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
iren2701 [21]
10 months ago
6

2 - 14. What is the equation of the line perpendicular to y - 4 = (x - 6) and passes through the point - (-3,2)? 5 5 - 2 5 = O -

2= O A. y-2=-(x + 3) x OB. y + 3 = -(x - 2) (- 2 O c. y - 2 = = (x + 3) OD. y + 3 = (x - 2) 2 2 2 5

Mathematics
1 answer:
Oduvanchick [21]10 months ago
5 0

Solution:

The equation of a line that passes through a point is expressed as

\begin{gathered} y-y_1=m(x-x_1)\text{ ---- equation 1} \\ where \\ m\Rightarrow slope\text{ of the line} \\ y\Rightarrow y-intercept\text{ of the line} \\ (x_1,y_1)\Rightarrow coordinate\text{ of the point through which the line passes} \end{gathered}

Two lines A and B are said to be perpendicular if the slope of line A is equal to the negative reciprocal of the slope of line B.

Thus, lines A and B are perpendicular if

m_A=-\frac{1}{m_B}\text{ ---- equation 2}

Let the line equation

y-4=\frac{2}{5}(x-6)

represent the line A.

step 1: Evaluate the slope of line A.

Comparing the equation of line A with equation 1, we can conclude that the slope of the line A is

m_A=\frac{2}{5}

step 2: Evaluate the slope of line B.

Since lines A and B are perpendicular, we have

\begin{gathered} From\text{ equation 2,} \\ \begin{equation*} m_A=-\frac{1}{m_B} \end{equation*} \\ where \\ m_A=\frac{2}{5} \\ thus, \\ \frac{2}{5}=-\frac{1}{m_B} \\ cross-multiply \\ -2m_B=5 \\ divide\text{ both sides by -2} \\ \frac{-2m_B}{-2}=\frac{5}{-2} \\ \Rightarrow m_B=-\frac{5}{2} \end{gathered}

step 3: Evaluate the line B.

Since the line B passes through the points (-3,2), recall from equation 1

\begin{equation*} y-y_1=m(x-x_1)\text{ } \end{equation*}

where

\begin{gathered} x_1=-3 \\ y_1=2 \\ m=m_B=-\frac{5}{2} \end{gathered}

Substitute these values into equation 1.

Thus,

\begin{gathered} y-2=-\frac{5}{2}(x-(-3)) \\ \Rightarrow y-2=-\frac{5}{2}(x+3) \end{gathered}

Hence, the equation of the line is

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

The correct option is A

You might be interested in
Hellppppppp with this twoooooooo
liberstina [14]
15.

0.20*x = 0.01*x + 38 => 0.19*x = 38 =>( 19/100 )*x = 38 => x = 3800/19 => x = 200.
6 0
3 years ago
You are planning to email to two lists. the first list has 1,200 names. the second list has 900 names. there are 150 names that
Snezhnost [94]

Answer:  There are 1800 unique names from both the lists.

Explanation:

Since we have given that

there are two lists :

In First list, number of names = 1200

In Second list, number of names = 900

According to question , we have also given that

there are 150 names that appear on both lists,

So,

Number of unique names in the first list  is given by

1200-150=1050

Number of unique names in the second list is given by

900-150=750

Therefore, total number of unique names is given by

1050+750=1800

Hence, there are 1800 unique names from both the lists.

3 0
3 years ago
Read 2 more answers
Beau and Bella's grandmother gave them a pack of 54 pencils for school. How many pencils will each get?
rusak2 [61]
27 because you have to divide 54 pencils by two people
4 0
3 years ago
Read 2 more answers
Given the function f(x) = The quantity of 2x minus 5, divided by 3, which of the below expressions is correct?
adell [148]
Hello : 
f(x) = (2x-5)/3
<span>f−1(x) = (3x+5)/2 
because : f(x) 0 </span>f−1(x) = x and  f−1(x) 0 f(x) = x
f(x) 0 f−1(x) = f( f−1(x) ) = f ((3x+5)/2) = (2(3x+5)/2  - 5))/3 = 3x /3 =x
same cacul for :  f−1(x) 0 f(x) = x 
3 0
3 years ago
Find the interest rate for a $4100 deposit accumulating to $5994.78, compounded monthly for 6 years.
rodikova [14]

Answer:

r = [1 + (i/n)]n - 1. Where: r =

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • If someone doesn’t help me with this stupid hw you’re a burnt garbanzo bean
    12·1 answer
  • Mark put his dog on a diet. The dog's total weight change for the first 2 weeks was −3/4 pound. The dog lost the same amount of
    11·2 answers
  • The ordered pairs on the graph represent a proportional relationship. What is the constant proportionality of Y to X
    14·1 answer
  • The owner of a candy store wants to mix some peanuts worth $3 per pound, some cashews worth $10 per pound, and some Brazil nuts
    8·1 answer
  • What numbers can I multiply to get 24 and add to get negative 4
    9·2 answers
  • Simplify each expression.<br><br> 2(10m-7a) + (8a-3m)
    7·2 answers
  • Could you please help me......
    9·1 answer
  • I need help is it A b C or D
    11·1 answer
  • The graph above is a linear equation that includes the points (-3,-2) and (-1,2). Find the slope of the line. Explain how you ar
    6·1 answer
  • WILL GIVE BRAINLIEST
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!