The best and most correct answer among the choices provided by the question is the third choice .
In constructing a parallel line, "<span>Without changing the width of the compass, place the compass at S or P and draw an arc similar to the one drawn."</span>
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Answer:
The arithmetic combinations of given functions are (f + g)(x) = 2x, (f - g)(x) = 4, (f
g)(x) =
, ![\left(\frac{f}{g}\right)(\mathrm{x})=\frac{x+2}{x-2}](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7Bf%7D%7Bg%7D%5Cright%29%28%5Cmathrm%7Bx%7D%29%3D%5Cfrac%7Bx%2B2%7D%7Bx-2%7D)
<u>Solution: </u>
Given, two functions are f(x) = x + 2 and g(x) = x – 2
We need to find the arithmetic combinations of given two functions
.
Arithmetic functions of f(x) and g(x) are (f + g)(x), (f – g)(x), (f
g)(x), ![\left(\frac{f}{g}\right)(\mathrm{x})](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7Bf%7D%7Bg%7D%5Cright%29%28%5Cmathrm%7Bx%7D%29)
Now, (f + g)(x) = f(x) + g(x)
= x + 2 +x – 2
= 2x
Therefore (f + g)(x) = 2x
similarly,
(f - g)(x) = f(x) - g(x)
= x + 2 –(x – 2)
= x + 2 –x + 2
= 4
Therefore (f - g)(x) = 4
similarly,
(f
g)(x) = f(x)
g(x)
= (x + 2)
(x – 2)
= x
(x – 2) + 2
(x -2)
![=x^{2}-2 x+2 x-4](https://tex.z-dn.net/?f=%3Dx%5E%7B2%7D-2%20x%2B2%20x-4)
![=x^{2}-4](https://tex.z-dn.net/?f=%3Dx%5E%7B2%7D-4)
Therefore (f
g)(x) = ![x^{2}-4](https://tex.z-dn.net/?f=x%5E%7B2%7D-4)
now,
![\left(\frac{f}{g}\right)(\mathrm{x})=\frac{f(x)}{g(x)}](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7Bf%7D%7Bg%7D%5Cright%29%28%5Cmathrm%7Bx%7D%29%3D%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D)
![=\frac{x+2}{x-2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%2B2%7D%7Bx-2%7D)
= ![\frac{x+2}{x-2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7Bx-2%7D)
Hence arithmetic combinations of given functions are (f + g)(x) = 2x, (f - g)(x) = 4, (f
g)(x) =
, ![\left(\frac{f}{g}\right)(\mathrm{x})=\frac{x+2}{x-2}](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7Bf%7D%7Bg%7D%5Cright%29%28%5Cmathrm%7Bx%7D%29%3D%5Cfrac%7Bx%2B2%7D%7Bx-2%7D)
The compound inequality to show the possible length of the third side is; 25 ≤ x +9+12≤ 30 and it's solution is; 4 ≤ x ≤ 9.
<h3>What is the compound inequality to represent the situation?</h3>
The required compound inequality as described in the task content in terms of the sum of all three sides is;
25 ≤ x +9+12≤ 30
25 -9 -12 ≤ x; 4 ≤ x.
x +9+12≤ 30
x ≤ 30 -9 -12
x ≤ 9
The compound solution is therefore; 4 ≤ x ≤ 9.
Read more on compound inequality;
brainly.com/question/1485854
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Answer:
Your answer is (6x−1)(3x−2)
Step-by-step explanation:
Answer:
slope = 2.5 and the y intercept is 3
Step-by-step explanation:
To find the slope we can use the formula
m = (y2-y1)/(x2-x1)
I will use the point (2,8) (6,18) We can pick any 2 point we want.
= (18-8)/(6-2)
= (10/4)
= 2.5
To find the y intercept we need to find the equation of the line.
We will use the point slope form
y-y1= m(x-x1)
y-8 = 2.5(x-2)
Distribute the 2.5
y-8 = 2.5x-5
Add 8 to each side
y-8+8 = 2.5x-5+8
y = 2.5x+3
This equation is in slope intercept form y = mx+b
where the slope is 2.5 and the y intercept is 3