It is $202.50 because when when you write money, you have to write the whole value since there is nothing after 5 the nearest cent is 0
Answer:
B.12 ounces
Step-by-step explanation:
step 1
Find out the ounces of orange juice concentrate used yesterday
Let
x ----> ounces of orange juice concentrate used yesterday
y ---> ounces of water used yesterday
we know
that
----> equation A
----> equation B
substitute equation B in equation A
![\frac{x}{14}=\frac{3}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B14%7D%3D%5Cfrac%7B3%7D%7B7%7D)
solve for x
![x=\frac{3}{7}(14)](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B7%7D%2814%29)
![x=6\ oz](https://tex.z-dn.net/?f=x%3D6%5C%20oz)
step 2
today she wants to make twice as much orange juice.
To find out how much orange juice concentrate she needs, multiply the ounces of orange juice concentrate used yesterday by 2
so
![2(6)=12\ oz](https://tex.z-dn.net/?f=2%286%29%3D12%5C%20oz)
Answer:
y=-\frac{5}{3} x+\frac{10}{3} or what is the same: ![5x+3y=10](https://tex.z-dn.net/?f=5x%2B3y%3D10)
Step-by-step explanation:
First we find the slope of the line that goes through the points (-4,10) and (-1,5) using the slope formula: ![slope=\frac{10-5}{-4-(-1)} =\frac{5}{-3} =-\frac{5}{3}](https://tex.z-dn.net/?f=slope%3D%5Cfrac%7B10-5%7D%7B-4-%28-1%29%7D%20%3D%5Cfrac%7B5%7D%7B-3%7D%20%3D-%5Cfrac%7B5%7D%7B3%7D)
Now we use this slope in the general form of the slope- y_intercept of a line:
![y=-\frac{5}{3} x+b](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2Bb)
We can determine the parameter "b" by requesting the condition that the line has to go through the given points, and we can use one of them to solve for "b" (for example requesting that the point (-1,5) is on the line:
![y=-\frac{5}{3} x+b\\5=-\frac{5}{3} (-1)+b\\5=\frac{5}{3}+b\\5-\frac{5}{3}=b\\b=\frac{10}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2Bb%5C%5C5%3D-%5Cfrac%7B5%7D%7B3%7D%20%28-1%29%2Bb%5C%5C5%3D%5Cfrac%7B5%7D%7B3%7D%2Bb%5C%5C5-%5Cfrac%7B5%7D%7B3%7D%3Db%5C%5Cb%3D%5Cfrac%7B10%7D%7B3%7D)
Therefore, the equation of the line in slope y_intercept form is:
![y=-\frac{5}{3} x+\frac{10}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B10%7D%7B3%7D)
Notice that this equation can also be written in an equivalent form by multiplying both sides of the equal sign by "3", which allows us to write it without denominators:
![y=-\frac{5}{3} x+\frac{10}{3}\\3*y=(-\frac{5}{3} x+\frac{10}{3})*3\\3y=-5x+10\\5x+3y=10](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B10%7D%7B3%7D%5C%5C3%2Ay%3D%28-%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B10%7D%7B3%7D%29%2A3%5C%5C3y%3D-5x%2B10%5C%5C5x%2B3y%3D10)
Answer:
![4(2x+1)(x-5](https://tex.z-dn.net/?f=4%282x%2B1%29%28x-5)
Step-by-step explanation:
Add and subtract the second term to the expression and factor by grouping.