Answer:Add 44 liters blue
Step-by-step explanation:Mary has 20 liters of paint mixed white:blue in the ratio 2:3. So two fifths of that paint is white and three fifths is blue. So that's 8 liters white, 12 liters blue.
We want to add paint to get white:blue = 1:7. Clearly we need to add blue. We have our 8 liters of white, so we need a total of 7(8)=56 liters of blue. We already have 12, so we have to add 56-12=44 liters of blue paint:
6d+23=14(d-2)
6d+23=14d-28
6d+51=14d
51=8d
51/8= 6.375 or 6 3/8
Hope this helps :)
Answer:
The equation would be y + 1 = 3(x + 1)
Step-by-step explanation:
In order to find the equation of this line, we have to use the slope formula to find the slope.
m (slope) = (y2 - y1)/(x2 - x1)
m = (3 - -3)/(2 - 0)
m = (3 + 3)/(2 - 0)
m = 6/2
m = 3
Now that we have that, we can use it along with the second point to put into the point-slope equation.
y - y1 = m(x - x1)
y - -1= 3(x - -1)
y + 1 = 3(x + 1)
When you set
, you end up with the differentials
. Multiplying both sides by 2 gives
.
Then the integral is
Answer:
Step-by-step explanation:
(Let the point where the altitude from 
intersects 
be called as point 
.) First, let's find the area of parallelogram 
. The area of a parallelogram is simply 
, where 
is the parallelogram's base and 
is the parallelogram's height. If we let and 
be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram will be 
.
Now, how does this information matter, you might ask? Well, we can take either <em>or </em>
to be the base and either or 
to be the height. In this case, let's take the latter two options, as we are looking to find the length of .
Therefore, we know that the area of parallelogram can also be found by calculating 
. Since we know the values of the area and , we can write the following equation to solve for :
(Substitute 
and 
into the equation)
(Divide both sides of the equation by 
to get rid of 's coefficient)
(Simplify)
(Symmetric Property of Equality)
Hope this helps!
