Answer:
y = 2x^2 − 4x + 5
y = 2(x^2 − 2x) + 5
y = 2(x^2 − 2x + 1 - 1) + 5
y = 2(x^2 − 2x + 1) + 5 - 2
y = 2(x - 1)^2 + 3
x = 1 is the axis of symmetry.
Do you agree?
Answer:
38
Step-by-step explanation:
This is a right handed limit because there is a "+" next to the -19. This means that we have to find the limit as the function goes to -19 from the right side. This means that the limit is when it goes from -19.1 --> -19.
From the table we see that this area is aproaching 38 as it gets closer to -19.
The f(x) number will get increasingly closer to 38 but never reach 38, and that is why it is the limit.
Hope this helps!!!
Answer:
Step-by-step explanation:
Assuming the image is the shown below, we can use the following formula to find the length of arc
:
![L_{arc}=2 \pi R (\frac{\theta}{360 \°})](https://tex.z-dn.net/?f=L_%7Barc%7D%3D2%20%5Cpi%20R%20%28%5Cfrac%7B%5Ctheta%7D%7B360%20%5C%C2%B0%7D%29)
Where
is the angle in the arc and
is the radius of the circle.
Since we are not given the value of
, we will only work with this.
For
:
![L_{arc-GIF}=2 \pi R (\frac{71\°}{360 \°})](https://tex.z-dn.net/?f=L_%7Barc-GIF%7D%3D2%20%5Cpi%20R%20%28%5Cfrac%7B71%5C%C2%B0%7D%7B360%20%5C%C2%B0%7D%29)
![L_{arc-GIF}=1.239 R](https://tex.z-dn.net/?f=L_%7Barc-GIF%7D%3D1.239%20R)
For
:
We firstly need to find the value of this angle, taking into account the whole circumference is
:
![360 \°=71 \°+53 \°+HET+20 \°](https://tex.z-dn.net/?f=360%20%5C%C2%B0%3D71%20%5C%C2%B0%2B53%20%5C%C2%B0%2BHET%2B20%20%5C%C2%B0)
Finding
:
![HET=216 \°](https://tex.z-dn.net/?f=HET%3D216%20%5C%C2%B0)
Now, let's calculate the length of arc:
![L_{arc-HET}=2 \pi R (\frac{216\°}{360 \°})](https://tex.z-dn.net/?f=L_%7Barc-HET%7D%3D2%20%5Cpi%20R%20%28%5Cfrac%7B216%5C%C2%B0%7D%7B360%20%5C%C2%B0%7D%29)
![L_{arc-HET}=3.769 R](https://tex.z-dn.net/?f=L_%7Barc-HET%7D%3D3.769%20R)
Answer:
The number of half-page advertisements is 4.
The number of Full-page advertisements is 11.
Step-by-step explanation:
According to the Question,
- Given, An advertising company charges $60 per half-page advertisement and $100 per full-page advertisement. Michael has a budget of $1340 to purchase 15 advertisements.
Let, 'x' be the number of half-page advertisements and 'y' be the number of full-page advertisements.
- Thus, 60x + 100y is the money charged, and given that he has a budget of $ 1340.
60x + 100y = 1340
- And, the number of advertisements is 15. So, the other equation is
x + y = 15
Now, We have Two Equations,
60x + 100y = 1340 and x + y = 15
- the solution of the system is Put x=(15-y) in Equation 60x + 100y = 1340
60 (15-y) + 100y = 1340
900 - 60y + 100y = 1340
40y = 1340 - 900
40y = 440
y = 440/40
y = 11 So, For x = 15 - y ⇒ 15-11 ⇒ x=4 .
- Thus, the number of half-page advertisements is 4 and The number of Full-page advertisements is 11 .
Answer:
x = 3
Step-by-step explanation:
f(x) = g(x)
![6x^{2} - 54x + 100 = -3x^{2} + 19\\9x^{2} - 54x + 81 = 9(x^{2} - 6x + 9) = 0](https://tex.z-dn.net/?f=6x%5E%7B2%7D%20%20-%2054x%20%2B%20100%20%3D%20-3x%5E%7B2%7D%20%2B%2019%5C%5C9x%5E%7B2%7D%20%20-%2054x%20%2B%2081%20%3D%209%28x%5E%7B2%7D%20%20-%206x%20%2B%209%29%20%3D%200)
9(x - 3)(x - 3) = 0
x = 3