solve the radical. x+4=sqrt x+10 what is the extraneous solution to the radical equation

Solve The Radical. X+4=sqrt X+10 What Is The Extraneous Solution To The Radical Equation

Answers

Answer 1

Answer:

-6 is an extraneous solution.

Step-by-step explanation:

We can start by solving this problem.

First, to remove the square root, we can square both sides.

[tex](x+4)^{2} = x + 10\\x^2 + 8x + 16 = x + 10\\[/tex]

Next, we can subtract both sides by (x+10)

[tex]x^2 + 7x + 6 = 0\\[/tex]

Then, we can factor out the equation.

[tex](x+1)(x+6) = x^2 + 7x + 6 \\= 0[/tex]

Given this, it seems like -1 and -6 would be correct. Plugging this back into the original equation, though,

-1 + 4 = √(-1 + 10)

3 = 3

-6 + 4 = √(-6+10)

-2 ≠ 2

Therefore, -6 is an extraneous solution.


Related Questions

Evaluate 5 x3 - 2 + 7 when x = -2.

Answers

Answer:

57

Step-by-step explanation:

5|x^³-2|+7

let x=-2

5|(-2)^3-2|+7

work inside the absolute value first

5|-8-2|+7

5|-10|+7

Take the absolute value, which make it positive

5 *10+7

multiply

50+7

=57

nakita ko lng po yan but hope that helpsツ

I think it’s 57 the work above looks good^

Answers the question in the picture

Answers

Answer:

see explanation

Step-by-step explanation:

- 6 would represent a $6 debt

- 6 would represent 6 feet below sea level

Can someone help me please really need help? I’ll help you back please & thanks

Answers

The answer is 6 days.

This is the equation
30d-60=20d
10d=60
d=6

Combining functions: Consider functions f and g.

Answers

Answer:

option C

Step-by-step explanation:

Find the area of the circle.

452.16 ft2

37.68 ft2

1808.64 ft2

113.04 ft2

Answers

Answer:

113.04^2

Step-by-step explanation:

radius = diameter / 2

=12/2

=6 ft

area of circle = πr^2

=3.14 * 6^2

=3.14 *36

=113.04 ft^2

Answer:

[tex]{ \boxed{ \tt{ formular : { \tt{area}} = \pi {r}^{2}}}} \\ { \green{radius = \frac{diameter}{2} = \frac{12}{2}}} \\ area = \frac{22}{7} \times { (\frac{12}{2} )}^{2} \\ { \boxed{area = 113.04 \: {ft}^{2} }} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

What is 10000 - 82583 + 81627 X 2

Answers

Answer:

90,671

Step-by-step explanation:

10,000- 82,583+ (81,627 x 2)

Answer:

-235,837

Step-by-step explanation:

Given :

10000-82583+81627×2

Now,

10000-82583+163254

10000-245837

-235,837

Answer will be -235,837

What's the perimeter of this shape?​

Answers

Answer:

32m

Step-by-step explanation:

7+5+5+4+4+1+3+3=32

find the value of √(6-3√5)​

Answers

Answer:

There is no answer

Step-by-step explanation:

because 3√5=6,7082039232 > 6

So 6-3√5 < 0

But √x always >0

So there is no answer

I need to know the answer pleaseeee

Answers

Answer:

4:49

Step-by-step explanation:

If a + b = 2 and a - b = -4 what is the value of ab A. 5 B. -5 c.3 D. -3​

Answers

Answer:

D

Step-by-step explanation:

Given the 2 equations

a + b = 2 → (1)

a - b = - 4 → (2)

Add the equations term by term to eliminate b

2a + 0 = - 2

2a = - 2 ( divide both sides by 2 )

a = - 1

Substitute a = - 1 into (1) and solve for b

- 1 + b = 2 ( add 1 to both sides )

b = 3

Then

ab = - 1 × 3 = - 3 → D

Answer:

option d

Step-by-step explanation:

a+b=2. ,. a-b = -4

a= 2-b

substituting values, we get

(2-b) - b = -4

2 -b -b =-4

2 -2b =-4

-2b = -4-2

2b= 6

b =3

a = 2-3

a= -1

ab = 3×-1

ab = -3

Which choice is the range of f(x)=√x−3−1 ASAP

Answers

Range: [0,∞),{y|y≥0}

Help me on this pls!!!!!!

Answers

Step-by-step explanation:

bla bla bla bla123222222333333

Is Integer a Rational Number?

Answers

Hey there!

Before we get to know an Integer and Rational Number, we have to know the Real Number system first.

