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
Vesnalui [34]
2 years ago
14

Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?

Mathematics
1 answer:
BlackZzzverrR [31]2 years ago
8 0

Answer:

\boxed{\sf a = 9 }

Step-by-step explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,

\sf\longrightarrow 3x - 2y +7=0

\sf\longrightarrow 6x +ay -18 = 0

Step 1 : <u>Conver</u><u>t</u><u> </u><u>the </u><u>equations</u><u> in</u><u> </u><u>slope</u><u> intercept</u><u> form</u><u> </u><u>of</u><u> the</u><u> line</u><u> </u><u>.</u>

\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}

and ,

\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a}

Step 2: <u>Find </u><u>the</u><u> </u><u>slope</u><u> of</u><u> the</u><u> </u><u>lines </u><u>:</u><u>-</u>

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,

\sf\longrightarrow Slope_1 = \dfrac{3}{2}

And the slope of the second line is ,

\sf\longrightarrow Slope_2 =\dfrac{-6}{a}

Step 3: <u>Multiply</u><u> </u><u>the </u><u>slopes </u><u>:</u><u>-</u><u> </u>

\sf\longrightarrow \dfrac{3}{2}\times \dfrac{-6}{a}= -1

Multiply ,

\sf\longrightarrow \dfrac{-9}{a}= -1

Multiply both sides by a ,

\sf\longrightarrow (-1)a = -9

Divide both sides by -1 ,

\sf\longrightarrow \boxed{\blue{\sf a = 9 }}

<u>Hence </u><u>the</u><u> </u><u>value</u><u> of</u><u> a</u><u> </u><u>is </u><u>9</u><u> </u><u>.</u>

You might be interested in
Pedro charged $933 to his credit card. Even after the cost of his next
crimeas [40]

Answer:

b

Step-by-step explanation:

3 0
2 years ago
@apologiabiology
Romashka-Z-Leto [24]
V=(1/3)hpir^2
h=9
r=15
V=(1/3)9pi15^2
V=3pi225
V=675pi
aprox pi=3.14
V=2119.5 cm^3
A is answer
5 0
3 years ago
Read 2 more answers
0.05 is 1/10 the value of <br>A. 5 <br>B. 0.005<br>C. 0.5 <br>D. 50<br>​
anastassius [24]

Answer:

C.

Step-by-step explanation:

as 0.05 is 1/10 of a number, multiplying 0.05 by 10 will give you the number that when divided by 10 will give you 0.05. Hence just multiply 0.05 by 10 and you get 0.5.

8 0
3 years ago
1. What is 3/5+3/5+3/5+3/5 equal to?
nydimaria [60]

Answer:

12/5 or 2 2/5

Step-by-step explanation:

3/5+3/5+3/5+3/5

=> (3+3+3+3) / 5

=> 12/5

=> 2 2/5

Hope it helps......

8 0
2 years ago
Read 2 more answers
Please help asap !!!!!! what vaule of x makes the equation true 3(x-4)=15
DaniilM [7]

3(x-4) = 15

Distribute the 3:

3x-12 = 15

Add 12 to both sides:

3x = 27

Divide both sides by 3:

X = 9

The answer is D. 9

5 0
2 years ago
Other questions:
  • A sample of 100 women is​ obtained, and their heights​ (in inches) and pulse rates​ (in beats per​ minute) are measured.
    10·1 answer
  • Using the given​ diagram, solve for x.
    9·2 answers
  • If you answer ever single question I will mark you as brainliest :) plz hurry
    8·1 answer
  • Help me pleaseeeeee...
    14·1 answer
  • If the total cost of z apples is a ​cents, what is the general formula for the​ cost, in​ cents, of w ​apples?
    8·1 answer
  • Can you please answer fast and please explain thank you so much
    10·1 answer
  • Karl visited his doctor because he found he had difficulty sitting upright and controlling his hands and movements. Which neurol
    15·2 answers
  • Which graph might represent a polynomial function of degree 5 with a negative leading coefficient?
    7·1 answer
  • (giving brainiest)
    13·1 answer
  • 2(r+7) <br> ———— &lt; r+3<br> -6
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!