Answer:
Angle C = 55°
Do you want an explanation
Let 3<em>n</em> + 1 denote the "number" in question. The claim is that
(3<em>n</em> + 1)² = 3<em>m</em> + 1
for some integer <em>m</em>.
Now,
(3<em>n</em> + 1)² = (3<em>n</em>)² + 2 (3<em>n</em>) + 1²
… = 9<em>n</em>² + 6<em>n</em> + 1
… = 3<em>n</em> (3<em>n</em> + 2) + 1
… = 3<em>m</em> + 1
where we take <em>m</em> = <em>n</em> (3<em>n</em> + 2).
Answer:
The vertex is the point (6,-31)
Step-by-step explanation:
we have
![f(x)=x^2-12x+5](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-12x%2B5)
This is a vertical parabola open upward
The vertex represent a minimum
Convert to vertex form
Complete the square
![f(x)=(x^2-12x+6^2)+5-6^2](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E2-12x%2B6%5E2%29%2B5-6%5E2)
![f(x)=(x^2-12x+36)-31](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E2-12x%2B36%29-31)
Rewrite as perfect squares
-----> equation in vertex form
therefore
The vertex is the point (6,-31)
Answer: There are 2 batteries which he can buy with his earnings .
Step-by-step explanation:
Since we have given that
Selling price of cans at the recycling center = $0.40 per pound
Number of pounds of cans he sold on Monday = 16.2
Number of pounds of cans he sold on Tuesday = 11.8
Total earning of Samuel is given by
![(16.2+11.8)\times 0.40=\$11.2](https://tex.z-dn.net/?f=%2816.2%2B11.8%29%5Ctimes%200.40%3D%5C%2411.2)
Now, cost of battery =$5.60
So, number of batteries he can buy is given by
![\frac{\text{ Total earnings}}{\text{ Cost of each battery}}\\\\=\frac{11.2}{5.6}\\\\=2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7B%20Total%20earnings%7D%7D%7B%5Ctext%7B%20Cost%20of%20each%20battery%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B11.2%7D%7B5.6%7D%5C%5C%5C%5C%3D2)
So, there are 2 batteries which he can buy with his earnings .
Answer:
f(x) = 3x(x-1)(x-3)
Step-by-step explanation:
f(x) = 3x³-12x²+9x = 3x(x²-4x+3) =
= 3x(x²-x-3x+3) = 3x[x(x-1)-3(x-1)] =
= 3x[(x-1)(x-3)] = 3x(x-1)(x-3)