Answer:
Step-by-step explanation:
The properties of addition and multiplication allow you to rearrange and/or regroup the components of a sum or a product. That is the point of this exercise.
(2·8)·7 = 2·(8·7) . . . . parentheses have moved: associative property
2 + 7 + 8 = 8 + 2 + 7 . . . . order is rearranged: commutative property
5·3·12 = 12·5·3 . . . . . order is rearranged: commutative property
(3 +5) +12 = 3 +(5 +12) . . . . parentheses have moved: associative property
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<em>Additional comment</em>
Whenever you're in doubt about the equivalence of numerical expressions, you can use your calculator to evaluate them. They will give the same result if they are equivalent. (You need a good scientific or graphing calculator that uses parentheses for this. Some seriously good calculators are available as low-cost phone apps.)
The Google search box also serves as input to the Google calculator. You can use an asterisk (*) for multiplication.
The first letter can be any one of the 26 letters in the alphabet. For each one . . .
The second letter can be any one of the 25 remaining ones. For each one . . .
The third letter can be any one of the 24 remaining ones. For each one . . .
The fourth letter can be any one of the 23 remaining ones.
Total possible 4-letter codes = (26 x 25 x 24 x 23) = <em>358,800 </em>
Here a right angled triangle given. We know that one angle of a right angled triangle is 90°.
As the sum of three angles of a triangle is 180°, so we can say the sum of other two angles of a right angled triangle is (180-90)° = 90°.
Here in the figure the other two angles given 
and 
. Sum of these two angles is 90°.
So we can write the equation as,
We have to remove the parenthesis now.
Now we will add the like terms. Here x and 2x are like terms. By adding them we will get,
To solve it for x, now we have to move 15 to the other side by subtracting it from both sides.
Now to get x, we have to move 3 to the other side, by dividing it to both sides.
We have got the required value of x.
The solution is x= 25.
This is a permutations problem. There are only 7 comics you can move into different time slots, the 8th one being fixed in that last position. So you can look at it this way:
For the 1st position, you can choose from all 7 people. Once you've picked that one, you have 6 people to choose from for the 2nd position, and similarly for the remaining ones . This gives you 7x6x5x4x3x2x1 = 5040 ways to arrange them. And the last comic stays in the same position all the time so does not change this number. Make sense? If you need to demonstrate it to yourself, use a smaller number of comics, like 3 or 4, and write out the combinations to see that it works.
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