1. What is Real Number System?

Real Number System is very commonly used in mathematics. It is a number system that is "logical", at least when it comes to solving an equation.

But do you know that the Real Number system can be broken into two categorizes? And what are them?

Real Numbers can be broken into these main two categorizes which are:

Irrational NumberRational Number

These numbers can also be broken into other categorizes as well! Crazy, ain't it? Well that's how maths work!

Anyways, we will skip Irrational Number since it is off-topic and not related to your question. We will talk about Rational Number instead.

2. What is Rational Number?

Rational Number is a number that can be written in fraction form. That is a simple explanation for the Rational Number. Please lecture or note that approximations aren't considered as rational numbers. Even though π ≈ 22/7 which is in fraction form but it is just an approximation which is considered as Irrational Number. Also if infinity/endless decimal can be written in fraction form as well, they are considered as Rational Number too!

Now we know the meaning of Rational Number. But like I said, the Rational Number can be broken into other categorizes which are:

Integers - Whole number or number without fraction or decimal.Fractions and Decimals that can be written in fraction form.

And Integers can also be broken into:

Negative IntegersZeroPositive Integers

3. Conclusion and Answer

Since Integers are subset of Rational Number, we can conclude that Integers are Rational Number.

Hope this helps, and let me know if you have any doubts regarding Real Number system.

Simplify (−34.67) to the power of 0

Answers

Answer:

-1

Step-by-step explanation:

anything to the power of zero is always going to be 1 or -1

A kite is staked to the ground and blowing in the wind. It currently has a string let out to a length of 45 meters. It has an altitude of 38 feet. To the nearest tenth of a degree, find the angle of elevation. ______°

Answers

Answer:

40.2

Step-by-step explanation:

To better analyze this problem, we can first draw a picture. Looking at the one attached, we can see that the stake is represented by the point in the bottom right of the screen, and the kite is 45 meters away from it, representing the 45. Then, the height is 38, and this is directly above the 45 meters away from the stake.

This forms a right triangle, and we can use sohcahtoa to help use. As we don't have the hypotenuse, we can use tan. Tan(θ) = opposite/adjacent, or 38/45. Thus, arctan(38/45) = θ, and plugging that into a calculator, we get 40.2 as our answer

It twice the difference of a number and gig add to 4 the result is 22 more than four time the number. Find the number.

PLEASE HELP!!!!!!!!!!!!!!!!!

will mark brainlist​

Answers

Answer:

I have given the answer in the picture!

Step-by-step explanation:

Hey mate my answer is the correct one!

A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspected. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected?
A. H0:p=0.12Ha:p<0.12 A
B. H0:p=0.12Ha:p>0.12 B
C. H0:p=0.06Ha:p<0.06 C
D. H0:pˆ=0.06Ha:pˆ>0.06 D
E. H0:pˆ=0.12Ha:pˆ<0.12 E

Answers

Answer: A.

[tex]H_0:p=0.12\\\\H_a:p<0.12[/tex]

Step-by-step explanation:

Null hypothesis[tex](H_0)[/tex] : A statement describing population parameters as per the objective of the study. It usually takes "≤,≥,=" signs.  

Alternative hypothesis [tex](H_a)[/tex]: A statement describing population parameters as per the objective of the study. It usually takes ">, <, ≠" signs.

Let p be the proportion of screens that will be rejected.

12 percent of the screens manufactured using a previous process were rejected at the final inspection.

(i.e. p= 0.12)

Objective of the study = whether the new process reduces the population proportion of screens that will be rejected

i.e. p< 0.12

So, the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected:

[tex]H_0:p=0.12\\\\H_a:p<0.12[/tex]

The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.

Answers

Answer:

Correct Answer: A.

Step-by-step explanation:

A) The height of the water increases 2 inches per minute.

Step-by-step explanation:

Slope is the rate of change of height

m = (16 - 12)/(4 - 2) = 4/2 = 2

2 inch per min

Positive slope implies increase

A graph of f(x)=acos(bx) is shown, where b is a positive constant. Determine the values of a and b.

Answers

Answer:

Option (1)

Step-by-step explanation:

Equation of the given wave function,

f(x) = acos(bx)

Here, a = amplitude of the wave

Period of the wave = [tex]\frac{2\pi }{B}[/tex]

From the graph attached,

Amplitude = [tex]\frac{4-(-4)}{2}[/tex]

                 = [tex]\frac{4+4}{2}[/tex]

                 = 4

Period of the wave = π - 0

                                = π

From the formula of the period,

Period = [tex]\frac{2\pi }{b}[/tex]

[tex]\pi =\frac{2\pi }{b}[/tex]

b = 2

Therefore, a = 4 and b = 2.

