Is (2,2) a solution to x+y=4 and 5x+5y=20?
1 answer:
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1) Resultant fraction:
2) Total soil: pounds
3) Result of the product:
Step-by-step explanation:
1)
In this problem, we want to find the product between the two fractions
and
In order to find this product, we have to multiply the numerators of each fraction and the denominators of each fraction. We get:
Now we simplify, dividing both numerator and denominator by 2:
And the fraction cannot be further simplified.
2)
Here we have:
n = 5 (number of pots that Andy has)
(amount of soil (in pounds) that each pot can contain)
In order to find the amount of soil that Andy needs to fill all the pots, we have to multiply the number of pots (n) by the amount of soil that each pot can contain (s).
If we do so, we find:
Which can be rewritten as a mixed fraction as:
3)
Here we want to find the result of the following product:
In order to do so, we first have to rewrite each fraction as an improper fraction.
For the 1st fraction:
For the 2nd fraction:
Now we can finally find the product of the two fractions:
Where in the last step, we divide both the numerator and the denominator by 6.
Learn more about fractions:
#LearnwithBrainly
Answer:
V (max) = 2 ft³
and x side of the base is x = 0,5 feet
Step-by-step explanation: See annex ( two different cubes)
We have a square piece of cardboard of 3 inches wide
Let x be lenght of side to cut in each corner
Then the base of the (future cube) is 3 - 2x, and the area is
( 3 - 2x )²
And the height is x Then volume of the cube as a function of x is:
V(x) = ( 3 - 2x )² *x or V(x) = ( 9 + 4x² - 12x )*x
V(x) = 4x³ - 12x² + 9x
Taking derivatives on both sides of the equation
V´(x) = 12x² - 24x + 9
V´(x) = 0 12x² - 24x + 9 = 0 simplifying 4x² - 8x + 3 = 0
Second degree equation solving for x
x₁,₂ = [ 24 ± √( 576) - 432 /24
x₁,₂ = [24 ±√144 ]/24
x₁,₂ = ( 24 ± 12) /24 x₁ = 1.5 feet x₂ = 0,5 feet
Of these two values we have to dismiss x₁ because if x = 1.5 we don´t have a cube ( 0 height )
Then we take x = 0,5 feet
And
V (max) = (2)²*0,5 = 4*0,5
V (max) = 2 ft³
