solve for x
[tex] \sqrt{x^2-4x+8} +x=2 - x[/tex]
please show all workings​

Answers

Answer 1

Answer:

[tex]\displaystyle x=-\frac{2}{3}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]

We can isolate the square root. Subtract x from both sides:

[tex]\sqrt{x^2-4x+8}=2-2x[/tex]

And square both sides:

[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]

Expand:

[tex]x^2-4x+8=4-8x+4x^2[/tex]

Isolate the equation:

[tex]3x^2-4x-4=0[/tex]

Factor:

[tex]\displaystyle (3x+2)(x-2)=0[/tex]

Zero Product Property:

[tex]3x+2=0\text{ or } x-2=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]

Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.

Testing x = -2/3:

[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]

Since the resulting statement is true, x = -2/3 is indeed a solution.

Testing x = 2:

[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]

Since the resulting statement is not true, x = 2 is not a solution.

Therefore, our only solution to the equation is x = -2/3.  

Answer 2

Step-by-step explanation:

Hey there!

Given;

[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]

Take "X" in right side.

[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]

Squaring on both sides;

[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]

Simplify;

[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]

[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]

[tex]3 {x}^{2} - 4x - 4 = 0[/tex]

[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]

[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]

[tex]3x(x - 2) + 2(x - 2) = 0[/tex]

[tex](3x + 2)(x - 2) = 0[/tex]

Either;

3x+2 = 0

x= -2/3

Or;

x-2 = 0

x= 2

Check:

Keeping X= -2/3,

√(x²-4x+8 ) +X = 2-x

√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3

8/3 = 8/3 (True)

Now; Keeping X= 2

√{(2)²-4*2+8}+2 = 2-2

8 ≠0 (False)

Therefore, the value of X is -2/3.

Hope it helps!


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Answer:

A.

Step-by-step explanation:

To find the inverse of a function, first make f(x) a y

So,

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Then switch the x and the y

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A. Economic panics showed that the banking system was not stable.
B. The United States needed to have a single type of currency.
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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Hello!

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Good luck! :)

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Step-by-step explanation:

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10. The sum of the digits of a two digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27 . find the number​

Answers

Answer:

Step-by-step explanation:

Let "ab" represent the digits of the number. The value of "ab" is 10a+b.

a+b = 7

The value of "ba" is 10b+a

(10b+a) - (10a+b) = 9b-9a = 27

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a+b = 7

b-a = 3

------------

2b = 10

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The number is 25.

Select three ratios equivalent to 4:34:34, colon, 3.Select three ratios equivalent to 4:34:34, colon, 3.

Answers

Answer:

A

C

D

Step-by-step explanation:

Select three ratios that are equivalent to 4:3.

Choose 3 answers:

(Choice A)

8:6

(Choice B)

9:12

(Choice C)

20:15

(Choice D)

32:24

(Choice E)

36:28

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

To determine which fractions are equivalent to 4:3 express the options in their lowest terms

option 1 - 8 : 6

To transform to the simplest form. divide the numbers by 2

4 : 3 this is equivalent

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To transform to the simplest form. divide the numbers by 3

= 3 : 4 this is not equivalent

option 3 : 20:15

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Can someone please help me with this?

Answers

Answer:

x = 2/3

Step-by-step explanation:

-3x + 4 = 2

-3x = -2

x = 2/3

y = 2

(plug it into original equation)

(2/3. 2)

PLEASE HELP!! You are playing a game in which you must flip a coin and then roll a die. What is the probability of flipping a tails and then rolling a five?

Answers

The chances of that are 1/12 which is 0.083%
Answer:  1/12

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

Explanation:

1/2 is the probability of flipping tails because we have one side labeled tails out of 2 sides total.

1/6 is the probability of rolling a 5, because there's one side we want out of 6 total.

The two events (flipping the coin and rolling the die) are independent, allowing us to multiply those previously mentioned fractions:

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Write the equation of the graph y=

Answers

9514 1404 393

Answer:

  y = 6^x -3

Step-by-step explanation:

The graph is that of an exponential function that has been translated downward. We notice the horizontal asymptote is -3, and a couple of points on the graph are (0, -2) and (1, 3).

The shifted parent function will look like ...

  y = a·b^x +c

where c is the horizontal asymptote. Using the two points we found, we have ...

  -2 = a·b^0 -3 . . . . . using (x, y) = (0, -2)

  1 = a . . . . . . . . . . add 3 and simplify

Then using (x, y) = (1, 3), we have ...

  3 = b^1 -3

  6 = b . . . . . . . . . add 3 and simplify

So, the equation is ...

  y = 6^x -3

PLEAS ANSWER ASAP If you like peanut butter and chocolate, then you will love Reese's.

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Answers

The contrapositive of a statement negates the conclusion as well as the hypothesis. It is logically equivalent to the original statement asserted. Often it is easier to prove the contrapositive than the original statement. This section will demonstrate this fact.

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Answers

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Answers

Answer:

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Step-by-step explanation:

We have the expression:

[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}[/tex]

And we want to write the expression in terms of sine and cosine and simplify.

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Answers

Answer:

There is an infinite amount, but let say that x is 10, then:

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Answers

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Answers

Answer:

5/6

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

Any negative number couldn't count as more than a positive. 5 is more than 1, so the correct answer has to be 5/6.

