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Step-by-step explanation:

a) and b) have a finite number of digits after the decimal point. dy, they are automatically rational.

c) is the only one with an infinite number of digits after the decimal point. and while we do recognize a pattern, it is not a repeating pattern.

so, c) is NOT a rational number.

Answer:

Step-by-step explanation:

Given the function C(x) = x 2 + 78 x + 29 models the cost, in hundreds of dollars, to produce x thousand pens, we are to interpret C(0), C(2) and C(4).

For C(0), we are to substitute x = 0 into the given function;

C(0) = 0²+78(0)+29

C(0) = 0+0+29

C(0) = 29

Since the cost C(x) is in hundreds of dollars, C(0) = 2900

C(0) means that the cost of producing 0 thousand pen is $2,900

For C(2), we are to substitute x = 2 into the given function;

C(2) = 2²+78(2)+29

C(2) = 4+156+29

C(2) = 189

Since the cost C(x) is in hundreds of dollars, C(2) = 189*100 = $18900

C(2) means that the cost of producing 2 thousand pens is $18,900

For C(4), we are to substitute x = 4 into the given function;

C(4) = 4²+78(4)+29

C(4) = 16+312+29

C(4) = 357

Since the cost C(4) is in hundreds of dollars, C(4) = 357

C(4) means that the cost of producing 4 thousand pens is $35,700

Final answer:

C(x) = x^2 + 78x + 29 models the cost to produce x thousand pens. Calculating C(0), C(2), and C(4), we find that C(0) = 29, C(2) = 189, and C(4) = 357. These values represent the cost in hundreds of dollars for producing 0, 2, and 4 thousand pens, respectively.

Explanation:

To find and interpret C(0), C(2), and C(4), we substitute the given values of x into the function C(x).

1.For C(0), we substitute 0 into the function C(x):

1. C(0) = (0)^2 + 78(0) + 29
2. C(0) = 0 + 0 + 29
3. C(0) = 29
4. So, C(0) = 29 hundred dollars, meaning it costs $2900 to produce 0 thousand pens.
5. For C(2), we substitute 2 into the function C(x):
6. C(2) = (2)^2 + 78(2) + 29
7. C(2) = 4 + 156 + 29
8. C(2) = 189
9. So, C(2) = 189 hundred dollars, meaning it costs $18,900 to
10. produce
11. 2 thousand pens.
12. For C(4), we substitute 4 into the function C(x):
13. C(4) = (4)^2 + 78(4) + 29
14. C(4) = 16 + 312 + 29
15. C(4) = 357
16. So, C(4) = 357 hundred dollars, meaning it costs $35,700 to produce 4 thousand pens.

Learn more about Cost Function here:

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Answer:

Option d) (3,3)

Step-by-step explanation:

A function f(x) and its inverse f^(-1) (x) are symmetrical with respect the right line y=x, then their point of intersection is when they cross the right line y=x. In the attached graph we draw the right line y=x, and the function f(x) crooses this line at the point (3,3), then this point is their intersection point.

Answer:

answer is d

Step-by-step explanation: