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Answer:
He received 10 dimes and 15 quarters.
Step-by-step explanation:
Dimes = $0.10
Quarters = $0.25
Variable x = dimes
Variable y = quarters
Create a pair of linear equations:
0.10x + 0.25y = 4.75
x + y = 25
Isolate any variable, using an equation of your choice:
x + y = 25
x = 25 - y
Plug in this new value of x into the other equation:
0.10(25 - y) + 0.25y = 4.75
Use the distributive property:
2.5 - 0.10y + 0.25y = 4.75
Combine like terms:
2.5 + 0.15y = 4.75
Isolate variable y:
0.15y = 2.25
y = 15
Plug in the value of y into any equation:
x + y = 25
x + 15 = 25
Isolate variable x:
x = 10
15 - 9 + 2.65 + 1.35 + 3.48
6 + 2.65 + 1.35 + 3.48
8.65 + 1.35 + 3.48
10 + 3.48
13.48
Answer:
This case has NO solutions.
Step-by-step explanation:
Notice that you are in a case of an obtuse triangle (one of its angles is larger than 90 degrees), the side opposite to the obtuse triangle is shorter than the side adjacent to the angle, so no actual triangle can be formed.
This can be found by simply trying to apply the Law of Sines to solve for the value of angle "B" opposite to side "b":

As shown above, we get an impossible mathematical condition (also call an absurd), since the sine of an angle cannot give a value larger than 1 (one).
Therefore, there is no angle we can find to build a triangle with the given data.
Answer:
A trinomial of degree 5
Step-by-step explanation:
A monomial has only 1 term
A binomial has 2 terms
A trinomial has 3 terms
4
+ 3x³ - 7x ← has 3 terms and is therefore a trinomial
The degree of a polynomial is determined by the largest exponent of the variable in the expression
4
is the term with the largest exponent in the expression
Hence a polynomial of degree 5