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blsea [12.9K]
3 years ago
8

Write an equation of the line that passes through the given point and is perpendicular to the given line.

Mathematics
1 answer:
topjm [15]3 years ago
6 0

Answer:

y = - 3x - 22

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \frac{1}{3} x + 1 ← is in slope- intercept form

with slope m = \frac{1}{3}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{1}{3} } = - 3 , then

y = - 3x + c ← is the partial equation

To find c substitute (- 6, - 4) into the partial equation

- 4 = 18 + c ⇒ c = - 4 - 18 = - 22

y = - 3x - 22 ← equation of perpendicular line

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4 years ago
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What is the solution of sqrt1-3x=x+3
Ivanshal [37]

x = - 1

given \sqrt{(1-3x)} = x + 3

square both sides

1 - 3x = (x + 3 )² ( expand right side using FOIL )

1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )

0 = x² + 9x + 8

0 = ( x + 1)(x + 8)

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = -1

x + 8 = 0 ⇒ x = - 8

As a check

substitute these values into the equation and if both sides are equal then they are the solutions

x = - 1 : \sqrt{1+3 } = 2 and - 1 + 3 = 2 ← true

x = - 8 : \sqrt{1+24} = 5 and - 8 + 3 = -5 ← false

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3 years ago
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ziro4ka [17]

Answer:

1 is B

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Step-by-step explanation:

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6 0
3 years ago
In the 75th Congress (1937−1939) there were in the Senate 75 Democrats, 17 Republicans, and 4 members of other parties. Suppose
ira [324]

Answer:

42 Democrats members

12 Republicans members

2 other parties members

Step-by-step explanation:

We know that there are a total number of voters of

  • 75 (democrats)+17 (Republicans)+ 4( Other parties)=  96 voters

And we know that the bill has passed with 16 nore votes in favor that against, so let's calculate how many votes in favor of the bill we have:

  • 96 Votes = F (votes in Favor)+ A (votes against)

also: F= A+16= A = F-16, so:

  • 96= F+A= F+F-16 => F= 56 votes in favor of the bill

Thos 56 votes are the sum of the votes in favor from all the parties:

56 = D (votes in favor of democrats)+R ((votes in favor of Republicans)+OTH (votes in favor of other parties)

=> 56= D+R+OTH (A)

also democrat's votes in favor are three times the sum of non-democrat's votes in favor:

  • D= 3*( R+OTH) => OTH= D/3-R

and we have 30 more democrats thar republicans voting in favor:

  • D= R+30 => R=D-30

if we replace in the (A) formula:

56 = D+R+OTH => 56= D+D-30+D/3-D+30 =>

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  • R= D-30 => R= 12 (REPUBLICAN VOTES IN FAVOR)
  • OTH= D/3-R= 14-12= 2 (OTHER PARTIE'S VOTES IN FAVOR)

5 0
3 years ago
Select the properties that equilateral triangles and isosceles triangles have in common.
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The properties that equilateral triangles and isosceles triangles have in common is that they have two equal sides.

<h3>What is a triangle?</h3>

A triangle is a polygon that has three sides and three angles. Types of triangles are<em> isosceles, equilateral </em>and<em> scalene</em> triangle.

An equilateral triangle is a triangle that have three equal sides while isosceles triangle have two equal sides.

The properties that equilateral triangles and isosceles triangles have in common is that they have two equal sides.

Find out more on triangle at: brainly.com/question/17335144

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2 years ago
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