I think that the probability of winning a free drink, free desert, or free fries is less than what she thinks because there are 8 chances of winning one of the prizes. There is a 1/8 chance of winning a prize. If you put 1/3 and 1/8 in a calculator you will see that 1/3 is indeed larger.
Answer:
3
Step-by-step explanation:
The points they have in bold is probably a hint to the problem.
The points they have in bold are (1,2) on curve g which means g(1)=2
and (3,2) on curve f which means f(3)=2.
g(x)=f(kx)
We know g(1)=2 so if we replace the x's with 1, we get:
g(1)=f(k*1)
g(1)=f(k)
2=f(k).
Now we just need to solve f(k)=2 for k.
We know the point (3,2) is on f so f(3)=2.
If you compare:
f(k)=2
and
f(3)=2
then you should see that k=3.
Keywords:
<em>Quadratic equation, vertex shape, parabola
</em>
For this case we have to rewrite the given quadratic equation, in the form of vertex, for this, we must take into account that a quadratic equation of the form
, can be rewritten in the form of vertex as:
Vertice is the lowest or highest point of the parabola. The vertex is given by:
. So, let:
, to find the equation in the form of vertex, we follow the steps below:
Step 1:
We take the common factor to the first two terms of the equation:
![f (x) = 4 (x^2 + 12x) + 10](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%204%20%28x%5E2%20%2B%2012x%29%20%2B%2010)
Step 2:
We work square:
We divide the coefficient of the term
by 2 and its result is squared, that is:
![(\frac {12} {2}) ^ 2 = 36](https://tex.z-dn.net/?f=%28%5Cfrac%20%7B12%7D%20%7B2%7D%29%20%5E%202%20%3D%2036)
So, we have:
![f (x) = 4 (x^2 + 12x + 36-36) + 10](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%204%20%28x%5E2%20%2B%2012x%20%2B%2036-36%29%20%2B%2010)
Step 3:
We simplify:
![f (x) = 4 (x^2 + 12x + 36) + 10- (4 * 36)](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%204%20%28x%5E2%20%2B%2012x%20%2B%2036%29%20%2B%2010-%20%284%20%2A%2036%29)
Step 4:
We factor:
![f (x) = 4 (x + 6) ^ 2-134](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%204%20%28x%20%2B%206%29%20%5E%202-134)
Thus, ![h = -6\ and\ k = -134](https://tex.z-dn.net/?f=h%20%3D%20-6%5C%20and%5C%20k%20%3D%20-134)
Answer:
The equation in the form of vertex is:
, and the vertex is ![(h, k) = (- 6, -134)](https://tex.z-dn.net/?f=%28h%2C%20k%29%20%3D%20%28-%206%2C%20-134%29)
Answer:
X2 = (-2, 1), W2 = (-4, 1), Y2 = (4, -2), Z2 = (-3, 2)
Step-by-step explanation:
First, flip across the y-axis:
Coordinates: X1 = (2, -1), W1 = (4, -1), Y1 = (2, -4), and Z1 = (3, -2)
Then, rotate 180 degrees counterclockwise:
Coordinates: See above