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
Nonamiya [84]
3 years ago
9

Find all values of c such that c/(c - 5) = 4/(c - 4). If you find more than one solution, then list the solutions you find separ

ated by commas.
Mathematics
2 answers:
Deffense [45]3 years ago
6 0

Answer:

\large\boxed{\bold{NO\ REAL\ SOLUTIONS}}\\\boxed{x=4-2i,\ x=4+2i}

Step-by-step explanation:

Domain:\\c-4\neq0\ \wedge\ c-5\neq0\Rightarrow c\neq4\ \wedge\ c\neq5\\\\\dfrac{c}{c-5}=\dfrac{4}{c-4}\qquad\text{cross multiply}\\\\c(c-4)=4(c-5)\qquad\text{use the distributive property}\\\\c^2-4c=4c-20\qquad\text{subtract}\ 4c\ \text{from both sides}\\\\c^2-8c=-20\qquad\text{add 20 to both sides}\\\\c^2-8c+20=0\qquad\text{use the quadratic formula}

\text{for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x^2-8x+20=0\\\\a=1,\ b=-8,\ c=20\\\\b^2-4ac=(-8)^2-4(1)(20)=64-80=-16

\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\\text{therefore}\ \sqrt{b^2-4ac}=\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\\x=\dfrac{-(-8)\pm4i}{2(1)}=\dfrac{8\pm4i}{2}=\dfrac{8}{2}\pm\dfrac{4i}{2}=4\pm2i

stellarik [79]3 years ago
6 0

\frac{c}{c - 5}  =  \frac{4}{c - 4}

(c - 5)(c - 4) \times \frac{c}{c - 5} =  \frac{4}{c - 4}   \times (c - 5)(c - 4)

(c - 4) \times c = 4(c - 5)

With c≠4, 5

{c}^{2}  - 4c = 4c - 20

{c}^{2}  - 8c + 20 = 0

c =  \frac{2 - + \sqrt{2 - 20} }{2}

But 2-20 is negative, therefore there isn't any real solution to this equation.

You might be interested in
Identify the diameter of the circular base created by folding the figure into a right cone. HELP ASAP PLEASE!!
Akimi4 [234]

let's notice something, we have a circle with a radius of 12 and one 90° sector is cut off, so only three 90° sectors of the circle are left shaded, so namely the cone will be using 3/4 of that circle.

think of it as, this shaded area is some piece of paper, and you need to pull it upwards and have the cutoff edges meet, and when that happens, you'll end up with a cone-shaped paper cup, and pour in some punch.

now, once we have pulled up the center of the circle to make our paper cup, there will be a circular base, its diameter not going to be 24, it'll be less, but whatever that base is, we know that is going to have the same circumference as those in the shaded area.  Well, what is the circumference of that shaded area?

\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies C=2\pi 12\implies C=24\pi \implies \stackrel{\textit{three quarters of it}}{24\pi \cdot \cfrac{3}{4}} \\\\\\ 6\pi \cdot 3\implies 18\pi

well then, the circumference of that circle at the bottom will be 18π, so, what is the diameter of a circle with a circumferenc of 18π?

\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=18\pi \end{cases}\implies 18\pi =2\pi r\implies \cfrac{18\pi }{2\pi }=r\implies 9=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{diameter is twice the radius}}{d=18}~\hfill

3 0
3 years ago
Russian Walks to school Every day. Which one of the following is the best describe how long time russian takes to walk to school
ahrayia [7]

Answer:

Minutes answer B

hope it helps

8 0
2 years ago
Read 2 more answers
Explain how to simplify radical expressions without variables
vampirchik [111]
U just gotta do it you know
3 0
3 years ago
Read 2 more answers
Drag each object to show whether distance is proportional to time in the situation represented.
Kobotan [32]

Answer:

As you kno thankA

Step-by-step explanation:

Two bo to

7 0
2 years ago
Read 2 more answers
Which system of equations is graphed below
pychu [463]

Hello. I could help you with this question because i'm actually learning that too. Just create another question showing the entire graph so that I could help you.

7 0
2 years ago
Other questions:
  • A shop advertised a 27% off sale. If a coat originally sold for $25, find the decreased in price and sale price
    13·2 answers
  • Consider a sample space of three outcomes A,B,and C. Which of the following represent legitimate probability models? 
    10·2 answers
  • 8-
    8·1 answer
  • On a cloudy day, Yong Sun needed to know the height of a window in a building. Yong Sun positioned a mirror on the ground betwee
    5·1 answer
  • What is 400lb converted to tons
    13·2 answers
  • Hello, PLEASE ANSWER ASAP!!! Don't report my question or give me false answers but I'm freaking out. I was biking home from scho
    9·2 answers
  • What is the sine ratio for
    8·1 answer
  • 50 points. Please complete it, and I'll give you brainiest
    15·1 answer
  • What is the answer to pi squared?
    7·2 answers
  • The diagram shows a 15-meter wire attached to the top of a telephone pole. The wire is attached to the ground at a point 6 meter
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!