<span>The
associative rule is a rule about when it's safe to move parentheses
around. You can remember that because the parentheses determine which
expressions you have to do first--which numbers can associate with each
other. It looks like this:
For addition: (a + b) + c = a + (b + c)
For multiplication: (ab)c = a(bc)
The commutative property is about which operations you can do backward
and forward. You can remember this by thinking of people commuting to
work: they go to work every morning, then they repeat the same operation
backward when they commute home. It looks like this:
For addition: a + b = b + a
For multiplication: ab = ba
Finally, the distributive property tells you what happens when you
distribute one operation against another kind in parentheses. It looks
like this:
a * (b + c) = ab + ac
In other words, the a is "distributed" over the b and c.
Of course, you can make these work together:
a * (b + (c + d))
= a * ((b + c) + d) (by the associative property)
= a * (d + (b + c)) (by the commutative property)
= ad + a (b + c) (by the distributive property)
= ad + ab + ac (by the distributive property again).
Hope this helps. </span>
Answer:
6x x 6x
Step-by-step explanation:they are all actually like terms so just add then together and the multiply this
Answer:
480 different sandwiches
Step-by-step explanation:
To find how many sandwiches can be made, we need to find the number of possibilities for each choice: bread, protein, cheese, vegetables.
Bread: 3 types -> combination of 3 choose 1 -> 3
Protein: 4 types -> combination of 4 choose 1 -> 4
Cheese: 4 types -> combination of 4 choose 1 -> 4
Vegetables: 5 types -> combination of 5 choose 2 -> 5!/(3!*2!) = 5*4/2 = 10
So the number of different sandwiches is:
3 * 4 * 4 * 10 = 480
Answer:
Length is 20 meters and Width is 16 meters
Step-by-step explanation:
A parallelogram is a 4-sided figure with 2 pair of parallel sides.
The perimeter is the sum of all 4 sides of the parallelogram.
Let the length of parallelogram be x and width be y.
The perimeter is 72, thus we can write:
x + x + y + y = 72
or
2x + 2y = 72
Also, width is 4 less than length, thus we can write:
y = x - 4
Now, we replace the 1st equation with the 2nd equation and solve for x first. Shown below:
2x + 2y = 72
2x + 2(x - 4) = 72
2x + 2x - 8 = 72
4x = 72 + 8
4x = 80
x = 80/4 = 20
And now y:
y = x - 4
y = 20 - 4
y = 16
Thus, the Length is 20 meters and Width is 16 meters
