Answer:
16 miles
Step-by-step explanation:
Given that :
1 unit = 3 miles
High School = (2, 4)
Stadium = (7, 6)
Approximate distance between high school and stadium :
Distance between High school and Stadium
x1 = 2 ; y1= 4 ; x2 = 7 ; y2 = 6
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((7 - 2)^2 + (6 - 4)^2)
Distance = sqrt((5^2 + 2^2))
Distance = sqrt(25 + 4)
Distance =5.3851648 units
1 unit = 3 miles
Approximate Distance in miles :
3 * 5.3851648 = 16.155494
Approximate distance = 16 miles
Answer:
Slope = -3
y-intercept = (0,-4)
Equation: y = -3x-4
Step-by-step explanation:
We can take any two input-output pairs from the table to find the equation of given function.
Linear function is given by:
Here m is the gradient of the functions which is defined as:
The input-output pairs are:
(x1,y1) = (-1,-1)
(x2,y2) = (0,-4)
First of all,
Putting the value of slope in the equation
Putting (-1,-1) in the equation
The equation will be:
Hence,
Slope = -3
y-intercept = (0,-4)
Equation: y = -3x-4
Answer:
yes
Step-by-step explanation:
half of x which is 4 = y which is 2
you keep doing that with the rest of the xs and ys
True, because energy, frequency, and wavelength are all properties of sound, and sound is an electromagnetic wave. The electromagnetic spectrum encompasses a continuous range of frequencies or wavelengths of electromagnetic radiation, ranging from long wavelength, low energy radio waves to short wavelength, high frequency, high energy gamma rays.
Problem 1
<h3>Answer: False</h3>
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Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
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Problem 2
<h3>Answer: True</h3>
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Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
