How many ways can a person select 3 videotapes from a collection of 10 tapes?
1 answer:
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If you mean that you can only use each number along the four expressions, it looks impossible to me. Here's the proof.
Multiplications and divisions are the most restrictive operations, because only some triplets will work. In particular, you can choose
I'm listing them in triplets because you can use them in many ways. For example, the first triple can be used to generate
But it doesn't really matter, in all cases you used numbers 2,3, and 6.
If you look closely, all triplets but the last one involve 2. This means that we must use the last one, because otherwise we would use two triplets with two, and we would have repetitions.
So, we surely have to use (3,4,12), either to write or
.
This means that we can't use 3, 4 and 12 anymore. The only triplet remaining is (2,5,10).
For example, let's say that our multiplication is and our division is
.
We're left with the following numbers:
From here, we're left with a few choices for the addition: if we choose we're left with 8,9 and 11. We can't write any subtraction with these numbers.
If we choose , we're left with 6, 9 and 11. We can't write any subtraction with these numbers.
If we choose , we're left with 6, 7 and 11. We can't write any subtraction with these numbers.
To recap, we're forced to use 2,3,4,5,10 and 12 for the multiplication and the division, and the remaining numbers don't allow to write an addiction and a subtraction.
Thus, you can't use all the operations involving numbers 1-12 only once.
Answer:
Infinite solutions
Step-by-step explanation:
To determine the number of solutions a system has, you need its slope. If the slopes are the same, check if the equations are equivalent or not.
To find the slope, rearrange the equation to isolate "y", which makes it slope-intercept form y = mx + b.
"x" and "y" represent points on the line.
"m" represents the slope, which is how steep a line is.
"b" represents the y-intercept (where the graph hits the y-axis).
Isolate "y" in both equations:
x + 3y = 0
3y = -x Subtract 'x' from both sides
y = -x/3 Divide both sides by 3.
y =
The slope is -1/3.
9y = -3x
y = -3x/9 Divide both sides by 9
y = Reduce the fraction to lowest terms
y =
The slope is -1/3, but the two equations are the same.
Since the equations are the same, or <u>equivalent</u>, the two lines are always touching. The solution of a system means where two lines intersect, or meet. Therefore, <u>there are infinite solutions</u>.