 different permutations
Answer: 720
Note: you can use the nPr permutation formula with n = 10 and r = 3 to get the same answer
Answer:
infinitely many
Step-by-step explanation:
12x + 1 = 3(4x + 1) - 2
Distribute
12x + 1 = 12x + 3 - 2
Combine like terms
12x+1 = 12x +1
Subtract 12x from each side
1 =1
Since this is always true, we have infinite solutions
<h2>
Greetings!</h2>
Answer:
y = 
Step-by-step explanation:
First, we need to rearrange the equation to make it y = mx + c
4x - y = 3
y + 3 = 4x
y = 4x -3
So the slope of the line is 4.
The slope of a line perpendicular to an equation is:

So the slope of the perpendicular line is:
= -0.25
Now to find the equation of a line you can use the following equation:
y - y₁ = m(x - x₁)
Where y₁ is the y-coordinate, x₁ is the x-coordinate and m is the gradient. Plug the values in:
y₁ = 6
x₁ = -5
m = 
y - 6 =
(x - - 5)
To get rid of the fraction we need to multiply the whole equation by 4:
4y - 24 = -1(x - - 5)
The two negatives cancel out:
4y - 24 = -1(x + 5)
Multiply the brackets out:
4y - 24 = -x + 5
Now, to rearrange the formula back into y = mx + c
Move the -24 over to the other side making it a +24:
4y = 2x + 5 + 24
4y = 2x + 29
Divide everything by 4:
y = 
y = 
<h2>Hope this helps!</h2>