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
svetoff [14.1K]
3 years ago
5

How do you solve 1/x + 1/y + 1/z = 1 for z?

Mathematics
1 answer:
garri49 [273]3 years ago
5 0

Answer:

\large\boxed{z=\dfrac{xy}{xy-x-y}}

Step-by-step explanation:

\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1\qquad\text{multiply both sides by}\ xyz\neq0\\\\xyz\cdot\dfrac{1}{x}+xyz\cdot\dfrac{1}{y}+xyz\cdot\dfrac{1}{z}=xyz\cdot1\qquad\text{simplify}\\\\yz+xz+xy=xyz\qquad\text{subtract}\ xy\ \text{from both sides}\\\\xz+yz=xyz-xy\qquad\text{subtract}\ xyz\ \text{from both sides}\\\\xz+yz-xyz=-xy\qquad\text{distribute}\\\\(x+y-xy)z=-xy\qquad\text{divide both sides by}\ (x+y-xy)\\\\z=\dfrac{-xy}{x+y-xy}\\\\z=\dfrac{-xy}{-(xy-x-y)}\\\\z=\dfrac{xy}{xy-x-y}

You might be interested in
I need help :(:(:(:(
tigry1 [53]

The resulting matrix of the row operation is given as follows:

R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right]

<h3>How to find the resulting matrix?</h3>

We apply the row operation on the original matrix, given as follows:

A = \left[\begin{array}{ccc}4&3&0\\-6&-3&12\end{array}\right]

The operation is given by:

R_1 = R_1 - 0.5R_2

That is, applying to each element, we have that:

  • 4 - 0.5(-6) = 7.
  • 3 - 0.5(-3) = 4.5.
  • 0 - 0.5(12) = -6.

Hence the resulting matrix is:

R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right]

More can be learned about matrix operations at brainly.com/question/1821869

#SPJ1

3 0
2 years ago
A construction company needs new materials for the next job. It needs to purchase three wood beams. Each beam costs $45.25. The
Lena [83]
Answer: $210.75

Explanation: You multiply the price of the object by how many they buy.
So for the beams you calculate 3 x 45.25 and get 135.75. For the screws you multiply 6 x 12.50 and that equals 75. Then, for the total price you add the two together, so 135.75 + 75 = 210.75

Another way to do it is (3 x 45.25) + (6 x 12.50) = 210.75
7 0
3 years ago
Pls i need help my brain won't think straight
Vika [28.1K]

Rocky because of the product rule which says that when multiplying two terms with the same base you add the exponents.

7 0
3 years ago
Solve the equation 3- (2c - 8) = 7 .<br><br> c= ?
kenny6666 [7]

Answer:

here,

or, 3- 2c + 8 = 7

or, 11 - 2c = 7

or, -2c =7 - 11

or, -2c = -4

or, c = -4/ -2

or, c = 2#

hope this solution will be helpful for you!!

8 0
4 years ago
Noelle has 198 coins, all nickels and dimes. Noelle has 20 more nickels than dimes. How many of each coin does Noelle have?
sergey [27]

Answer: 109 nickels and 89 dimes

Step-by-step explanation: 198 minus 20 is 178 and 178 divided by 2 is 89 and 89 plus 20 is 109 so there are 109 nickels and 89 dimes

3 0
3 years ago
Read 2 more answers
Other questions:
  • A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6
    12·1 answer
  • IF YOU HELP I'LL MARK AS BRAINLIEST
    5·2 answers
  • How do you solve 1/4 + x = 4
    12·1 answer
  • M<br> e Mght. Find the<br> 4(2x – 7) – 2x = -10<br> 1<br> B
    14·1 answer
  • A container in the shape of a rectangular prism is shown. What is the volume, in cubic inches, of the container? V = lwh
    11·1 answer
  • You are supposed to place them in the order they are supposed to go in, that's all its asking. Need some help!!​
    6·1 answer
  • Helppppppppp please ​
    15·2 answers
  • WHAT IS THE SUM OF 3 X 3
    15·1 answer
  • What is the phase shift of the graph of y=−sin(x+π/4)+2
    8·1 answer
  • Find FH. Help Please.​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!