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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. 
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Please help thank you
CaHeK987 [17]

Answer:

a) x=-3

b) y=2,5

have a nice day

6 0
3 years ago
Read 2 more answers
You row a canoe x miles per hour down a river for 20 minutes. On the return trip, you travel 1 mile per hour slower. The return
ozzi

Answer:

Total Distance = 2 miles

Step-by-step explanation:

We know D = RT where

D is distance

R is rate (speed)

T is time

First Leg:

Rate = x mph

Time = 20/60 = 1/3 hour

Hence, D = RT, Distance = x * 1/3 = x/3 miles

Second Leg:

Rate = x - 1

Time = 30/60 = 1/2 hour

Distance = (x - 1) * 1/2 = (x-1)/2

Total distance is the sum of both the legs, hence,

Total distance = \frac{x}{3}+\frac{x-1}{2}=\frac{2x+3(x-1)}{6}=\frac{2x+3x-3}{6}=\frac{5x-3}{6} miles

Since both the distance are equal we can equate and solve:

\frac{x}{3}=\frac{x-1}{2}\\2x=3x-3\\x=3

Plugging this x = 3 into the total distance expression, we get:

\frac{5x-3}{6}\\\frac{5(3)-3}{6}\\=2

Total distance, 2 miles

5 0
3 years ago
Which is 196 written as a power of a number?<br><br> A) 98^2<br> B) 13^2<br> C) 49^4<br> D) 14^2
kap26 [50]
Its not A. because , 98^2 = 9,604
Its not B. because , 13^2 = 169
Its for sure not C. because, 49^4 = 5,764,801
It is most likey, D. because 14^2 = 196
Option: D 14^2 would most likely be your answer

Reason , because 14(14) = 196 = 14^2


☺

3 0
3 years ago
Find the equation of the line passing through (-2,8) and (5,-3)
Advocard [28]

y = -2/3x + 5

this is the slope intercept. -2/3 is the slope and 5 is where it intercepts the y axis.

hope this helps

4 0
3 years ago
-8(8v + 1) - 2 = -394
Bess [88]

Answer:

v = 6

Step-by-step explanation:

Solve for v:

-8 (8 v + 1) - 2 = -394

-8 (8 v + 1) = -64 v - 8:

-64 v - 8 - 2 = -394

Grouping like terms, -64 v - 8 - 2 = -64 v + (-8 - 2):

-64 v + (-8 - 2) = -394

-8 - 2 = -10:

-10 - 64 v = -394

Add 10 to both sides:

(10 - 10) - 64 v = 10 - 394

10 - 10 = 0:

-64 v = 10 - 394

10 - 394 = -384:

-64 v = -384

Divide both sides of -64 v = -384 by -64:

(-64 v)/(-64) = (-384)/(-64)

(-64)/(-64) = 1:

v = (-384)/(-64)

The gcd of -384 and -64 is -64, so (-384)/(-64) = (-64×6)/(-64×1) = (-64)/(-64)×6 = 6:

Answer:  v = 6

3 0
3 years ago
Read 2 more answers
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