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
My name is Ann [436]
3 years ago
5

Solving Rational and Radical Equations: Mastery Test

Mathematics
1 answer:
lisov135 [29]3 years ago
5 0

Answer:

<u>1 step:</u> Raise both sides of the equation to the power of 2.

<u>2 step:</u> Simplify to obtain the final radical term on one side of the equation.

<u>3 step:</u> Raise both sides of the equation to the power of 2 again.

<u>4 step: </u>Simplify to get a quadratic equation.

<u>5 step:</u> Use the quadratic formula to find the values of x.

<u>6 step:</u> Apply the Zero Product Rule.

Step-by-step explanation:

Given the equation

\sqrt{x+3}-\sqrt{2x-1}=-2

<u>1 step:</u> Raise both sides of the equation to the power of 2.

(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2\\ \\(\sqrt{x+3})^2-2\sqrt{x+3}\sqrt{2x-1}+(\sqrt{2x-1})^2=4\\ \\x+3-2\sqrt{x+3}\sqrt{2x-1}+2x-1=4

<u>2 step:</u> Simplify to obtain the final radical term on one side of the equation.

x+3-2\sqrt{x+3}\sqrt{2x-1}+2x-1=4\\ \\3x+2-2\sqrt{x+3}\sqrt{2x-1}=4\\ \\-2\sqrt{x+3}\sqrt{2x-1}=4-3x-2\\ \\-2\sqrt{x+3}\sqrt{2x-1}=2-3x

<u>3 step:</u> Raise both sides of the equation to the power of 2 again.

(-2\sqrt{x+3}\sqrt{2x-1})^2=(2-3x)^2\\ \\4(x+3)(2x-1)=(2-3x)^2

<u>4 step: </u>Simplify to get a quadratic equation.

4(2x^2-x+6x-3)=2^2-2\cdot 2\cdot 3x+(3x)^2\\ \\8x^2-4x+24x-12=4-12x+9x^2\\ \\8x^2+20x-12-4+12x-9x^2=0\\ \\-x^2+32x-16=0\\ \\x^2-32x+16=0

<u>5 step:</u> Use the quadratic formula to find the values of x.

D=(-32)^2-4\cdot 1\cdot 16=1,024-64=960\\ \\x_{1,2}=\dfrac{-(-32)\pm \sqrt{960}}{2\cdot 1}=\dfrac{32\pm 8\sqrt{15}}{2}=16\pm 4\sqrt{15}

Then the equation is

(x-16-4\sqrt{15})(x-16+4\sqrt{15})=0

<u>6 step:</u> Apply the Zero Product Rule.

(x-16-4\sqrt{15})(x-16+4\sqrt{15})=0\\ \\x-16-4\sqrt{15}=0\text{ or }x-16+4\sqrt{15}=0\\ \\x_1=16+4\sqrt{15}\text{ or }x_2=16-4\sqrt{15}

You might be interested in
A company has 300 items to post, they have packages and
swat32

Answer:

£162.35.

Step-by-step explanation:

Total of letters + packages = 300.

Number of packages =  300 * 16 / ( 16+59)

= 300 * 16/75

= 64

So number of letters = 300 - 64 = 236.

No. of first class letters = 236 * 1/4 = 59.

No. of 2nd class letters = 236 - 59 = 177.

Total cost

=  64*1.2 + 0.52*59 + 0.31*177

= 162.35.

4 0
2 years ago
11. Given a matrix A, what is A^1?<br>A=[0 12 0 1]<br>​
pogonyaev

\text{Since  det(A) = 0, the  inverse of the matrix does not exist.}

3 0
2 years ago
What units will you use to measure an Indian ocean
Anastaziya [24]

Answer:

Kilometers most likely for any other measurement would be to small to do so otherwise.

8 0
3 years ago
Gary's car travel 30 miles on 1 1/5 gallon of gas. Gary wants to travel 90 miles. How many gallons of gas will his car use?
3241004551 [841]
Gary car will use 18 miles/gallons
7 0
3 years ago
F(1) = 4, f(n) = (−9) · f(n − 1) + 18
8090 [49]

f,n=4 and 27/20

this is the answer


3 0
3 years ago
Other questions:
  • You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profi
    12·1 answer
  • What is the mode of the data?<br> Q:<br> A:<br> A) 9 <br> B) 12 <br> C) 26 <br> D) 35
    15·2 answers
  • (2x + 3)3<br> I need help please
    7·2 answers
  • A researcher wishes to determine the average amount of money a student at UH spends on lunch. To accomplish this, he asks the fi
    8·1 answer
  • Decide wether the function is one to one y=8x-6
    9·1 answer
  • . To sketch y = -x?, reflect the graph of x? across:
    8·2 answers
  • Division the following simply your answer​
    7·1 answer
  • Find the value of x when 6 - 4x +6x - 8x +6 , what is the vaule of x ?
    7·1 answer
  • Help<br> pleasee<br><br><br><br><br><br><br> ...............
    14·1 answer
  • Jon spent 1 hour 17 minutes less than Camden reading last week. Camden spent 47 minutes less than Pete. Pete spent 3 hours readi
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!