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dem82 [27]
2 years ago
9

He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0. which best

describes the reasonableness of the student’s solution? his solution for x is correct and his explanation of the extraneous solution is reasonable. his solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x. his solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x. his solution for x is incorrect. when solved correctly, there are no extraneous solutions.
Mathematics
1 answer:
seropon [69]2 years ago
5 0

The question is incomplete. Completed question is given below the answer.

His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

Given  

Then the solution follows thus:

Step 1: 8(x – 4) = 2(x + 2)

Step 2: 4(x – 4) = (x + 2)

Step 3: 4x – 16 = x + 2

Step 4: 3x = 18

Step 5: x = 6

It can be seen that his solution is correct. But 6 is not an extraneous solution.

An extraneous solution is a solution to an equation that emerges from the process of solving the problem but is not a valid solution to the original problem.

When 6 is substituted into the original equation, the original equation holds.

Therefore, his solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

Learn more about extraneous solution here: brainly.com/question/3751209

#SPJ4

Completed question:-

A student solves the following equation for all possible values of x:His solution is as follows:

Step 1: 8(x – 4) = 2(x + 2)

Step 2: 4(x – 4) = (x + 2)

Step 3: 4x – 16 = x + 2

Step 4: 3x = 18

Step 5: x = 6

He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.

Which best describes the reasonableness of the student’s solution?

His solution for x is correct and his explanation of the extraneous solution is reasonable.

His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.

His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

His solution for x is incorrect. When solved correctly, there are no extraneous solutions.

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I’d appreciate help ASAP please and thank you!
White raven [17]
<h3>Answer:  Choice C) 40 </h3>

==========================================================

Work Shown:

Plug in x = 0

g(x) = 3^{2x}\\\\g(0) = 3^{2*0}\\\\g(0) = 3^{0}\\\\g(0) = 1\\\\

This indicates that (0,1) is on the curve. This is the y intercept.

Do the same for x = 2

g(x) = 3^{2x}\\\\g(2) = 3^{2*2}\\\\g(2) = 3^{4}\\\\g(2) = 81\\\\

So we know that (2,81) is another point on this curve.

We need to find the slope of the line through (0,1) and (2,81) to get the slope of the secant line we want.

m = \text{slope}\\\\m = \frac{\text{rise}}{\text{run}}\\\\m = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{g(2)-g(0)}{2-0}\\\\m = \frac{81-1}{2-0}\\\\m = \frac{80}{2}\\\\m = 40\\\\

The slope of the line through (0,1) and (2,81) is m = 40. This value of m is exactly the slope of the secant line your teacher is asking for. This is why the answer is choice C.

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j

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