If the total value of the coins is $15. The number of each type of coin is: 31 quarters, 72 dimes.
<h3>Number of each type of coin</h3>
Let D = number of dimes
Let Q = the number of quarters
Equations
d + q = 103
0.10d + 0.25q = 15
d = 103 -q
0.10(103 -q) + 0.25q = 15
10.3 - 0.10q + 0.25q = 15
0.15q = 4.7
q=4.7/0.15
q=31 quarters
Substitute q into second equation
D+31=103
D=72 dimes
Therefore the number of each type of coin is: 31 quarters, 72 dimes.
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The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.
<h3>Which inequality explains why the three segments cannot be used to construct a triangle?</h3>
Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.
Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.
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