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.
Answer:
It is an arithmetic sequence and the common difference is 5
Step-by-step explanation:
4+5 = 9; 9+5=14 (adding is arithmetic, multiplying is geometric)
Answer:
Bobby around 131 minutes and Billy around 111 minutes
Step-by-step explanation:
To solve the problem it is important to raise equations regarding what happens.
They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:
1 / Bo + 1 / Bi = 1/60 (1)
They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore
1 / Bi = 1 / (Bo-20) (2)
Replacing (2) in (1) we have:
1 / Bo + 1 / (Bo-20) = 1/60
Resolving
(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60
120 * Bo - 1200 = Bo ^ 2 - 20Bo
Rearranging:
Bo ^ 2 - 140Bo -1200 = 0
Now applying the general equation
Bo = 130.82 or Bo = 9.17, <em>this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together</em>, therefore Bobby only takes around 131 minutes and Billy around 111 minutes
Checking with equation 1:
1/131 +1/111 = ~ 1/60
Answer:
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Step-by-step explanation:jhgjfghfghghdfdhdth
2x + 4 > 8
Step 1: Subtract 4 from both sides.
2x + 4 − 4 > 8 − 4
2x > 4
Step 2: Divide both sides by 2.
2x/2 > 4/2
x > 2
2x − 3 < 5
Step 1: Add 3 to both sides.
2x − 3 + 3 < 5 + 3
2x < 8
Step 2: Divide both sides by 2.
2x/2 < 8/2
x < 4
