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2 years ago

How do i find the shorted distance between the point and the line

Mathematics

1 answer:

m_a_m_a [10]2 years ago

3 0

Answer:

5 units

Step-by-step explanation:

3x + 4y = 8

4y = -3x+8

y = -3/4+2

The shortest distance between a point and a line is the perpendicular line.

Slope of the perpendicular line: 4/3 and point (-3,-2)

b = -2-(4/3)(-3) = 2

Equation of the perpendicular line: y=4/3x+2

y is equal y

4/3x+2= -3/4x+2

4/3x +3/4x = 2-2

x = 0

Plug x=0 into one of the equations to find y

y = 4/3(0) + 2

y = 2

(0,2) and (-3,-2)

Distance = sqrt [(-3-0)^2 + (-2-2)^2]

Sqrt (-3)^2+ (-4)^2

Sqrt 25 = 5

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Write a real-world problem that involves dividing a decimal by a whole number. Solve.

marysya [2.9K]

In 15 hours bob makes 7.5 boxes. how many boxes can he make in one hour?

so 15 hours=7.5 boxes
divide both sides by 15 to get hours
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answer is 1 hour=0.5 boxes

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3 years ago

According to the 2008 U.S. census, California had a population of approximately 4 × 10^7 people and Florida had a population of

qaws [65]

Answer:

D. The population of California was approximately two times the population of Florida.

Step-by-step explanation:

California's population was 4 x 10^7= 40,000,000

Florida's population was 2 x 10^7= 20,000,000

So therefore Califirnia's population was approximately two times the population of Florida.

I hope this helps!!

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3 years ago

Katie has a cube with an edge length of

k0ka [10]

Answer:

3 x 8 = ____16____

Step-by-step explanation:

8+8+8= 16 or 3+3+3+3+3+3+3+3= 16

Hope this helps :)

6 0

2 years ago

A baseball team had 75 players show up for tryouts last year and this year had 90 players show up for tryouts. Find the percent

olga_2 [115]

Answer: 33.3%

Step-by-step explanation:

First find the difference between the players in try-outs over the years.

= 90 - 75

= 25

Then use this difference to find the percent increase:

= Difference / Players last years * 100%

= 25 / 75 * 100%

= 33.3%

3 0

3 years ago

For what values of the numbers a and b does the function below have maximum value f(1) = 4? (Round the answers to three decimal

Georgia [21]

F (x) = $a x e^{b x^{2} }$
f ` (x) = $a( e^{b x^{2} } +x e ^{b x^{2} } *2 b x )=a e ^{b x^{2} } (1+2b x^{2} )$
f ( 1 ) = 4
f ` ( 1 ) = 0
$4 = a e ^{b} \\ a e ^{b} (1 + 2 b ) = 0 \\ 4 ( 1 + 2 b )= 0
$
b = -1/2
$4=a e ^{-1/2} = \frac{a}{ \sqrt{e} } \\ a = 4 \sqrt{e}$
Answer: a = 4√e, b = -1/2

4 0

3 years ago