312016 that is the nearest whole number
Density of water = 1000 kg/m^3
1 m^3 = 1000 litres
Therefore,
1000 kg/1000 l => 1 kg/l => 1000 g/l
Then, 300 g of water = 300/1000 l = 0.3 l
The concentration of the syrup = mass/amount of water = 60 g/0.3 l = 200 g/l
Answer:
![y=5x+3](https://tex.z-dn.net/?f=y%3D5x%2B3)
Step-by-step explanation:
Slope-intercept form:
where
is the slope and
is the y-intercept (the value of y when the line crosses the y-axis)
<u>1) Plug the given slope 5 into the equation</u>
![y=mx+b\\y=5x+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D5x%2Bb)
<u>2) Find the y-intercept </u>
<u> by plugging in the point (-1,-2)</u>
![y=5x+b\\-2=5(-1)+b\\-2=-5+b](https://tex.z-dn.net/?f=y%3D5x%2Bb%5C%5C-2%3D5%28-1%29%2Bb%5C%5C-2%3D-5%2Bb)
Add 5 to both sides
![-2+5=-5+b+5\\3=b](https://tex.z-dn.net/?f=-2%2B5%3D-5%2Bb%2B5%5C%5C3%3Db)
<u>3) Plug the y-intercept back into the equation</u>
![y=5x+3](https://tex.z-dn.net/?f=y%3D5x%2B3)
I hope this helps!
Answer:
C. ![y + \frac{1}{2} = 3(x - 2)](https://tex.z-dn.net/?f=y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D%203%28x%20-%202%29)
Step-by-step explanation:
Given
![Point: (2,\frac{-1}{2})](https://tex.z-dn.net/?f=Point%3A%20%20%282%2C%5Cfrac%7B-1%7D%7B2%7D%29)
![Slope: 3](https://tex.z-dn.net/?f=Slope%3A%203)
Required
Equation of line
Let m represents the slope of the line;
m is calculated as thus
![m = \frac{y - y_1}{x - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By%20-%20y_1%7D%7Bx%20-%20x_1%7D)
![where (x_1,y_1) = (2,\frac{-1}{2})](https://tex.z-dn.net/?f=where%20%28x_1%2Cy_1%29%20%3D%20%282%2C%5Cfrac%7B-1%7D%7B2%7D%29)
![So; x_1 = 2; y_1 = \frac{-1}{2}](https://tex.z-dn.net/?f=So%3B%20x_1%20%3D%202%3B%20y_1%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
![m = 3](https://tex.z-dn.net/?f=m%20%3D%203)
By substituting the right values in the formula above;
becomes
![3 = \frac{y - \frac{-1}{2}}{x - 2}](https://tex.z-dn.net/?f=3%20%3D%20%5Cfrac%7By%20-%20%5Cfrac%7B-1%7D%7B2%7D%7D%7Bx%20-%202%7D)
Multiply both sides by ![(x - 2)](https://tex.z-dn.net/?f=%28x%20-%202%29)
![3 *(x - 2) = \frac{y - \frac{-1}{2}}{x - 2} *(x - 2)](https://tex.z-dn.net/?f=3%20%2A%28x%20-%202%29%20%3D%20%5Cfrac%7By%20-%20%5Cfrac%7B-1%7D%7B2%7D%7D%7Bx%20-%202%7D%20%2A%28x%20-%202%29)
![3 *(x - 2) = (y - \frac{-1}{2})](https://tex.z-dn.net/?f=3%20%2A%28x%20-%202%29%20%3D%20%28y%20-%20%5Cfrac%7B-1%7D%7B2%7D%29)
![3 *(x - 2) = (y + \frac{1}{2})](https://tex.z-dn.net/?f=3%20%2A%28x%20-%202%29%20%3D%20%28y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%29)
![3(x - 2) = (y + \frac{1}{2})](https://tex.z-dn.net/?f=3%28x%20-%202%29%20%3D%20%28y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%29)
![3(x - 2) = y + \frac{1}{2}](https://tex.z-dn.net/?f=3%28x%20-%202%29%20%3D%20y%20%2B%20%5Cfrac%7B1%7D%7B2%7D)
Reorder
![y + \frac{1}{2} = 3(x - 2)](https://tex.z-dn.net/?f=y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D%203%28x%20-%202%29)
Hence, the equation that represents the line is ![y + \frac{1}{2} = 3(x - 2)](https://tex.z-dn.net/?f=y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D%203%28x%20-%202%29)