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Ksju [112]
3 years ago
14

G is the centroid of triangle ABC. If BF=12, what is BG? BG=?

Mathematics
1 answer:
lutik1710 [3]3 years ago
3 0

Answer:

BG = 8

EXPLANTAION :

we know that centroid of a triangle divides the median into ratio of 2 : 1 so,

BG : GF = 2 : 1

now, let's take BG as 2x and GF as x

and here, BG + GF = BF

So,

=》2x + x = 12

( because, BF = 12 )

=》3x = 12

=》x = 12 ÷ 3

=》x = 4

hence, x = 4

from here,

=》BG = 2x

=》BG = 2 × 4 = 8

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A^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.
Verdich [7]

Answer:

2a - 3b + 4c = 1

Step-by-step explanation:

Given

a^2 + b^2 + c^2 = 2(a - b - c) - 3

Required

Determine 2a - 3b + 4c

a^2 + b^2 + c^2 = 2(a - b - c) - 3

Open bracket

a^2 + b^2 + c^2 = 2a - 2b - 2c - 3

Equate the equation to 0

a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0

Express 3 as 1 + 1 + 1

a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0

Collect like terms

a^2 - 2a + 1 + b^2 + 2b + 1 + c^2  + 2c + 1 = 0

Group each terms

(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

Factorize (starting with the first bracket)

(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

(a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + b+b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)(b + 1)) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c^2  + c+c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c(c  + 1)+1(c + 1)) = 0

((a - 1)^2) + ((b + 1)^2) + ((c  + 1)(c + 1)) = 0

((a - 1)^2) + ((b + 1)^2) + ((c  + 1)^2) = 0

Express 0 as 0 + 0 + 0

(a - 1)^2 + (b + 1)^2 + (c  + 1)^2 = 0 + 0+ 0

By comparison

(a - 1)^2 = 0

(b + 1)^2 = 0

(c  + 1)^2 = 0

Solving for (a - 1)^2 = 0

Take square root of both sides

a - 1 = 0

Add 1 to both sides

a - 1 + 1 = 0 + 1

a = 1

Solving for (b + 1)^2 = 0

Take square root of both sides

b + 1 = 0

Subtract 1 from both sides

b + 1 - 1 = 0 - 1

b = -1

Solving for (c  + 1)^2 = 0

Take square root of both sides

c + 1 = 0

Subtract 1 from both sides

c + 1 - 1 = 0 - 1

c = -1

Substitute the values of a, b and c in 2a - 3b + 4c

2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)

2a - 3b + 4c = 2 +3  -4

2a - 3b + 4c = 1

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4 years ago
An office manager estimates that she spends 40% of her 30-minute lunch
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Answer:

answer = 12 min

Step-by-step explanation:

40% of 30 min = ?

10% of 30 min = 3

3*4 = 12

Thus, she spends 12 min of her 30 min lunch driving

P.S.

If the answer is wrong, then multiply it by two and retry

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3 years ago
Please help I don’t understand please
irinina [24]

Answer:

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