Answer: hmmm no!
Step-by-step explanation:
So,
We'll just use A to represent both Jan and Mya's miles, since they ran the same number.
We have the equations:
1. Jan (J) = Mya (M)
2. Sara (S) = M - 8
3. 2A + S = 64
J = M
S = M - 8
We'll just use A to represent both J and M.
S = M - 8
We'll use Elimination by Substitution.
2A + A - 8 = 64
Collect Like Terms
3A - 8 = 64
Add 8 to both sides
3A = 72
Divide both sides by 3
A = 24
Since
A = J
and
A = M
and
J = M
then
J = 24
M = 24
Substitute
S = 24 - 8
S = 16
Check
24 + 24 + 16 = 64
64 = 64 This checks.
So,
J = 24
M = 24
S = 16
Answer:
To complete the required $m dollars for her college, she needs $(m - 60,000).
Step-by-step explanation:
Suppose Rebecca needs $m to complete her college education,
because she has a yearly scholarship of $10,000, she would have $10,000 × 4 = $40,000 for the four years she would spend in college.
Together with her savings of $20,000, she has $20,000 + $40,000 = $60,000 in total.
Therefore to complete the required $m dollars for her college, she needs $(m - 60,000).
There are two cases to consider.
A) The removed square is in an odd-numbered column (and row). In this case, the board is divided by that column and row into parts with an even number of columns, which can always be tiled by dominos, and the column the square is in, which has an even number of remaining squares that can also be tiled by dominos.
B) The removed square is in an even-numbered column (and row). In this case, the top row to the left of that column (including that column) can be tiled by dominos, as can the bottom row to the right of that column (including that column). The remaining untiled sections of the board have even numbers of rows, so can be tiled by dominos.
_____
Perhaps the shorter answer is that in an odd-sized board, the corner squares are the ones that there is one of in excess. Cutting out one that is of that color leaves an even number of squares, and equal numbers of each color. Such a board seems like it <em>ought</em> to be able to be tiled by dominos, but the above shows there is actually an algorithm for doing so.
ANSWER
The value of the expression is

EXPLANATION
Method 1: Rewrite as product of

The expression given to us is,

We use the fact that

to simplify the above expression.

This implies,

We substitute to obtain,


Method 2: Use indices to solve.

This implies that,