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Answers

Answer:

(-7,-2)  

Step-by-step explanation:

y = 3x + 19

y = 5x + 33

Substitute in y. Basically set equal to each other.

3x + 19 = 5x + 33

-2x = 14

x = -7

y = 3 (-7) + 19

y = -21 + 19

y = -2

Answer:

y = -2

x = -7

Step-by-step explanation:

Substitute y= 5x + 33

5x + 33 = 3x + 19

Isolate x for 5x + 33 = 3x + 19: x = -7

For y = 5x + 33

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y = -2

So the solution is y= -2, x=-7

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Answers

9514 1404 393

Answer:

  WR ≅ WX

Step-by-step explanation:

To use the SAS postulate, you need congruent sides bounding a congruent angle.

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Answers

Answer:

Can't See 7 clearly

8) (9,9)

Step-by-step explanation:

[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]

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Answers

Answer:

[tex]7b^2+6b-3[/tex]

Step-by-step explanation:

Given:

[tex]2b+7b^2-2+3b-1+b[/tex]

Combine like terms.

[tex]7b^2+6b-3[/tex]

Hope this helps.

Write L if it is Likely to happen and Write U if it is unlikely to happen. Topic is probability
1. 2:3 __

2. 4:15 __

3. 3/10__

4. 13/21__

5. 6/16 __

6. 8:11 __

7. 9:20__

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Answers

Answer:

1h b+h boi gate

Step-by-step explanation:

Will mark brainlest helpppp pleaseeeee​

Answers

Answer:

come to mya massanger dk khanal fb user

Step-by-step explanation:

i will teach you by sending picture

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations to their solutions.

Answers

Answer:

Step-by-step explanation:

1). 2x + y = 12 -----(1)

   x = 9 - 2y -------(2)

   By substituting the value of x from equation (2) to equation (1)

   2(9 - 2y) + y = 12

   18 - 4y + y = 12

   18 - 3y = 12

   3y = 18 - 12

   y = 2

   By substituting the value of x in equation (2)

    x = 9 - 2(2)

    x = 9 - 4

    x = 5

2). x + 2y = 9 ------(1)

    2x + 4y = 20

    x + 2y = 10 -------(2)

    Since, both the equations are the parallel equations,

    Therefore, No solutions will be the answer.

3). x + 3y = 16 -------(1)

    2x - y = 11 ---------(2)

    Multiply equation (2) by 3 the add to equation (1)

    6x - 3y + (x + 3y) = 16 + 33

    7x = 49

     x = 7

     From equation (1),

     7 + 3y = 16

     3y = 9

     y = 3

4). y = 11 - 2x -------(1)

    4x - 3y = -13 -------(2)

    By substituting the value of y from equation (1) to (2),

    4x - 3(11 - 2x) = -13

     4x - 33 + 6x = -13

     10x = 33 - 13

     10x = 20

     x = 2

      From equation (1)

     y = 11 - 2(2)

    y = 7

5). y = 10 + x -------(1)

    -3x + 3y = 30

    -x + y = 10

     y = 10 + x ------(2)

    Equations (1) and (2) are same.

    Therefore, Infinite solutions will be the answer.

6). 2x + y = 11 --------(1)

    x - 2y = -7 ---------(2)

    Multiply equation (1) by 2 then add to equation (2)

    4x + 2y + (x - 2y) = 22 - 7

    5x = 15

    x = 3

    From equation (2)

    3 - 2y = -7

    2y = 3 + 7

     y = 5

Which equation in slope-intercept form represents a line that passes through the point (5,−1) and is parallel to the line y=2x-7?

Answers

Answer:

y = 2x - 11

Step-by-step explanation:

y = 2x + b

-1 = 2(5) + b

-1 = 10 + b

-11 = b

Question 5 can I have as much as you can do please

Answers

Answer:

x = 12

Step-by-step explanation:

The sum of angles in a triangle is 180°

Thus,

(x + 20) + (10x) + (x + 16) = 180°

Collect like terms

x + 10x + x + 20 + 16 = 180°

12x + 36 = 180°

12x = 180 - 36

12x = 144

Divide both sides by 12

x = 144 ÷ 12

x = 12

Substitute the value of x into the question

Therefore,

x + 20 = 12 + 20

= 32°

10x = 10(12)

= 120°

x + 16 = 12 + 16

= 28°

24 is 8 times as great as q

Answers

Answer:

Q = 3

Step-by-step explanation:

24 divided by 8 = 3
q = 3

Can someone help me with this math homework please!

Answers

Answer:

-1

Step-by-step explanation:

we match the input to the output to find that f(3) points towards -1

Find the lateral surface area of this
cylinder. Round to the nearest tenth.
r = 5 cm
5 cm
LSA = [ ? ] cm2
Enter

Answers

Answer:

[tex]A=157.07\ cm^2[/tex]

Step-by-step explanation:

Given that,

The radius of a cylinder, r = 5 cm

Height of the cylinder, h = 5 cm

We need to find the lateral surface area of the  cylinder. The formula for the lateral surface area of the cylinder is given by :

[tex]A=2\pi r h[/tex]

Put all the values,

[tex]A=2\pi\times 5\times 5\\\\=157.07\ cm^2[/tex]

So, the lateral surface area of the cylinder is [tex]157.07\ cm^2[/tex].

the sum of all the exponents on all the variables of a term
plsss answer

Answers

Answer:

Answer: for polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial

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