9514 1404 393
Answer:
21x² +20x +100 = 0
Step-by-step explanation:
We know the sum of the roots of x² +bx +c = 0 is -b, and their product is c. If the roots are α and β, then ...
The sum of the roots of the new equation will be ...
-b' = (α+1/β)+(β+1/α) = (α+β) +(1/α +1/β) = (α+β)(1 +1/(αβ))
The product of the roots of the new equation will be ...
c' = (α+1/β)(β+1/α) = αβ +2 +1/(αβ)
Using the above relations for (α+β) and αβ, we find that ...
-b' = (-b)(1 +1/c)
c' = c + 2 + 1/c
For the given equation, our definition of b and c is ...
b = 2/3
c = 7/3
so the new equation has values ...
b' = (2/3)(1 + 1/(7/3) = (2/3)(10/7) = 20/21
c' = 7/3 + 2 + 1/(7/3) = 13/3 + 3/7 = 100/21
So, the equation with the roots of interest is ...
x² +20/21x +100/21 = 0
Multiplying by 21 gives ...
21x² +20x +100 = 0
Answer:
f^-1(x)=(x-4)/-8
Step-by-step explanation:
2 1/3=7/3=14/6
4 1/2=9/2=27/6
14/6 : 27/6
Simplified: 14 ：27
That's your answer.
To find K, we must use the fact that
on the day 200 books were printed
the average cost was $ 9 per book.
Thus, substituting the values, we have:
c (x) = (5.5x + k) / (x)
9 = (5.5 (200) + k) / (200)
Clearing K
(200) * 9 = 5.5 (200) + k
k = (200) * 9 - 5.5 * (200)
k = 700
answer
the value of the constant k is 700
Answer:
The equation to determine the length is 
.
The Length of the exercise mat is 16 feet.
Step-by-step explanation:
Given:
Perimeter of Rectangular mat = 
Let the length of the mat be denoted by 'l'
And width be denoted by 'w'.
Also Given:
The length of the mat is twice the width of the mat.
So we can say that;
⇒ equation 1
Now we know that;
Perimeter of Rectangle is equal to twice the sum of length and width.
framing in equation form we get;
⇒ equation 2
Now Substituting equation 1 in equation 2 we get;
Applying Distributive property we get;
Hence, The equation to determine the length is .
On Solving the above equation we get;
Dividing both side by 6 we get;
Now Substituting the value of 'w' in equation 1 we get;
Hence The Length of the exercise mat is 16 feet.
