Volume of first oil = A, volume of second oil = B, volume of mixture = M
A = ?, B = 4l, M = A + B
40%A + 25%B = 30%M
40%A + 25%4l = 30%(A+4l)
<span>40%A + 25%4l = 30%A + 30%4l
40A + 100l = 30A + 120l
40A - 30 A = 120l - 100l
10A = 20l
A = 2l
</span>
Answer: 2 litres of 40% oil dressing.
Also note: That's an approximation, because the volumes are not strictly additive. For example: mixing 50ml pure ethanol with 50ml water will give you about 95ml of mixture. To get an accurate answer, you'd have to measure the volume of the final mixture and then divide your total oil content by that<span>.</span>
Well, you have to ask the question first.
The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
Answer:
and 
Step-by-step explanation:
We have the following system of equations:
and 
To solve the problem, we need to equal the two equations:
⇒ 
⇒ 
⇒ 
So you need to find two numbers that added equal to 5 and multiplied equal to 4. These two numbers are 
and 
.
Then, the factorized form of the polynomial is: 
.
The, the solution to the system of equations is: and .
Answer:
The correct answers are with side lengths 1 feet and 8 feet, the perimeter is 18 feet; and with side lengths 2 feet and 4 feet, the perimeter is 12 feet.
Step-by-step explanation:
The area of a rectangular banner is 8 square feet.
The side lengths of this rectangular banner are whole numbers.
Thus the possible pairs of side lengths that would give 8 when multiplied with each other are (1 , 8) ; (2 , 4).
So the possible side lengths are 1 feet and 8 feet or 2 feet and 4 feet.
The perimeter when the side lengths are 1 feet and 8 feet are 18 feet.
The perimeter when the side lengths are 2 feet and 4 feet are 12 feet.
