Israel started to solve a radical equation in this way:

square root of x plus 6 − 4 = x
square root of x plus 6 − 4 + 4 = x + 4
square root of x plus 6 = x + 4
(square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 − 6 = x2 + 8x + 16 − 6
x = x2 + 8x + 10
x − x = x2 + 8x + 10 − x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)

x + 2 = 0 x + 5 = 0
x + 2 − 2 = 0 − 2 x + 5 − 5 = 0 − 5
x = −2 x = −5

Solutions = −2, −5

What error did Israel make?

He subtracted 6 before subtracting x.
He added 4 before squaring both sides.
He factored x2 + 7x + 10 incorrectly.
He did not check for extraneous solutions.

Answers

Answer 1

Answer:

He did not check for extraneous solutions.

Step-by-step explanation:

He solved the equation correctly and obtained solutions -2 and -5, but there is one final step he did not do.

Every time you square both sides of an equation to solve it, you must check for extraneous solutions. If he did, he would have eliminated x = -5.

Answer: He did not check for extraneous solutions.

Related Questions

Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.a) 91.69 < μ < 98.31b) 92.95 < μ < 97.05c) 91.68 < μ < 98.32d) 92.03 < μ < 97.97

Answers

Answer: c) 91.68 < μ < 98.32

Step-by-step explanation:

Let μ be the mean score of all students.

Let [tex]\overline{x}[/tex] represents the sample mean score.

As per given , we have

Sample size : n= 30

Sample mean : [tex]\overline{x}=95[/tex]

Sample standard deviation: [tex]s=6.6[/tex]

Significance level [tex]\alpha=0.01[/tex]

Now, Confidence interval of mean when population standard deviation is unknown is given by :-

[tex]\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}[/tex]

Degree of freedom = n-1 = 29

Critical two-tailed t-value : [tex]t_{0.01/2,29}=t_{0.005,29}=2.756[/tex] [By students' t distribution table]

Confidence interval of mean will be:

[tex]95\pm (2.756)\dfrac{6.6}{\sqrt{30}}\\\\=95\pm (2.756)\dfrac{6.6}{5.47722557}\\\\=95\pm (2.756)(1.205)\\\\=95\pm 3.32\\\\= (95-3.32, 95+3.32)\\\\=(91.68,\ 98.32)[/tex]

i.e. a 99% confidence interval for the mean score of all students : 91.68 < μ < 98.32

So correct option is c) .

State whether the data described below are discrete or continuous, and explain why.
The number of car accidents on a given stretch of highway each year
Choose the correct answer below.
O A. The data are continuous because the data can take on any value in an interval.
OB. The data are discrete because the data can take on any value in an interval.
C. The data are continuous because the data can only take on specific values.
D. The data are discrete because the data can only take on specific values.

Answers

Answer: D. The data are discrete because the data can only take on specific values.

Step-by-step explanation:

Discrete data refers to data that has a specific value in a specific period and so can be counted as opposed to continuous data that cannot be counted as it goes on to infinity. An example of continuous data would be the height of students in a class. This is continuous because a person's height could be 1.02325845...... metres.

The number of car accidents on a particular stretch of highway can be counted and the data can only take on a specific value thereby making it discrete data.

In this exercise we have to use the knowledge of distance to understand which the best alternative corresponds to car accidents, in this way we find that:

Letter D. The data are discrete because the data can only take on specific values.

Discrete information in visible form refers to data that bear a distinguishing value fashionable a distinguishing period accordingly can be check in order as opposite to continuous information in visible form that cannot be deem as it continue to infinity.

An instance of constant data hopeful the height of person actively learning fashionable a class. This is constant cause a person's crest could be 1.02325845 metres.

The number of vehicle driven on streets accidents in contact a particular stretch of heavily traveled maybe have importance and the data can only oppose a particular financial worth by that making it discrete information in visible form.

See more about distance at brainly.com/question/989117

у (x) = 5x - 9 find each value

Answers

y (x) = 5x - 9

x = 9/5

How many thousands are in 30 hundreds

Answers

Answer:

Step-by-step explanation:

30 hundreds = 30*100 which = 3000 and 3000/1000 = 3

Answer:

Step-by-step explanation:

30x100=3000 is the answer to solving your problem

For the function f(x) = 16x^3 - x, make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at x = 1. Complete the table. (Round the final answer to three decimal places as needed. Round all intermediate values to four decimal places as needed.) An accurate conjecture for the slope of the tangent line at x = 1 is (Round to the nearest integer as needed.)

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

Interval Slope of secant lines

[1,2] 113.000

[1, 1.5] 75.000

[1, 1.1 ] 51.960

[1, 1.01] 47.482

[1, 1.001] 47.048

Step-by-step explanation:

From the question we are told that

The function is [tex]f(x) = 16x^3 -x[/tex]

Now considering the intervals

For [1, 2]