Answer:
vertex = (- 1, - 4.5 )
Step-by-step explanation:
Given
f(x) =
(x - 2)(x + 4)
The vertex lies on the axis of symmetry which is positioned at the midpoint of the zeros.
To find the zeros let f(x) = 0, that is
(x - 2)(x + 4) = 0
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 4 = 0 ⇒ x = - 4
The x- coordinate of the vertex is therefore
x =
=
= - 1
Substitute x = - 1 into f(x) for corresponding y- coordinate
f(- 1) =
(- 1 - 2)(- 1 + 4) =
× - 3 × 3 = 0.5 × - 9 = - 4.5
Coordinates of vertex = (- 1, - 4.5 )
Woo-Jin and Kiran were asked to find an explicit formula for the sequence 64\,,\,16\,,\,4\,,\,1,...64,16,4,1,...64, comma, 16, c
olya-2409 [2.1K]
Answer:
![f(n)=64(\frac{1}{4})^{n-1}](https://tex.z-dn.net/?f=f%28n%29%3D64%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn-1%7D)
Step-by-step explanation:
The given sequence is
64, 16, 4, 1
![r_1=\dfrac{a_2}{a_1}=\dfrac{16}{64}=\dfrac{1}{4}](https://tex.z-dn.net/?f=r_1%3D%5Cdfrac%7Ba_2%7D%7Ba_1%7D%3D%5Cdfrac%7B16%7D%7B64%7D%3D%5Cdfrac%7B1%7D%7B4%7D)
![r_2=\dfrac{a_3}{a_2}=\dfrac{4}{16}=\dfrac{1}{4}](https://tex.z-dn.net/?f=r_2%3D%5Cdfrac%7Ba_3%7D%7Ba_2%7D%3D%5Cdfrac%7B4%7D%7B16%7D%3D%5Cdfrac%7B1%7D%7B4%7D)
![r_3=\dfrac{a_4}{a_3}=\dfrac{1}{4}](https://tex.z-dn.net/?f=r_3%3D%5Cdfrac%7Ba_4%7D%7Ba_3%7D%3D%5Cdfrac%7B1%7D%7B4%7D)
It is a geometric series because it has a common ratio
.
First term is 64.
The explicit formula of a geometric series is
![f(n)=ar^{n-1}](https://tex.z-dn.net/?f=f%28n%29%3Dar%5E%7Bn-1%7D)
where, a is first term and r is common ratio.
Substitute a=64 and r=1/4 in the above function.
![f(n)=64(\frac{1}{4})^{n-1}](https://tex.z-dn.net/?f=f%28n%29%3D64%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn-1%7D)
Therefore, the required explicit formula is
.
Answer:
Enter the equations.
Multiply each equation by a number to get the lowest common multiple for one of the variables.
Add or subtract the two equations to eliminate that variable .
Substitute that variable into one of the equations and solve for the other variable.
75390
7 is in the ten thousand place
5 is in the thousand place
3 is in the hundreds place
9 is in the tens place
1 is in the ones place
7.158 * 10^9 rounds to 7 * 10^9
7 * 10^9 = 7,000,000,000