1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yanka [14]
3 years ago
9

Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

Mathematics
1 answer:
RideAnS [48]3 years ago
3 0

<u>ANSWER</u>

Extraneous solution: x=6

Real solution: x=11

<u>EXPLANATION</u>

The given expression is

\sqrt{x - 2}  + 8 = x

Add -8 to both sides:

\sqrt{x - 2}  + 8  +  - 8= x +  - 8

\implies\sqrt{x - 2} = x - 8

Square both sides.

\implies(\sqrt{x - 2} )^{2} =( x - 8)^{2}

x - 2=( x - 8)^{2}

We expand the to get

x - 2 =  {x}^{2}  - 16x + 64

Write in standard quadratic form.

{x}^{2}  - 16x - x + 64 + 2 = 0

{x}^{2}  - 17x + 66 = 0

Factor to get:

(x - 6)(x - 11) = 0

x = 6 \: or \:  \: x = 11

We check for extraneous solutions by substituting each value of x into the original equation.

When x=6

\sqrt{6 - 2}  + 8 = 6

\sqrt{4}  + 8 =6

2 + 8  = 10 \ne8

Hence x=6 is an extraneous solution.

When x=11

\sqrt{11- 2}  + 8 = 11

\sqrt{9}  + 8 = 11

3 + 8 = 11

This statement is true.

Hence x=11 is the only solution.

You might be interested in
Jonathan put ice cream in the freezer, and the ice cream remained frozen.
Phantasy [73]

Answer:

C- Based on the data, this is an example of causation

Step-by-step explanation:

This is because by him putting the ice cream into a freezing area, the ice cream remained frozen. Imagine if he put in in a warm area, it would melt. Hope this helps!

8 0
2 years ago
Read 2 more answers
An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in sh
larisa86 [58]

The amount of rim needed for each window is 141.4 in

<h3>How to find the length of the outer rim?</h3>

Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.

<h3>What is an arc?</h3>

An arc is part of section of the circumference of a circle

<h3>What is the length of an arc?</h3>

So, length of arc, L = Ф/360 × 2πR where

  • Ф = central angle of arc and
  • R = radius of circle.

Gven that for the window rim

  • Ф = angle of the rim = 270° and
  • R = radius of the rim = 30 in

Substituting the values of the variables into the equation for L, we have

L = Ф/360 × 2πR

L = 270°/360° × 2π × 30 in

L = 3/4 × 2π × 30 in

L = 3/2 × π × 30 in

L = 3 × π × 15 in

L = 45π in

L = 141.37 in

L ≅ 141.4 in

So, the amount of rim needed for each window is 141.4 in

Learn more about length of an arc here:

brainly.com/question/8402454

#SPJ1

7 0
1 year ago
I’m confused on this one
ad-work [718]

The question is "What is the scale of the model to the actual statue"


That means you must put 2/15.


2 being the model


15 being the actual statue


Take that fraction and equal is to 1/x.


Multiply 15 to 1 and 2 to x.


In the end, to solve, you divide 15 by 2x.


The answer is X=7.5


1 : 7.5


7 0
3 years ago
Find the factors of each number in classify each number as a prime or composite<br> 18,37,48
zepelin [54]

18=1,2,3,9,18

37=1,37

48=1,2,3,16,24,12,4,6,8,48

Prime no. is a number that is divisible only by itself and 1

So, here 37 is a prime no.

18 and 48 are composite no.s

7 0
2 years ago
Need help asap!!! please
Mama L [17]

Answer:

x = -8

Step-by-step explanation:

g(x) = 8x + 2

given: g(x) = 8x + 2 = -62

8x = -62 -2

8x = -64

x = -8

7 0
3 years ago
Other questions:
  • You need to find the distance across a river, so you make a triangle. BC is 661 feet, m∠B=103.2° and m∠C=14.4°. Find AB.
    8·1 answer
  • Bill owes $425.07 on his credit card. He returns two items, one for $45.55 and the other for $54.68. Then he makes purchases of
    11·1 answer
  • Calculate the volume of the 3-D composite figure please!! show how you got the volume
    6·1 answer
  • Find the answers to these two problems. PLEASE HELP!!
    6·1 answer
  • Look at the data set below,
    6·1 answer
  • Please help!! I’ve been stuck on 3 &amp; 4!
    13·1 answer
  • 4x - y = 6<br> -5x + y = -9
    14·1 answer
  • Find the missing length, i’ll give brainliest
    8·1 answer
  • Neil and his mom are volunteering at an emergency relief center. To help prepare in case of a flood, they pack emergency kits wi
    5·1 answer
  • A dairy needs 336 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk contai
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!