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4 years ago

AC has endpoints with coordinates A(−5,2) and C(4,−10). If B is a point on AC and AB:BC = 1:2, what are the coordinates of B?

Mathematics

1 answer:

PSYCHO15rus [73]4 years ago

7 0

Answer:

B(x, y) = (-2, -2)

Step-by-step explanation:

Given: AB: AC (m₁: m₂) = 1 : 2, A (x₁, y₁) = (-5, 2) and B(x₂, y₂) = (4, -10)

To find: Coordinates of B (x, y)

Using section formula:

$x = \frac{m_1x_2+ m_2x_1}{m_1 + m_2}\ and\ y = \frac{m_1y_2+ m_2y_1}{m_1 + m_2}$

∴ $x = \frac{(1\times 4) + (2\times(-5))}{1 + 2} = \frac{4 - 10}{3} = \frac{-6}{3} = -2$

and $x = \frac{(1\times (-10)) + (2\times 2)}{1 + 2} = \frac{-10 + 4}{3} = \frac{-6}{3} = -2$

Therefore Coordinates of B (x, y) is (-2, -2).

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You are on a ski trip with your friends. Your friend Meg asks you to lend her $250. Write down the conditions that will help you

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4 years ago

A meteor crater is 3000 feet in diameter. Approximate the distance around the crater use 3.14 for pi

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C= pi x d
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4 years ago

PLEASE HELP! The table shows the number of championships won by the baseball and softball leagues of three youth baseball divisi

Irina18 [472]

Answer:

Question 1: $P ( B | Y ) = \frac{ P ( B and Y)}{ P (Y)} = \frac{ \frac{2}{16}}{ \frac{4}{16}} = \frac{1}{2}$

Question 2:

A. $P ( Y | B ) = \frac{ P(Y and B) }{ P(B) } = \frac{ \frac{2}{16} }{ \frac{6}{16} } = \frac{1}{3}$

B. $P( Z | B ) = \frac{ P ( Z and B)}{ P (B)}= \frac{ \frac{1}{16} }{ \frac{6}{16} } = \frac{1}{6}$

C. $P((Y or Z)|B) = \frac{ P ((Y or Z) and B)}{P(B)}= \frac{ \frac{3}{16}}{ \frac{6}{16}}= \frac{1}{2}$

Step-by-step explanation:

Conditional probability is defined by

$P(A|B)= \frac{P(A and B)}{P(B)}$

with P(A and B) beeing the probability of both events occurring simultaneously.

Question 1:

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

$P ( B | Y ) = \frac{ P ( B and Y)}{ P (Y)} = \frac{ \frac{2}{16} }{ \frac{4}{16} } = \frac{1}{2}$

Question 2.A:

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

$P ( Y | B ) = \frac{ P(Y and B) }{ P(B) } = \frac{ \frac{2}{16} }{ \frac{6}{16} } = \frac{1}{3}$

Question 2.B:

Z: Championships won by the 13 - 15 years old, beeing

$P ( Z)= \frac{ 1 }{ 16 }$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

then

P( Z and B)= \frac{ 1 }{ 16 }[/tex]

By definition,

$P( Z | B ) = \frac{ P ( Z and B)}{ P (B)}= \frac{ \frac{1}{16} }{ \frac{6}{16} } = \frac{1}{6}$

Question 3.B

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

Z: Championships won by the 13 - 15 years old, beeing

$P ( Z)= \frac{ 1 }{ 16 }$

then

$P (Y or Z) = P(Y) + P(Z) = \frac{6}{16}$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

$P((YorZ) and B)= \frac{3}{16}$

By definition,

$P((Y or Z)|B) = \frac{ P ((Y or Z) and B)}{P(B)}= \frac{ \frac{3}{16}}{ \frac{6}{16}}= \frac{1}{2}$

3 0

3 years ago

a baseball glove was on sale for 5/6 of the original price. if the original price was $90 what was the sale price

grandymaker [24]

since the original price was ninety we have to multiply 5/6 by 90
90/1(5/6)
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4 years ago

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Suppose a lake has a surface area of about 748 acres and an average depth of about 18 feet. About how many cubic feet are in the

zloy xaker [14]

Answer: There are 13464 cubic feet in the lake.

Step-by-step explanation:

Since we have given that

Surface area of lake = 748 acres

Average depth of lake = 18 feet

So, Volume of lake would be

Surface area of lake × Average depth

$=748\times 18\\\\=13464$

Hence, there are 13464 cubic feet in the lake.

6 0

3 years ago