Answer:
Ques 16)
We have to simplify the expression:
![\dfrac{t^2}{t^2+3t-18}-(\dfrac{5t}{t^2+3t-18}-\dfrac{t-3}{t^2+3t-18})\\ \\=\dfrac{t^2}{t^2+3t-18}-(\dfrac{4t+3}{t^2+3t-18})\\ \\=\dfrac{t^2-4t-3}{t^2+3t+18}](https://tex.z-dn.net/?f=%5Cdfrac%7Bt%5E2%7D%7Bt%5E2%2B3t-18%7D-%28%5Cdfrac%7B5t%7D%7Bt%5E2%2B3t-18%7D-%5Cdfrac%7Bt-3%7D%7Bt%5E2%2B3t-18%7D%29%5C%5C%20%20%20%5C%5C%3D%5Cdfrac%7Bt%5E2%7D%7Bt%5E2%2B3t-18%7D-%28%5Cdfrac%7B4t%2B3%7D%7Bt%5E2%2B3t-18%7D%29%5C%5C%20%20%5C%5C%3D%5Cdfrac%7Bt%5E2-4t-3%7D%7Bt%5E2%2B3t%2B18%7D)
Ques 17)
![\dfrac{3w^2+7w-7}{w^2+8w+15}+\dfrac{2w^2-9w+4}{(2w^2+9w-5)(w^2-w-12)}\\ \\=\dfrac{3w^2+7w-7}{w^2+8w+15}+\dfrac{(2w-1)(w-4)}{(2w-1)(w+5)(w+3)(w-4)}\\\\=\dfrac{3w^2+7w-7}{(w+3)(w+5)}+\dfrac{1}{(w+3)(w+5)}\\\\=\dfrac{3w^2+7w-7+1}{(w+3)(w+5)}\\\\=\dfrac{(3w-2)(w+3)}{(w+5)(w+3)}\\\\=\dfrac{3w-2}{w+5}](https://tex.z-dn.net/?f=%5Cdfrac%7B3w%5E2%2B7w-7%7D%7Bw%5E2%2B8w%2B15%7D%2B%5Cdfrac%7B2w%5E2-9w%2B4%7D%7B%282w%5E2%2B9w-5%29%28w%5E2-w-12%29%7D%5C%5C%20%20%5C%5C%3D%5Cdfrac%7B3w%5E2%2B7w-7%7D%7Bw%5E2%2B8w%2B15%7D%2B%5Cdfrac%7B%282w-1%29%28w-4%29%7D%7B%282w-1%29%28w%2B5%29%28w%2B3%29%28w-4%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B3w%5E2%2B7w-7%7D%7B%28w%2B3%29%28w%2B5%29%7D%2B%5Cdfrac%7B1%7D%7B%28w%2B3%29%28w%2B5%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B3w%5E2%2B7w-7%2B1%7D%7B%28w%2B3%29%28w%2B5%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%283w-2%29%28w%2B3%29%7D%7B%28w%2B5%29%28w%2B3%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B3w-2%7D%7Bw%2B5%7D)
Ques 18)
Let the blank space be denoted by the quantity 'x'.
![\dfrac{x}{12a^2+8a}+\dfrac{15a^2}{12a^2+8a}=\dfrac{7a}{3a+2}\\ \\\dfrac{x+15a^2}{12a^2+8a}=\dfrac{7a}{3a+2}\\\\=\dfrac{x+15a^2}{4a(3a+2)}=\dfrac{7a}{3a+2}\\\\=\dfrac{x+15a^2}{4a}=7a\\\\x+15a^2=28a^2\\\\x=28a^2-15a^2\\\\x=13a^2](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B12a%5E2%2B8a%7D%2B%5Cdfrac%7B15a%5E2%7D%7B12a%5E2%2B8a%7D%3D%5Cdfrac%7B7a%7D%7B3a%2B2%7D%5C%5C%20%5C%5C%5Cdfrac%7Bx%2B15a%5E2%7D%7B12a%5E2%2B8a%7D%3D%5Cdfrac%7B7a%7D%7B3a%2B2%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bx%2B15a%5E2%7D%7B4a%283a%2B2%29%7D%3D%5Cdfrac%7B7a%7D%7B3a%2B2%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bx%2B15a%5E2%7D%7B4a%7D%3D7a%5C%5C%5C%5Cx%2B15a%5E2%3D28a%5E2%5C%5C%5C%5Cx%3D28a%5E2-15a%5E2%5C%5C%5C%5Cx%3D13a%5E2)
Ques 19)
Let the missing quantity be denoted by 'x'.
