The angle measures of a triangle are shown in the diagram.

What is the solution of x=2+ square root x-2?

alex41 [277]

So I'm going to assume that this question is asking for <u>non extraneous solutions</u>, or solutions that are found in the equation <em>and</em> are valid solutions when plugged back into the equation. So firstly, subtract 2 on both sides of the equation:

$x-2=\sqrt{x-2}$

Next, square both sides:

$(x-2)^2=x-2\\(x-2)(x-2)=x-2\\x^2-4x+4=x-2$

Next, subtract x and add 2 to both sides of the equation:

$x^2-5x+6=0$

Now we are going to be factoring by grouping to find the solution(s). Firstly, what two terms have a product of 6x^2 and a sum of -5x? That would be -3x and -2x. Replace -5x with -2x - 3x:

$x^2-2x-3x+6=0$

Next, factor x^2 - 2x and -3x + 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

$x(x-2)-3(x-2)=0$

Now you can rewrite the equation as $(x-3)(x-2)=0$

Now, apply the Zero Product Property and solve for x as such:

$x-3=0\\x=3\\\\x-2=0\\x=2$

Now, it may appear that the answer is C, however we need to plug the numbers back into the original equation to see if they are true as such:

$2=2+\sqrt{2-2}\\2=2+\sqrt{0}\\2=2+0\\2=2\ \textsf{true}\\\\3=2+\sqrt{3-2}\\3=2+\sqrt{1}\\3=2+1\\3=3\ \textsf{true}$

Since both solutions hold true when x = 2 and x = 3, <u>your answer is C. x = 2 or x = 3.</u>

8 0

3 years ago

Drag each tile to the correct box. Each tile shows an investor's tax bracket along with the tax-free yield of a bond the investo

shusha [124]

The tax bracket and tax-free yield will be (18%, 3%) < (32%, 3%) < (32% , 4%) < (22% , 5%) < (24% , 6%) .

<h3>Taxable equivalent yield based problem:</h3>

The taxable equivalent yield will be:

= Tax-free yield / (100 - Tax bracket)

Taxable equivalent yield = 3 / (100 - 18) = 0.03659

Taxable equivalent yield = 6 / (100 - 24) = 0.07895

Taxable equivalent yield = 3 / (100 - 32) = 0.04412

Taxable equivalent yield = 5 / (100 - 22) = 0.06410

Taxable equivalent yield = 4 / (100 - 32) = 0.05882

Find out more information about Tax on:

brainly.com/question/22852392

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5 0

2 years ago

This is review, please help it’s due tomorrow!

Svet_ta [14]

I dont see anything

3 0

2 years ago

n a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However,

timurjin [86]

The difference (faculty-student) in the sample proportions of those who believe that five minutes is not enough time for students to change classes typically varies about 0.096 from the true difference in proportions. Option D is correct.

<h3>What is the standard deviation?</h3>

It is a measurement of statistical data dispersion. The degree to which the value varies is known as standard deviation.

The standard deviation of the sampling distribution is found as;

$\rm \sigma_F-\sigma_s= \sqrt{\frac{0.37 \times (1-0.37)}{28}+\frac{0.89 \times (1-0.89)}{100} } \\\\ \sigma_F-\sigma_s=0.096$

The difference in the sample proportions of those who think five minutes is not enough time for students to switch classrooms generally differs by roughly 0.096 from the actual difference in proportions.

Hence option D is correct.

To learn more about the standard deviation, refer to: brainly.com/question/16555520.

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6 0

2 years ago

What are. the coordinates of the quadrilateral STUV when reflected over the X-axis.

wolverine [178]

Step-by-step explanation:

hi friend I can help you in this geometry work via Wazapp

5 0

3 years ago