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
Artyom0805 [142]
3 years ago
5

How to simplify rational expressions

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
7 0
So, what we will do is, multiply both top and bottom, by the conjugate of the denominator, so, the denominator is 7 + 10i, so its conjugate is 7 - 10i then, let's do so.

\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)
\\\\\\
\textit{also recall that }i^2=-1\\\\
-------------------------------\\\\

\bf \cfrac{-3-7i}{7+10i}\cdot \cfrac{7-10i}{7-10i}\implies \cfrac{(-3-7i)(7-10i)}{(7+10i)(7-10i)}\implies \cfrac{(-3-7i)(7-10i)}{7^2-(10i)^2}
\\\\\\
\cfrac{-21+30i-49i+70i^2}{7^2-(10^2i^2)}\implies \cfrac{-21+30i-49i+70\left( \boxed{-1} \right)}{7^2-\left[10^2\left( \boxed{-1} \right)\right]}
\\\\\\
\cfrac{-21+30i-49i-70}{49-(-100)}\implies \cfrac{-91-19i}{149}\implies -\cfrac{91}{149}-\cfrac{19i}{149}
You might be interested in
What is -2(3x+12y-5-17x-16y+4) simplified?
kirill [66]

Answer:

28x+8y+2

Step-by-step explanation:

-2\left(3x+12y-5-17x-16y+4\right) -> =-2\left(-14x-4y-1\right)

\mathrm{Distribute\:parentheses}

=\left(-2\right)\left(-14x\right)+\left(-2\right)\left(-4y\right)+\left(-2\right)\left(-1\right)

\mathrm{Apply\:minus-plus\:rules}\\\left(-a\right)\left(-b\right)=ab\\=2\cdot \:14x+2\cdot \:4y+2\cdot \:1\\=28x+8y+2

6 0
2 years ago
Read 2 more answers
Jacob needs to know the volume of the cylinder shown below. Which expression will give him the correct volume?
Lilit [14]

Answer:

B

Step-by-step explanation:

3.14(24 square)(2.5)                        

PIE X radius squared X height

6 0
3 years ago
Read 2 more answers
If the property tax on a 300,000 Is 2,220 what is the tax on a 100,000 home
ikadub [295]

Answer:

SO first you have to divise 300,000 by 2,220 and then multiply it by 100,000.To get 13636363.6364.SO the tax on a 100k home would be about 13636363.6364

Step-by-step explanation:

6 0
3 years ago
Question 7 PLEASE HELP Describe the transformation from the graph of f(x)=x to the graph of g(x)=1/5x+4
sladkih [1.3K]

i think the graph g(x) has been shrunk vertically by a factor of 1/5 and shifted up by 4 units :)

6 0
3 years ago
How would I find angle B for this bridge? What formula would I use?
astraxan [27]
The bridge attached is drawn according to given dimensions, and it doesn't look right.  Please double check the given dimensions.

Calculations:
Horizontal part of bottom chord below the 70 degree triangle 
= 15.1*cos(70) = 5.16  (which is a major prt of the 6.3 units.
Height of vertical pieces DF and EH
= 15.1*sin(70) = 14.19
Note that structurally, DF and EH do not help in reducing stress on the bridge, since they are perpendicular to the bottom chord.

Therefore 
angle B = atan(14.19/(6.3-5.16))=85.41 degrees

I believe the whole geometry does not look right, esthetically, and structurally, since the compression members are much longer than the tension members in the middle.  (The vertical members carry no force.) 
If  you can review the input data, or post a new question, I will be glad to help.

4 0
3 years ago
Read 2 more answers
Other questions:
  • 8. Albert's father is 24 years older than Albert is. In 8 years, his father will be twice as old as Albert. How old is Albert no
    9·1 answer
  • Solve 12 – (2 × 3)a.6b.12c.12(2)d. 2 to the 3rd power
    7·1 answer
  • -3-3 (2x+7)-4(6x+7)-10
    10·1 answer
  • Omg plz help have no idea question below
    10·1 answer
  • Find the slope and reduce. P=(2, 3) Q=(9, 7) Slope =​
    14·1 answer
  • Nirja has 24 marbles. The number of marbles Nirja has is 6 more than the number of marbles Tim has.
    15·1 answer
  • 5. You sell candy bars for a fundraiser. Each box contains 50 bars and costs $30. If you want to make $45 profit for each box, h
    10·2 answers
  • A building casts a shadow that is 50 feet in length. If the distance from the end of the shadow to the top of the building is 25
    11·1 answer
  • What is 3 5/8 *1 3/4
    9·2 answers
  • Un comerciante compra una pieza de 45m
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!