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.
Learn more number of each coin here:brainly.com/question/13934075
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Answer: Sam = $225 George = $300
<u>Step-by-step explanation:</u>
NOTES:
Sam: s
George: g = s + 75
Together: s + g = 525
a.
The two equations that can be created are "George" and Together"
The system is: 
b.
see attached graph
c.
The intersection of the two lines is at (225, 300). Since Sam represented the x-axis and Georege represented the y-axis, then Sam = $225 and George = $300.
BONUS:
This system can also be solved algebraically using the substitution method.
Replace "g" with "s + 75" into the second equation:
s + (s + 75) = 525
2s + 75 = 525
2s = 450
s = 225
Next, input the s-value into the George equation to solve for g:
g = s + 75 = (225) + 75 = 300
A (-12,-8), B(6,-3), C(3,3)
Answer:
D. 4
Step-by-step explanation:
![[(p^2) (q^{-3}) ]^{-2}.[(p)^{-3}(q)^5] ^{-2}\\\\=[(p^2) (q^{-3}) \times(p)^{-3}(q)^5 ]^{-2}\\\\=[(p^{2}) \times(p)^{-3} \times (q^{-3}) \times(q)^5 ]^{-2}\\\\=[(p^{2-3}) \times (q^{5-3}) ]^{-2}\\\\=[(p^{-1}) \times (q^{2}) ]^{-2}\\\\=(p^{-1\times (-2)}) \times (q^{2\times (-2) }) \\\\=p^{2}\times q^{-4} \\\\= \frac{p^2}{q^4}\\\\= \frac{(-2)^2}{(-1)^4}\\\\= \frac{4}{1}\\\\= 4](https://tex.z-dn.net/?f=%20%5B%28p%5E2%29%20%28q%5E%7B-3%7D%29%20%5D%5E%7B-2%7D.%5B%28p%29%5E%7B-3%7D%28q%29%5E5%5D%20%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E2%29%20%28q%5E%7B-3%7D%29%20%5Ctimes%28p%29%5E%7B-3%7D%28q%29%5E5%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E%7B2%7D%29%20%5Ctimes%28p%29%5E%7B-3%7D%20%5Ctimes%20%28q%5E%7B-3%7D%29%20%5Ctimes%28q%29%5E5%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E%7B2-3%7D%29%20%5Ctimes%20%28q%5E%7B5-3%7D%29%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E%7B-1%7D%29%20%5Ctimes%20%28q%5E%7B2%7D%29%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%28p%5E%7B-1%5Ctimes%20%28-2%29%7D%29%20%5Ctimes%20%28q%5E%7B2%5Ctimes%20%28-2%29%20%7D%29%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3Dp%5E%7B2%7D%5Ctimes%20q%5E%7B-4%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%20%5Cfrac%7Bp%5E2%7D%7Bq%5E4%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%20%5Cfrac%7B%28-2%29%5E2%7D%7B%28-1%29%5E4%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%20%5Cfrac%7B4%7D%7B1%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%204)
The definition of the tangent function tells you
tan(angle) = (300 ft) / (distance to mountain)
This equation can be rearranged to
(distance to mountain) = (300 ft) / tan(angle)
For the far end of the river,
distance to far end = (300 ft) / tan(24°) ≈ 673.8 ft
For the near end of the river
distance to near end = (300 ft) / tan(40°) ≈ 357.5 ft
Then the width of the river can be calculated by finding the difference of these distances:
width of river = distance to far end - distance to near end
width of river = 673.8 ft - 357.5 ft
width of river = 316.3 ft
The appropriate answer choice is
316 ft.
