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
Varvara68 [4.7K]
3 years ago
15

Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parenthe

ses 6 minus 6 i close parentheses.
Mathematics
1 answer:
AlekseyPX3 years ago
7 0
The answer is
\frac{-6i-3}{5}.

Before we rationalize the denominator, we must simplify the numerator and denominator.  We evaluate the square root on the top, and combine like terms on the bottom:
\frac{\sqrt{-9}}{(4-7i)-(6-6i)}
\\
\\=\frac{\sqrt{9i^2}}{4-6-7i--6i}
\\
\\=\frac{3i}{-2-i}

To rationalize the denominator, we multiply by the conjugate.  The conjugate is found by making the imaginary term of the complex number, the i part, the opposite sign.  The conjugate of -2-i is -2+i:

\frac{3i}{-2-i}\times \frac{-2+i}{-2+i}
\\
\\=\frac{3i(-2+i)}{(-2-i)(-2+i)}
\\
\\=\frac{3i\times -2 + 3i\times i}{-2\times -2 + -2\times i + -2\times -i + -i\times i}
\\
\\=\frac{-6i+3i^2}{4-2i+2i-i^2}
\\
\\=\frac{-6i+3(-1)}{4-i^2}=\frac{-6i-3}{4-(-1)}=\frac{-6i-3}{5}
You might be interested in
What number should be added to both sides of the equation to complete the square?
baherus [9]
-4 is what you put on both sides Bc it’s half of b
4 0
2 years ago
Find the value of x.
ella [17]

Answer:

502.4

Step-by-step explanation:

Use tangent because the side you know and the side with x are both legs.  

Do 203/tan(22) and you should get your awnser.  

You devide by 203 because the rule is opposite over ajacent and 203 is the opposite side.

4 0
2 years ago
How to calculate the mode 5 10 12 4 6 11 13 5
Yuki888 [10]
The mode is the number that occurs the most so if you look at the numbers, thee only one that occurs twice is 5 so 5 is the mode.
7 0
3 years ago
Read 2 more answers
Find the distance between the points (0, 10) and (–9, 1).
Assoli18 [71]
D=sqrt[(x1-x2)^2+(y2-y1)^2]
(0,10) x1=0 y1=10 and (-9,1) x2=-9 y2=1
now d=sqrt[(-9-0)^2+(1-10)^2]=12.72792206 units
6 0
3 years ago
Can someone solve this for me please.
nika2105 [10]

Answer:

  • The value of PR is 21 ft.

Step-by-step explanation:

<u>We know that:</u>

  • 3(PQ + QT + TP) = PR + RS + SP
  • PQ = 7 ft.
  • QT = 4 ft
  • RS = 12 ft.

<u>Work:</u>

  • 3(PQ + QT + TP) = PR + RS + SP
  • => 3(7 + 4 + TP) = PR + 12 + SP
  • => 21 + 12 + 3TP = PR + 12 + SP
  • => 21 + 3TP = PR + SP
  • => 21 + SP = PR + SP                                                                       [3TP = SP]
  • => 21 = PR

Hence, <u>the value of PR is 21 ft.</u>

Hoped this helped.

BrainiacUser1357

6 0
2 years ago
Other questions:
  • BRAINLIEST
    5·1 answer
  • A jar of jelly that weighs 4.25 Oz cost $2.89 what is the cost of 1 oz of jelly
    10·1 answer
  • Write an expression that shows the product of 5 and the difference of 12 and 9.
    5·1 answer
  • 2x + y = -8<br> 3x - 5y = -25
    15·1 answer
  • Which lines are parallel is m∠1 + m∠2 = 180? Justify your answer.
    6·1 answer
  • What two numbers multiply to get 40 but add to get -14
    7·2 answers
  • How much time is needed for a 15,000 W engine to do 1,800,000 J of work? (Power: P = W/t) 0.008 s 8 s 120 s 1,785,000 s
    9·2 answers
  • Let g be the function given by g(x)=√ 1−sin2x. Which of the following statements could be false on the interval 0≤x≤π ?
    14·1 answer
  • The graph shows two lines, A and B. Based on the graph, which statement is correct about the solution to the system of equations
    11·2 answers
  • What is the value of x if 2x - 7 = 103 x=__________
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!