2x² - 15x + 7
(2x - 1)(2x-14)
(2x - 1)(x - 7) x= 1/2 or 7
Answer: Commutative Property of Multiplication
<u>Step-by-step explanation:</u>
Commutative property is when two terms trade places.
(a · 3) × b = b × (a · 3)
Notice that (a · 3) switched places with b
solution:
Consider the differential equation,
7ty + (1+t2)1/2y1 = 0
Rewrite the DE as,
(1+t2)1/2dy = - 7ty
dy/y = -7t/√1+t2 dt
in y = -7(1+t2) + c
y = ce-7(1+t2)
given,
y(0) = 1 => ce-7 = -1 => c = e7
ᴪ (t,y) = y -ce ᴪ(0,1)(1+t2)
Given:
The given function is:

To find:
The range of the given function.
Solution:
We have,

It is a quadratic function because the highest power of the variable x is 2.
Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.
If a quadratic function is
, then the vertex of the quadratic function is:

In the given function,
.



The value of the given function at
is:


The vertex of the given downward parabola is
. It means the maximum value of the function is
. So,

![Range=\left(-\infty, \dfrac{2121}{32}\right ]](https://tex.z-dn.net/?f=Range%3D%5Cleft%28-%5Cinfty%2C%20%5Cdfrac%7B2121%7D%7B32%7D%5Cright%20%5D)
Therefore, the range of the given function is
.