Answer: ![1\dfrac{1}{4}](https://tex.z-dn.net/?f=1%5Cdfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
Given
The equation in terms of a is
![\Rightarrow \dfrac{a}{a-1}-\dfrac{a+5}{a}=0\\\\\Rightarrow \dfrac{a}{a-1}=\dfrac{a+5}{a}\\\\\Rightarrow a^2=(a-1)(a+5)\\\\\Rightarrow a^2=a^2+4a-5\\\\ \Rightarrow 4a=5\\\\\Rightarrow a=\dfrac{5}{4}\ \text{or}\ 1\dfrac{1}{4}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7Ba%7D%7Ba-1%7D-%5Cdfrac%7Ba%2B5%7D%7Ba%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7Ba%7D%7Ba-1%7D%3D%5Cdfrac%7Ba%2B5%7D%7Ba%7D%5C%5C%5C%5C%5CRightarrow%20a%5E2%3D%28a-1%29%28a%2B5%29%5C%5C%5C%5C%5CRightarrow%20a%5E2%3Da%5E2%2B4a-5%5C%5C%5C%5C%20%5CRightarrow%204a%3D5%5C%5C%5C%5C%5CRightarrow%20a%3D%5Cdfrac%7B5%7D%7B4%7D%5C%20%5Ctext%7Bor%7D%5C%201%5Cdfrac%7B1%7D%7B4%7D)
Answer: ![a=-1/2](https://tex.z-dn.net/?f=a%3D-1%2F2)
<u>Simplify both sides of the equation</u>
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![(Distribute)](https://tex.z-dn.net/?f=%28Distribute%29)
![14a=2a+-6](https://tex.z-dn.net/?f=14a%3D2a%2B-6)
![14a=2a-6](https://tex.z-dn.net/?f=14a%3D2a-6)
<u>Subtract 2a from both sides</u>
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<u>Divide both sides by 12</u>
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Final Answer: ![a=-1/2](https://tex.z-dn.net/?f=a%3D-1%2F2)
Answer:
B. 61
Step-by-step explanation:
Given that ∆PQR and PQS are congruent, it follows that their corresponding sides are of the same length.
Therefore,
![RQ = SQ](https://tex.z-dn.net/?f=%20RQ%20%3D%20SQ%20)
![3x + 16 = 7x - 24](https://tex.z-dn.net/?f=%203x%20%2B%2016%20%3D%207x%20-%2024%20)
Collect like terms
![16 + 24 = 7x - 3x](https://tex.z-dn.net/?f=%2016%20%2B%2024%20%3D%207x%20-%203x%20)
![40 = 4x](https://tex.z-dn.net/?f=%2040%20%3D%204x%20)
Divide both sides by 4
![\frac{40}{4} = \frac{4x}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B40%7D%7B4%7D%20%3D%20%5Cfrac%7B4x%7D%7B4%7D%20)
![10 = x](https://tex.z-dn.net/?f=%2010%20%3D%20x%20)
![x = 10](https://tex.z-dn.net/?f=%20x%20%3D%2010%20)
Find PQ:
![PQ = 2x + 41](https://tex.z-dn.net/?f=%20PQ%20%3D%202x%20%2B%2041%20)
substitute x = 10 into the equation
![PQ = 2(10) + 41](https://tex.z-dn.net/?f=%20PQ%20%3D%202%2810%29%20%2B%2041%20)
![PQ = 20 + 41](https://tex.z-dn.net/?f=%20PQ%20%3D%2020%20%2B%2041%20)
![PQ = 61](https://tex.z-dn.net/?f=%20PQ%20%3D%2061%20)
The question is an example of a ratio problem. This implies that
![\begin{gathered} \text{Domestic vehicles ratio=6} \\ \text{Foreign vehicles ratio=5} \\ Sum\text{ of vehicles ratio =5+6=11} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BDomestic%20vehicles%20ratio%3D6%7D%20%5C%5C%20%5Ctext%7BForeign%20vehicles%20ratio%3D5%7D%20%5C%5C%20Sum%5Ctext%7B%20of%20vehicles%20ratio%20%3D5%2B6%3D11%7D%20%5Cend%7Bgathered%7D)
Therefore, le the number of domestic vehicles be x. We can say that;
![\begin{gathered} \frac{6}{11}=\frac{x}{2673} \\ 11x=16038 \\ x=\frac{16038}{11} \\ x=1458 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B6%7D%7B11%7D%3D%5Cfrac%7Bx%7D%7B2673%7D%20%5C%5C%2011x%3D16038%20%5C%5C%20x%3D%5Cfrac%7B16038%7D%7B11%7D%20%5C%5C%20x%3D1458%20%5Cend%7Bgathered%7D)
Answer: 1458