PLEASE HELP

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

BlackZzzverrR [31]

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 : Convert the equations in slope intercept form of the line .

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

and ,

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

Step 2: Find the slope of the lines :-

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: Multiply the slopes :-

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

Multiply ,

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

Multiply both sides by a ,

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

Divide both sides by -1 ,

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

Hence the value of a is 9 .

8 0

2 years ago

It takes 3 hours to wash every window on a building.there are 30 windows. How many minutes does it takes to wask each window

Sveta_85 [38]

Answer:6minutes

Step-by-step explanation:

3 hours =180min

180min divided by 30 windows is 6

8 0

3 years ago

Read 2 more answers

The original price of a ski jacket was $220. It was on sale at a 25% discount. Arianna had a coupon for an additional 10% off th

Simora [160]

$143
add the two discounts of 25 and 10 percent. then your item will be 65% of the price now.

5 0

2 years ago

What is the interquartile range (IQR) of the data set represented by this box plot?

Zinaida [17]

Answer:

B

Step-by-step explanation:

The interquartile range is the difference between the upper quartile and the lower quartile.

The upper quartile is the right side value of the box

The lower quartile is the left side value of the box

upper quartile = 61 and lower quartile = 39

IQR = 61 - 39 = 22 → B

7 0

3 years ago

Read 2 more answers

there are 12 boys and 16 girls in a classroom which represents the simplified ratio of girls to students in a classroom? 3 to 4,

Marat540 [252]

Answer:

Ratio of girls to students = 4 : 7

Step-by-step explanation:

Number of boys= 12

Number of girls= 16

Total number of students= 12+16= 28

Number of girls to number of students= $\frac{16}{28}$ = $\frac{4}{7}$

Ratio of girls to students = 4:7

Hope this helps.

4 0

3 years ago

Read 2 more answers