Let d = # of dimes
Let q = # of quarters
equation #1: number of coins
d + q = 1234
equation #2: value of coins
0.10d + 0.25q = 290.05
Solve #1 for d:
d=1234-q
Sub #1 into #2 and solve for q:
0.10d + 0.25q = 290.05
0.10(1234-q) + 0.25q = 290.05
123.4 - 0.10q + 0.25q = 290.05
0.15q = 166.65
q = 1111
Now go back to d=1234-q and sub in 1111 for q to find d:
d = 1234 - 1111
d = 123
1111 quarters and 123 dimes.
In general, for these kinds of problems, repeatedly subtract 360 degrees until you get something that lies between 0 and 360 degrees, since two coterminal angles will always differ by some multiple of 360 degrees.
In this case, our desired angle is 495-360=135 degrees.
The equation that matches the given situation is . So, after two moves, Eric's elevation changed meters above.
We know that in mathematics, subtraction means removing something from a group or a number of things. What is left in the group gets smaller when we subtract. The minuend is the first element we use. The subtrahend is the part that is being removed. The difference is the portion that remains after subtraction.
Assume that "negative" means climbing down and "positive" means climbing up. We must locate the elevation change in this area.
Given that Eric climbed straight down meters. So we can write .
Again Eric climbed straight up meters. So, we can write .
Then the change =
=
=
=
=
=
=
=
Therefore, the equation that matches the given situation is . So, after two moves, Eric's elevation changed meters above.
Learn more about subtraction here -
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The answers are A, C, and E because during those intervals the slope is negative