Do you remember how to find the equation of a line when you know two points on the line ? Well, that little table gives you FIVE points on the line, and in case some students didn't notice that, the table even labels the columns 'x' and 'y' as a hint. With 5 points given, there are 20 different ways to find the equation of the line. Get to work.
Look for the graph where the line crosses the y axis at y=-1, and whose slope is -3. The answer is b.
Answer:
Second Option
![\frac{5\sqrt{11} +5\sqrt{3}}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B11%7D%20%2B5%5Csqrt%7B3%7D%7D%7B8%7D)
Step-by-step explanation:
To simplify the expression you must multiply the numerator and the denominator of the fraction by the conjugate of the denominator.
If you have an expression of the form
then its conjugate will be ![a + b.](https://tex.z-dn.net/?f=a%20%2B%20b.)
The result of that multiplication will be
![a ^ 2 -b ^ 2](https://tex.z-dn.net/?f=a%20%5E%202%20-b%20%5E%202)
Therefore we have the expression
![\frac{5}{\sqrt{11} -\sqrt{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B%5Csqrt%7B11%7D%20-%5Csqrt%7B3%7D%7D)
By multiplying by the conjugate of the denominator we have
![\frac{5}{\sqrt{11} -\sqrt{3}}*\frac{\sqrt{11} +\sqrt{3}}{\sqrt{11} +\sqrt{3}}\\\\\\\frac{5(\sqrt{11} +\sqrt{3})}{(\sqrt{11})^2 -(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{11 -3}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B%5Csqrt%7B11%7D%20-%5Csqrt%7B3%7D%7D%2A%5Cfrac%7B%5Csqrt%7B11%7D%20%2B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B11%7D%20%2B%5Csqrt%7B3%7D%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B5%28%5Csqrt%7B11%7D%20%2B%5Csqrt%7B3%7D%29%7D%7B%28%5Csqrt%7B11%7D%29%5E2%20-%28%5Csqrt%7B3%7D%29%5E2%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B5%5Csqrt%7B11%7D%20%2B5%5Csqrt%7B3%7D%7D%7B11%20-3%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B5%5Csqrt%7B11%7D%20%2B5%5Csqrt%7B3%7D%7D%7B8%7D)
Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
Step-by-step explanation:
Since we have given that
Total number of students and teachers = 409
Let the number of vans be x
Let the number of buses be x+5
Number of students and teachers each bus transported = 55
Number of students and teachers each van transported = 12
According to question,
![55(x+5)+12x=409\\\\55x+275+12x=409\\\\67x=409-275\\\\67x=134\\\\x=\frac{134}{67}\\\\x=2](https://tex.z-dn.net/?f=55%28x%2B5%29%2B12x%3D409%5C%5C%5C%5C55x%2B275%2B12x%3D409%5C%5C%5C%5C67x%3D409-275%5C%5C%5C%5C67x%3D134%5C%5C%5C%5Cx%3D%5Cfrac%7B134%7D%7B67%7D%5C%5C%5C%5Cx%3D2)
Total number of students and teachers who rode to the zoo in buses will be
![55(x+5)\\\\=55(2+5)\\\\=55\times 7\\\\=385](https://tex.z-dn.net/?f=55%28x%2B5%29%5C%5C%5C%5C%3D55%282%2B5%29%5C%5C%5C%5C%3D55%5Ctimes%207%5C%5C%5C%5C%3D385)
Total number of students and teachers who rode to the zoo in vans will be
![12x\\\\=12\times 2=24](https://tex.z-dn.net/?f=12x%5C%5C%5C%5C%3D12%5Ctimes%202%3D24)
Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.