Answer:
<h3>The given set of polynomials f(x) and g(x) are closed under subtraction.</h3>
Step-by-step explanation:
Given that the functions f ad g are defined by
and 
respectively.
<h3>To show that the set of polynomials is closed under subtraction :</h3>
Now subtract the given polynomials
∴ 
- When subtracting the polynomials the variables and their exponents remains same only variation in their coefficients.
<h3>Hence the given polynomials f(x) and g(x) are closed under subtraction.</h3>
∴ are closed under subtraction,
Hence showed.
1. 44
2. 126.854
3. 9 5/12
4. so 0.00635
5. 5*5*11
6. 704
7. 4
8. 8,3'9
9. $1296
10. absolute value meas that whatever the result is in between the abolute value signs you make it positive so if 2-3 wer in absolute value signs the answer would be +1
11. prime 2=2
12. composite 9=3*3
13. prime 29=29
14. composite 51=3*17
15. composite 77=
16. prime 101=101
17. composite 231=3*7*11
18. composite 4924=2*2*1231
19. prime 1=1
20. prime 31=31
4 trillion pounds.
1 gigawatt-hour is equal to 1,000,000 kilowatt-hours.
Out of our 4,000,000 gigawatt-hours, 50% of it comes from coal; this is 2,000,000 gigawatt-hours.
2,000,000(1,000,000) = 2,000,000,000,000 (2 trillion) kilowatt-hours.
Since each kilowatt-hour is 2 lbs of carbon dioxide, 2 trillion * 2 = 4 trillion lbs of carbon dioxide.
The intercepts and the standard form of each polynomial are listed below:
- x-Intercept: x = - 4 or x = 6, Standard form: f(x) = x² - 2 · x - 24, y-Intercept: f(0) = - 24
- x-Intercept: x = 1 / 4 or x = 3, Standard form: f(x) = 2 · x² - 10 · x + 12, y-Intercept: f(0) = 12
<h3>How to find the intercepts and the standard form of quadratic equations</h3>
In this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.
Now we proceed to find each element:
Case 1
x-Intercept
x = - 4 or x = 6
Standard form
f(x) = (x + 4) · (x - 6)
f(x) = x² - 2 · x - 24
y-Intercept
f(0) = - 24
Case 2
x-Intercept
x = 1 / 4 or x = 3
Standard form
f(x) = (2 · x - 4) · (x - 3)
f(x) = 2 · (x - 2) · (x - 3)
f(x) = 2 · (x² - 5 · x + 6)
f(x) = 2 · x² - 10 · x + 12
y-Intercept
f(0) = 12
To learn more on quadratic equations: brainly.com/question/1863222
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