Step-by-step explanation:
1/2 represents every fraction, where the denominator (bottom part) is twice the numerator (top part).
like 4/8 or 6/12 or 128/256 or ...
what do we need in the denominator to calculate with 15/16 ?
the same : 16.
and what is half of 16 ? 8.
so, we need the 1/2 based on 16th = 8/16.
so, the dog ate 8/16 (1/2) of the original 15/16.
what was left was
15/16 - 8/16 = 7/16 pound
Answer:
180, 180, 148, 180, 148
Step-by-step explanation:
The two rules in play here are ...
- the sum of interior angles of a triangle is 180°
- the angles of a linear pair are supplementary (they total 180°)
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The first of these rules answers the first two questions:
- interior angles total 180°
- angles 1, 3, 4 total 180°
We can subtract the measure of angle 1 from both sides of the previous equation to find the sum of the remaining two angles.
- angles 3 and 4 total 148°
The second rule answers the next question:
- angles 1 and 2 total 180°
As before, subtracting the value of angle 1 from both sides of the equation gives ...
_____
<em>Additional comment</em>
Of course, the subtraction property of equality comes into play, also. For some unknown, X, you have (in both cases) ...
X + 32° = 180°
X +32° -32° = 180° -32° . . . . . . subtraction property of equality
X = 148° . . . . . . . . simplify
In the first case, X is the sum of angles 3 and 4. In the second case, X is angle 2 only.
Answer:
20
Step-by-step explanation:
nPr = n!/(n-r)!
5P2 = 5!/(5-2)!
= 5!/3!
= 5×4×3!/3!
= 5×4
= 20
Step-by-step explanation:
1/8 x 8 = 1
3/8 x 8 = 3
1/8 x 8 = 1
3/8 x 8 = 3
The equation which can be used to find the number of quarters and nickels is; n + q = 84, 0.05n + 0.25q = 17.80.
<h3>Quarters and nickels</h3>
- Total coins = 84
- Total value = $17.80
let
- Number of quarters = q
- Number of nickels = n
n + q = 84
0.05n + 0.25q = 17.80
From equation (1)
n = 84 - q
Substitute into (2)
0.05n + 0.25q = 17.80
0.05(84 - q) + 0.25q = 17.80
4.2 - 0.05q + 0.25q = 17.80
- 0.05q + 0.25q = 17.80 - 4.2
0.20q = 13.60
q = 13.60 / 0.20
q = 68
Substitute q = 68 into
n + q = 84
n + 68 = 84
n = 84 - 68
n = 16
Therefore, the number of quarters and nickels are 68 and 16 respectively.
Learn more about quarters and nickels:
brainly.com/question/17127685
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