We are given the following sequence:
The formula that we can use to obtain the sequence is the following:
Because when we replace the given terms we get:
For the next term:
Answer:
x=2*root(41) or x=root(164)
Step-by-step explanation:
By using Pythagoras theorem, we have 8^2+10^2=x^2. 164=x^2, x=2*root(41)
For this case we have the following equation:
We want to clear x:
For this we must follow a series of steps, the first consists of adding 4x to both sides of the equation to obtain:
In this way, the variable term remains on one side of the equation.
Thus, the first step will be:
Add 4x to both sides
Answer:
Option D
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
5x - 2(x+1) = 1/4
5x - 2x + 1 = 1/4
3x + 1 = 1/4
3x = -0.75
x = -0.25
Hope this helps, and please mark brainliest!
