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
Rom4ik [11]
3 years ago
6

If XY=18, YZ=14, and XZ=20, find the radius of each circle.

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
8 0
Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P  are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P  + Y M = 18 X P - M Z  = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6  /* ( - 1 )X P  - M Z = 4 X P + Y M = - 6  X P - M Z = 4    Y M - M Z = - 2           Y M + M Z = 14            2 Y M = 12  =>  Y M = 6M Z - 6 = 2  =>   M Z = 8X P + 6 = 18 
 X P = 12
Radii of the circles are: 12, 8 and 6. 
You might be interested in
Explain determination ......?? ​
kolezko [41]

Determination is your will power of doing something. Someone who is determined has the firmness of purpose and the resolve to achieve a goal.

Synonyms:  

<em>resolution, resolve, resoluteness, character.</em>

<em />

Antonyms:

<em>weak-mindedness, pusillanimity. </em>

3 0
3 years ago
Read 2 more answers
Write the formula for the volume of a square prism, V = s-h, in terms of h. Then find the height h of a square prism with volume
vodomira [7]

Answer:

h = \frac{3V}{s^2}

height (h) = 5 cm

Step-by-step explanation:

Volume of prism in terms of h (height):

V = \frac{1}{3}s^2h

V = \frac{s^2h}{3}

Multiply both sides by 3

V*3 = \frac{s^2h}{3}*3

3V = s^2h

Divide both sides by s^2

\frac{3V}{s^2} = \frac{s^2h}{s^2}

\frac{3V}{s^2} = h

h = \frac{3V}{s^2}

Find height (h) given V = 60 cm³ and side length (s) = 6 cm. Plug the values into the formula above:

h = \frac{3(60)}{6^2}

h = \frac{180}{36}

h = 5

Height = 5 cm

6 0
3 years ago
Isabella is ordering invitations
MrMuchimi
Clear Print: y = 2x
Sue: y = 36 + 0.50x

Clear Print: y = 2(60) = $120
Sue: y = 36 + 0.50(60) = $66

Sue offers the better price for 60 invitations
6 0
3 years ago
At the school store, pencils sell for $.12 each. The pencils come in boxes of 30. The school store buys each box for $2.00.
juin [17]

Answer:

c

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Seperate 90 into two parts so that one part is four times the other
aalyn [17]

Answer:

18 and 72

Step-by-step explanation:

the smaller part can be assigned as x while the larger will be 4x. Both numbers need to add up to 90, giving the equation: 4x+x = 90

Solve:

4x+x = 90

5x = 90

x = 18

4x = 72

5 0
2 years ago
Other questions:
  • Which shows the expression below in simplified form? (5 × 10^5) × (7 × 10^-5)
    9·1 answer
  • What is the lowest value in the set of data represented by the following box-and-whisker plot?
    9·2 answers
  • A national standardized test is graded on a scale from 1 to 5 the scores for a particular school are given below if a student Is
    12·1 answer
  • Labeling Parts of a Circle
    15·1 answer
  • If f(x) = -x + 5 and g(x) = 3x + 2, Find f(2)*g(2).
    13·1 answer
  • WILL MARK BRAINLIEST IF YOU GET IT RIGHT GET IT WRONG ON PURPOSE ILL REPORT U!
    5·2 answers
  • Solve.<br> x - 2y + 32 = 8<br> 3y +z = 12<br> -2x + 2z=-4
    11·1 answer
  • Hurry Please It due today!!!!
    14·1 answer
  • 2. Which is equivalent to the calculator output 8.954 E - 15?
    9·1 answer
  • Evaluate the expression,<br> if x = 9, y = 3, and z = 5.<br> z²(x - y)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!