1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alexandr1967 [171]
3 years ago
11

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select t

hree options. y = –Two-fifthsx – 2 2x + 5y = −10 2x − 5y = −10 y + 4 = –Two-fifths(x – 5) y – 4 = Five-halves(x + 5)
Mathematics
2 answers:
Alchen [17]3 years ago
4 0

Answer:

Option B) is the correct equation.

Step-by-step explanation:

We are given the following information in the question:

We are given a line:

5x -2y = -6\\-2y = -6-5x\\2y = 5x + 6\\\\y = \displaystyle\frac{5}{2}x + 3

Comparing the given equation with the general equation of line:

y = mx + c\\\text{where m is the slope of line and c is the y-intercept}

We get,

m_1 = \displaystyle\frac{5}{2}, c_1 = 3

When two lines are perpendicular, then the slopes of lines satisfy:

m_{1}\times m_2 = -1

Hence, a line perpendicular to given line will have slope:

m_{1}\times m_2 = -1\\\displaystyle\frac{5}{2}\times m_2 = -1\\\\m_2 = \frac{-2}{5}

Point slope form of a straight line:

(y-y_1) = m(x-x_1)

To find equation of line perpendicular to the given line and passing through the point (5,-4), we put the following in the above equation of line:

m = \diplaystyle\frac{-2}{5}, (x_1, y_1) = (5,-4)

Equation of line:

y-(-4) = \displaystyle\frac{-2}{5}(x-5)\\\\5(y + 4) = -2(x-5)\\5y + 20 = -2x + 10\\2x + 5y = -10

Option B) is the correct equation.

nignag [31]3 years ago
3 0

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

y = mx + b

Where:

m: It's the slope

b: It is the cut-off point with the y axis

On the other hand we have that if two lines are perpendicular, then the product of their slopes is -1. So:

m_ {1} * m_ {2} = - 1

The given line is:

5x-2y = -6\\-2y = -6-5x\\2y = 5x + 6\\y = \frac {5} {2} x + \frac {6} {2}\\y = \frac {5} {2} x + 3

So we have:

m_ {1} = \frac {5} {2}

We find m_ {2}:m_ {2} = \frac {-1} {\frac {5} {2}}\\m = - \frac {2} {5}

So, a line perpendicular to the one given is of the form:

y = - \frac {2} {5} x + b

We substitute the given point to find "b":

-4 = - \frac {2} {5} (5) + b\\-4 = -2 + b\\-4 + 2 = b\\b = -2

Finally we have:

y = - \frac {2} {5} x-2

In point-slope form we have:

y - (- 4) = - \frac {2} {5} (x-5)\\y + 4 = - \frac {2} {5} (x-5)

ANswer:

y = - \frac {2} {5} x-2\\y + 4 = - \frac {2} {5} (x-5)

You might be interested in
Involves triangle centroid
Rasek [7]
Here, you do the same as the previous one, keeping in mind that X cuts TW in a 2:1 ratio.

\bf TW-TX=XW\implies \cfrac{8a}{5}+\cfrac{1}{10}-\left(a +\cfrac{4}{5} \right)=XW
\\\\\\
\cfrac{8a}{5}+\cfrac{1}{10}-a-\cfrac{4}{5}=XW\implies \cfrac{3a}{5}-\cfrac{7}{10}=XW\\\\
-------------------------------\\\\

\bf TX:XW\qquad 2:1\qquad \cfrac{TX}{XW}=\cfrac{2}{1}\implies \cfrac{a+\frac{4}{5}}{\frac{3a}{5}-\frac{7}{10}}=\cfrac{2}{1}
\\\\\\
\cfrac{\frac{5a+4}{5}}{\frac{6a-7}{10}}=\cfrac{2}{1}\implies \cfrac{5a+4}{5}\cdot \cfrac{10}{6a-7}=\cfrac{2}{1}\implies \cfrac{10a+8}{6a-7}=\cfrac{2}{1}
\\\\\\
10a+8=12a-14\implies 22=2a\implies \cfrac{22}{2}=a\implies 11=a
6 0
3 years ago
Four ponds of banana cost $6 what is the cost per pound of bananas
vodomira [7]

Answer:

1.50

Step-by-step explanation:

6÷4=1.50, 1.50×4= 6.00

3 0
2 years ago
Read 2 more answers
Richard is selling candy bars for a school fundraiser on Monday he has 225 bars Remaining he sells an average of 30 bars per day
Softa [21]

Answer:

Mon - Fri: 4 days 4*30 = 120 bars given away. 225 - 120 = 135 bars

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
These two polygons are similar.
Jet001 [13]

Answer:

\huge\boxed{z=3}

Step-by-step explanation:

If two polygons are similar, then corresponding sides are in proportion.

The corresponding sides:

4 → x

y → 15

3 → w

2 → 6

z → 9

therefore:

\dfrac{z}{9}=\dfrac{2}{6}         <em>cross multiply</em>

(z)(6)=(9)(2)

6z=18         <em>divide both sides by 6</em>

z=3

4 0
3 years ago
Write the equition of the line that passes through the pair of points (8,-8) and (9,-4)
ANTONII [103]

Answer: More Info

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • How do you solve this?
    12·1 answer
  • Suppose that g(x)=f (x-1)-5 which statement best compares the graph of g(x) with the graph of f(x)
    5·2 answers
  • 4. which property is illustrated by the following statement?
    6·2 answers
  • Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to
    7·2 answers
  • What is the prime factorization of 430
    7·2 answers
  • Write an expression for "777 times rrr."
    14·1 answer
  • Find the rational approximation of √15.
    5·1 answer
  • Y = (x)(x) is a parent function that makes a graph of a(n)
    15·2 answers
  • PLEASE THEY WOLL CANCEL EVERYTHING I DONE THIS YEAR:
    10·1 answer
  • Help me please I will give 20 points and mark u as brainliest
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!