Answer:
The correct option is a.
Step-by-step explanation:
Given information:
Number of elements in set A = 4
Number of elements in set B = 3
We need to find n(A × B). It means we have to find the number of elements in set A × B.
If P and Q are two sets with elements m and n respectively, then the number of element in the set P × Q is m × n.
The value of n(A × B) is 12. Therefore the correct option is a.
The volume of a box like this is found by multiplying the length times the width times the height. We are told that the length is 8 more inches than the width, so the width is w and the length is w + 8. If we cut away 3 square inches from each corner, the height when we fold up those corners is going to be 3. The volume is given as 27, so our formula looks like this:
. When we do that multiplication, we have
. We need to solve for w so we can then solve for h. Move the 27 over and set the quadratic equal to 0.
. We can then factor out a 3 to make the job easier:
. Now we can factor to solve for w. The 2 numbers that add up to 8 and multiply to -9 are 9 and -1. So (w+9) = 0, (w-1) = 0, or 3 = 0. Of course 3 doesn't equal 0, so that's out. w + 9 = 0 so w = -9. w - 1 = 0 so w = 1. There are 2 things in math that can never EVER be negative and those are time and distance/length. So -9 is out. That means that w = 1. But don't forget that there was 6 inches cut off each side, so the width is 1 + 3 + 3 which is 7. The length is w + 8 which means that the length is 7 + 8 or 15. Those are the dimensions of the rectangle before it was cut.
Answer:
the third function
Step-by-step explanation:
when looking at x=-1 the value goes from (x=-2) 0 to -3, when x=0 it goes to 0, and then only increases after that.
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Answer:
the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.
Step-by-step explanation:
Recall that the area of a rectangle is Length times Width
If we name the length "L" and the width "W", we have:
L * W = 46
Also: "the length is 4 times the width" can be written in math form as:
L = 4 * W
and now we can replace the length L by 4 * W in the formula for the area:
and now we find the value of L:
Therefore, the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.
