Answer:
33 1/3 L of the 40% solution, 16 2/3 L of the 25% solution
Step-by-step explanation:
Set up two equations...
Let x represent the number of Liters of the 40% solution
Let y represent the number of Liters of the 25% solution
We need 50 liters total, so
x + y = 50
and we need the 50 L to be 35% solution, so
0.4x = 0.25y = 0.35(50)
Solve the first equation for one variable...
x = 50 - y (subtract y from both sides in equation 1)
Now substitute that value into the second equation...
0.4(50 - y) + 0.25y = 17.5 (x becomes 50 - y, 0.35(50) = 17.5)
Now solve for y...
20 - 0.4y + 0.25y = 17.5
-0.15y = -2.5
y = 16.66666667
y = 16 2/3 L
So we need to plug that into the first equation to find 'x'
x + 16 2/3 = 50
x = 50 - 16 2/3
x = 33 1/3
Yes. It is equivalent to 3. Combine like terms
Answer:
Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle. If you are working with equilateral triangles, divide 180 by three to find the value of X.
Step-by-step explanation:
I hope this helps you.
The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
<em>Your question is not complete, but most probably your full questions was</em>
<em>Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?</em>
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
Learn more about intermediate value theorem here:
brainly.com/question/28048895
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