Since a polynomial is where we have like terms such as (1 x 10²) and (4 x 10²), we can add these up using the distributive property to get (5 x 10²) but still keep the 10². For example, it's similar to if we had 2x²+3x²=5x². The x² is still there, but we add up the 2 and 3. Similarly, we can add these up for 10^1 and 10^0
Answer:
Step-by-step explanation:
We know that the vertex(lowest point) of 
is 
.
By inspection, we can see that the vertex of the graph is 
.
So, the lowest point of 
is , which means 
The <em><u>correct answers</u></em> are:
B=(xy + x)(xy + x)
; C=(2x – 3)(–3 + 2x)
; and E=(4y² + 25)(25 + 4y²)
Explanation:
In order to have a perfect square trinomial, we must multiply two binomials that are exactly the same. For (xy+x)(xy+x), are multiplying two identical binomials.
For (2x-3)(-3+2x), we are multiplying two binomials that are the same but written in a different order. The same is true of (4y² + 25)(25 + 4y²).
Answer:
Step-by-step explanation:
![f(x)=4\sqrt{2x^3-1}=4\left(2x^3-1\right)^\frac{1}{2}\\\\f'(x)=4\cdot\dfrac{1}{2}(2x^3-1)^{-\frac{1}{2}}\cdot3\cdot2x^2=\dfrac{12x^2}{(2x^3-1)^\frac{1}{2}}=\dfrac{12x^2}{\sqrt{2x^3-1}}\\\\\text{used}\\\\\sqrt{a}=a^\frac{1}{2}\\\\\bigg[f\left(g(x)\right)\bigg]'=f'(g(x))\cdot g'(x)\\\\\bigg[nf(x)\bigg]'=nf'(x)\\\\(x^n)'=nx^{n-1}](https://tex.z-dn.net/?f=f%28x%29%3D4%5Csqrt%7B2x%5E3-1%7D%3D4%5Cleft%282x%5E3-1%5Cright%29%5E%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5Cf%27%28x%29%3D4%5Ccdot%5Cdfrac%7B1%7D%7B2%7D%282x%5E3-1%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Ccdot3%5Ccdot2x%5E2%3D%5Cdfrac%7B12x%5E2%7D%7B%282x%5E3-1%29%5E%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cdfrac%7B12x%5E2%7D%7B%5Csqrt%7B2x%5E3-1%7D%7D%5C%5C%5C%5C%5Ctext%7Bused%7D%5C%5C%5C%5C%5Csqrt%7Ba%7D%3Da%5E%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Cbigg%5Bf%5Cleft%28g%28x%29%5Cright%29%5Cbigg%5D%27%3Df%27%28g%28x%29%29%5Ccdot%20g%27%28x%29%5C%5C%5C%5C%5Cbigg%5Bnf%28x%29%5Cbigg%5D%27%3Dnf%27%28x%29%5C%5C%5C%5C%28x%5En%29%27%3Dnx%5E%7Bn-1%7D)
Easy, that is the slope from (2,f(2)) to (3,f(3))
remember that the slope between the points (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
find f(2) and f(3)
f(2)=2²+6(2)+5=4+12+5=21
f(3)=3²+6(3)+5=9+18+5=32
so the slope from (2,21) to (3,32) is (32-21)/(3-2)=11/1=11
answer is 11