Option (1) will be the answer.

What is the value of x in the equation 1/3 X- 2/3= -18
-56
0-52
52
56

Answers

Answer:

x = - 52

Step-by-step explanation:

Given

[tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] = - 18 ( multiply through by 3 to clear the fractions )

x - 2 = - 54 ( add 2 to both sides )

x = - 52

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {b. \:-52}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex] \frac{1}{3} x - \frac{2}{3} = - 18\\[/tex]

➺[tex] \: \frac{1}{3} x = - 18 + \frac{2}{3}\\ [/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 18 \times 3}{1 \times 3} + \frac{2}{ 3} \\[/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 54 + 2}{3}\\ [/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 52}{3} \\[/tex]

➺[tex] \: x = \frac{ - 52 \times 3}{3}\\ [/tex]

➺[tex] \: x = - 52\\[/tex]

[tex]\sf\pink{Therefore, \:the \:value \:of\: x\:is \:-52.}[/tex]

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY:}}}[/tex]

[tex] \frac{1}{3} \times ( - 52) - \frac{2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 52}{3} - \frac{2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 52 - 2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 54}{3} = - 18\\[/tex]

➼[tex] \: - 18 = - 18\\[/tex]

➼ L. H. S. = R. H. S.

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Look below at the picturess!!! pls help me i will give you 100 points !

Answers

Answer:

1/4

Step-by-step explanation:

because there 25% change

Answer:

for the blue its 1/4 or 2/8 and not likely.

For the yellow one it is 7/8 and likely.


Simplify (12^0)(12^6). Write your answer using an exponent. Explain how you found your answer.​

Answers

Step-by-step explanation:

(12^0)(12^6)

1 ×12⁶. (a⁰=1, a is a number)

=12⁶

find the value of x and y, (3x - 2y, 7) = (11, x + y)

Answers

Answer:

Step-by-step explanation:

Given,(3x-2y,7)=(11,x+y)

So,3x-2y=11...............(i)

      7=x+y

   or,x+y=7................(ii)

Now,Multiplying eqn.(ii) by 2,we get,

       2x+2y=14...........(iii)

Adding eqn(i) and eqn(iii),

        3x-2y+2x+2y=11+14

     or,5x=25

     or,x=5

Substituting value of x in eqn(i),

         5+y=7

      or,y=2

Hence,the values of x and y are 5 and 2 respectively.    

find the percentage profit when a car was bought for 60,000k and sold for 140,000k.​

Answers

Step-by-step explanation:

profit = sold price - bought price

= 140,000 - 60,000 k

= 80,000 k

% profit = (80,000/60,000)×100

= 133.33 %

please help me its due nowww

Answers

The angles represented by (2x - 60) and (60 - 2x) cannot be supplementary because their sum add up to zero instead of 180°.

if you can bake 14 cupcakes in one hour how long will it take to bake 126 cupcakes?

Answers

Answer:

9 hours

Step-by-step explanation:

126 dived by 14 is 9, so it will take 9 hours to bake 126 cupcakes.

Answer: It will take maybe 9 hours

hope this helps :)

Step-by-step explanation:

Which fraction equals the ratio of rise to run between the points (0, 0) and (6, 7)? A. B. C. D.

Answers

Answer:

7 / 6

Step-by-step explanation:

Given the points:

points (0, 0) and (6, 7)

Point 1 : x1 = 0 ; y1 = 0

Point 2 : x2 = 6 ; y2 = 7

The rise = y2 - y1 = 7 - 0 = 7

The run = x2 - x1 = 6 - 0 = 6

Ratio of Rise to Run = Rise / Run = 7 / 6

y(0.5 + 4)
PLEASE HELP!!

Answers

Answer: 8

Step-by-step explanation:

Answer:

4.5y

Step-by-step explanation:

0.5y + 4y

4.5y

help me with this please. classify the following triangle
A.right
B.isosceles
C.equilateral
D. abtuse
E.acute
F.scalene​

Answers

Answer:

isosceles triangle

Step-by-step explanation:

Answer:

A, B, and, D

Step-by-step explanation:

I'm not 100% sure but i'm pretty sure these are it.

Hope thus helps!

Consider the following system of two equations.



{y=−8x+10
y=x−8


What are the coordinates (x,y) of the solution to the system of equations?



Enter the coordinates in the space provided.

Answers

y & x = 5/4, 8 .........



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