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
Order of operations solve 1/3+4/9*12=
OlgaM077 [116]
You would use PEMDAS, which means Parenthesis, exponents, multiplication, division, addition" and then subtraction. You would solve the problem in that order
6 0
3 years ago
Read 2 more answers
At Harry's discount hardware everything is sold for 20 percent less than the price marked. If Harry buys tool kits for $80,what
ICE Princess25 [194]

Answer:

$120.

Step-by-step explanation:

The amount he sells the tool kit for  = 80 + 20% of 80

= 80 + 16

= $96.

Let m be the marked price, then

m - 0.20m = 96

0.8m = 96

m = $120.

5 0
3 years ago
Write an equation of the line that passes through the points (-2,-2) and (0,5)
marshall27 [118]
\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&&(~ -2 &,& -2~) 
&&(~ 0 &,& 5~)
\end{array}
\\\\\\
% slope  = m
slope =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-(-2)}{0-(-2)}\implies \cfrac{5+2}{0+2}\implies \cfrac{7}{2}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-2)=\cfrac{7}{2}[x-(-2)]
\\\\\\
y+2=\cfrac{7}{2}(x+2)\implies y+2=\cfrac{7}{2}x+7\implies y=\cfrac{7}{2}x+5
3 0
3 years ago
A closing is March 5 for a rental property with an annual tax bill of $2800. Calculate and show the debit and credits for the ta
kicyunya [14]

Answer:

The debit and credits for the tax proration will be as follows:

Debit seller for $483.29; and Credit buyer for $483.29.

Step-by-step explanation:

The assignment of how much is owed to the responsible party is the major reason of a proration.

For the days owned by the seller, the buyer needs money from the seller since the buyer will pay the taxes at end of the year.

Amount per day = Annual tax bill / 365 = $2800 / 365 = $7.67

Total number of days from January 1 to a day before March 5 = Number of days in January + Number of days in February + Number of days from March 1 to March 4 = 31 + 28 + 4 = 63

Amount the seller owes for the time he owned = Amount per day * Total number of days from January 1 to a day before March 5 = $7.67 * 63 = $483.29

Therefore, the debit and credits for the tax proration will be as follows:

Debit seller for $483.29; and Credit buyer for $483.29.

8 0
3 years ago
Helppp can someone solve this please
Norma-Jean [14]

Answer:

\displaystyle x=-15

Step-by-step explanation:

<u>Solution Of A System Of Equations </u>

A system of linear equations is given as

\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.

There are many methods to solve them. We will use the method of reduction

The given system is

\displaystyle \left\{\begin{matrix}2x+3y=45\\ x+y=10\end{matrix}\right.

Multiplying the second equation by -3

\displaystyle \left\{\begin{matrix}2x+3y=45\\ -3x-3y=-30\end{matrix}\right.

Adding the resulting equations

\displaystyle -x=15

\displaystyle x=-15

5 0
3 years ago
Other questions:
  • what is the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang???
    5·1 answer
  • Write an equation using the image below and then solve for x.
    13·1 answer
  • Lisa wants to use her calculator to square a two-digit positive integer, but she accidentally enters the tens digit incorrectly.
    15·1 answer
  • What's the quotient of 13 divided by 1690?
    12·1 answer
  • Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds
    10·2 answers
  • If 3/p = 6 and 3/q = 15 then p - q =?
    11·1 answer
  • What is the slope of line a?<br> THIS IS A TEST AND MY GRADE IS ALR BAD ENOUGH PLS ANSWER CORRECTLY
    6·2 answers
  • Mr. Tankard's minivan has a 21 gallon
    12·1 answer
  • There were 200 people who voted at the town council meeting
    12·1 answer
  • Im confused please help
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!