![\dfrac{p^2+7p+2}{p^2+5p-14}-\dfrac{x}{p^2+5p-14}=\dfrac{p-1}{p-2}\\ \\\dfrac{p^2+7p+2-x}{p^2+5p-14}=\dfrac{p-1}{p-2}\\\\\dfrac{p^2+7p+2-x}{(p-2)(p+7)}=\dfrac{p-1}{p-2}\\\\p^2+7p+2-x=(p-1)(p+7)\\\\p^2+7p+2-x=p^2+6p-7\\\\x=p+9](https://tex.z-dn.net/?f=%5Cdfrac%7Bp%5E2%2B7p%2B2%7D%7Bp%5E2%2B5p-14%7D-%5Cdfrac%7Bx%7D%7Bp%5E2%2B5p-14%7D%3D%5Cdfrac%7Bp-1%7D%7Bp-2%7D%5C%5C%20%5C%5C%5Cdfrac%7Bp%5E2%2B7p%2B2-x%7D%7Bp%5E2%2B5p-14%7D%3D%5Cdfrac%7Bp-1%7D%7Bp-2%7D%5C%5C%5C%5C%5Cdfrac%7Bp%5E2%2B7p%2B2-x%7D%7B%28p-2%29%28p%2B7%29%7D%3D%5Cdfrac%7Bp-1%7D%7Bp-2%7D%5C%5C%5C%5Cp%5E2%2B7p%2B2-x%3D%28p-1%29%28p%2B7%29%5C%5C%5C%5Cp%5E2%2B7p%2B2-x%3Dp%5E2%2B6p-7%5C%5C%5C%5Cx%3Dp%2B9)
Answer:
x=−y−1
Step-by-step explanation:
y=−x−1
Step 1: Flip the equation.
−x−1=y
Step 2: Add 1 to both sides.
−x−1+1=y+1
−x=y+1
Step 3: Divide both sides by -1.
−x
−1
=
y+1
−1
x=−y−1
Answer: This is a type of Synthesis reaction.
Explanation:
- Synthesis reaction is a type of chemical reaction in which two or more substances combine to form a single substance.
![A+B\rightarrow AB](https://tex.z-dn.net/?f=A%2BB%5Crightarrow%20AB)
- Decomposition reactions are a type of chemical reactions in which a substance breaks down into two or more substances.
![AB\rightarrow A+B](https://tex.z-dn.net/?f=AB%5Crightarrow%20A%2BB)
- Combustion reaction is a type of chemical reaction in which a hydrocarbon reacts with oxygen gas to produce carbon dioxide and water.
![Hydrocarbon+O_2\rightarrow H_2O+CO_2](https://tex.z-dn.net/?f=Hydrocarbon%2BO_2%5Crightarrow%20H_2O%2BCO_2)
For the given reaction:
![2Na(s)+Cl_2(g)\rightarrow 2NaCl](https://tex.z-dn.net/?f=2Na%28s%29%2BCl_2%28g%29%5Crightarrow%202NaCl)
Here, 2 substances are combining together to form a single substance. Hence, it is considered as a synthesis reaction.
Answer: (8a^3x^3)/81
Step-by-step explanation: Simplifying the expression :)
1/4 hour = 75 gallons
1 hour = 75 x 4 = 300 gallons
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Answer: The rate is 300 gallons/hour
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