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3 years ago

What is an equation of the line that passes through the point (3,-3) and is perpendicular to the line 3x+2y=12 ?

Mathematics

2 answers:

Gennadij [26K]3 years ago

6 0

Answer:

y=2/3x-5

Step-by-step explanation:

1. find the slope of the given line

2. find its opposite reciprocal(slope of the perpendicular line)

3. create a new linear equation using the new slope

4. substitute (3,-3) to find b

tatiyna3 years ago

4 0

Answer:y = 2x/3 - 5

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

3x+2y=12

We would rearrange it so that it will form of the y = mx + c. It becomes

2y = -3x + 12

y = -3x/2 + 6

Comparing with the slope intercept form, slope = - 3/2

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line passing through (3,-3) is 2/3

To determine the intercept, we would substitute m = 2/3, x = 3 and y = -3 into y = mx + c. It becomes

- 3 = 2/3×3 + c = 2 + c

c = - 3 - 2 = - 5

The equation becomes

y = 2x/3 - 5

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In the given figure ABCD is a tripepizeum with AB||CD. If AO = x-1, CO = BO = x+1 and CD = x+4. Find the value of x.

Hitman42 [59]

$\longmapsto$ The value of "x" is 5.

$\large\underline{\sf{Solution-}}$

Given that,

A trapezium ABCD in which AB || CD such that

AO = x - 1

CO = BO = x + 1

OD = x + 4

Now,

$\rm In \: \triangle \: AOB \: and \: \triangle \: COD$

$\rm \: \angle \: AOB \: and \: \angle \: COD \: \: \{vertically \: opposite \: angles \}$

$\rm \: \angle \:ABO \: and \: \angle \: CDO \: \: \{alternate \: interior \: angles \}$

$\bf \: \triangle \: AOB \: \sim \: \triangle \: COD \: \: \: \{AA \: similarity \}$

$\bf\longmapsto\:\dfrac{AO}{CO} = \dfrac{BO}{DO}$

$\rm \longmapsto\:\dfrac{x - 1}{x + 1} = \dfrac{x + 1}{x + 4}$

$\rm \longmapsto\:(x - 1)(x + 4) = {(x + 1)}^{2}$

$\rm \longmapsto\: {x}^{2} - x + 4x - 4 = {x}^{2} + 1 + 2x$

$\rm \longmapsto\: 3x - 4 = 1 + 2x$

$\rm \longmapsto\: 3x - 2x= 1 +4$

$\bf\longmapsto \:x = 5$

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3 years ago

A rectangular prism has a volume of 600 cubic inches.

choli [55]

Answer:

The length is 12 inches.

Step-by-step explanation:

The volume of a rectangular prism is given by:

V=LBH

It was given that; the rectangular prism has a volume of 600 cubic inches.

The height of the prism is 5 inches and the width is 10 inches.

We want to find the length of the rectangular prism.

We substitute V=600, H=5,and W=10 into the formula:

600=5×10×L

600=20L

$L = \frac{600}{50}$

$L = 12in$

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Answer:

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3 years ago

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3 years ago

Help math math math ASAP

STALIN [3.7K]

<h3><u>Solution</u>:-</h3>

The equation of any straight line can be written as in slope intercept form as -

$\green{ \underline { \boxed{ \sf{y=mx+c}}}}$

where,

m is its slope
c is its y-intercept.

<em><u>Given equation:- </u></em>

$\begin{gathered}\\\implies\quad \sf 5x+y = 10 \\\end{gathered}$

<u>Arranging it in slope intercept form by transposing 5x to RHS </u>

$\begin{gathered}\\\implies\quad \sf y = 10 -5x \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf y = -5x +10\\\end{gathered}$

$\leadsto$ Comparing the equation y = -5x +10 with the standard form of the equation, we get -

$\quad \bull\: \sf m= -5$

$\quad \bull \: \sf c= 10$

Thus , 5 is our required answer.

4 0

2 years ago

Read 2 more answers