Answer:
![\frac{4x}{2x+y} +\frac{2y}{2x+y}=2](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B2x%2By%7D%20%2B%5Cfrac%7B2y%7D%7B2x%2By%7D%3D2)
Step-by-step explanation:
Given:
The expression to simplify is given as:
![\frac{4x}{2x+y} +\frac{2y}{2x+y}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B2x%2By%7D%20%2B%5Cfrac%7B2y%7D%7B2x%2By%7D)
Since, the denominator is same, we add the numerators and divide it by the same denominator. This gives,
![\frac{4x+2y}{2x+y}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%2B2y%7D%7B2x%2By%7D)
Now, we simplify further by factoring out the common terms from the numerator and denominator if possible.
We observe that, 2 is a common factor to both
. So, we factor out 2 from the numerator. This gives,
![\frac{2(2x+y)}{2x+y}](https://tex.z-dn.net/?f=%5Cfrac%7B2%282x%2By%29%7D%7B2x%2By%7D)
Now, the term
is common in both the numerator and denominator. Hence, ![\frac{2x+y}{2x+y}=1](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2By%7D%7B2x%2By%7D%3D1)
So, the simplified form is:
![=2\times \frac{2x+y}{2x+y}\\\\=2\times 1\\\\=2](https://tex.z-dn.net/?f=%3D2%5Ctimes%20%5Cfrac%7B2x%2By%7D%7B2x%2By%7D%5C%5C%5C%5C%3D2%5Ctimes%201%5C%5C%5C%5C%3D2)
Answer:
true, true, false
Step-by-step explanation:
the sales do not decrease between week 4 and 5
Answer:
The quadratic function is f(x) = (x − 2) (x − 4)
Step-by-step explanation:
Given a vertex with an x-coordinate of 3. we have to write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two distinct roots.
As the vertex lies on the axis of symmetry, so the axis of symmetry is x = 3. Now we have to take two x-intercepts that are equal distance from the axis of symmetry i.e from point of vertex and we can use these x-intercepts to write factors of the function by subtracting from x.
we take 2 and 4 ∴ factors becomes (x-2) and (x-4)
Hence, the quadratic function is
f(x) = (x − 2) (x − 4)