HELP THIS IS A TEST!! ILL GIVE 20 points!!!

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

3 years ago

What property 8 + 43 = 43 + 8

zysi [14]

Answer:

commutative property

Step-by-step explanation:

It's basically just changing the order of the equation.

3 0

3 years ago

Mara is building a set of shelves supported by a diagonal brace, as shown in the diagram. Answer the questions to decide whether

Kazeer [188]

Answer:

Step-by-step explanation:

1). Since, m∠1 + m∠2 = 180° [Supplementary angles]

If m∠2 = 120°

m∠1 + 120° = 180°

m∠1 = 180° - 120°

m∠1 = 60°

2). If a transversal intersects two parallel lines on the top and middle,

∠1 and ∠5 will be corresponding angles.

3). Since, m∠1 = m∠5 = 60° (Corresponding angles)

Therefore, both the lines on top and middle will be parallel.

4). Since, m∠9 + m∠11 = 180° [Supplementary angles]

If m∠11 = 120°

m∠9 + 120° = 180°

m∠9 = 60°

Since, m∠1 = m∠9 = 60° [Corresponding angles]

Therefore, both the lines on the top and bottom shelves will be parallel.

5). Since, m∠5 = m∠9 = 60° [Corresponding angles]

Therefore, middle and bottom shelves will be parallel.

4 0

4 years ago

On a particular Saturday, 60% of the visitors to an art museum were students. If 144 visited the museum, how many total visitors

Bad White [126]

Answer:

240 visitors

Step-by-step explanation:

We are given the following in the question:

Percentage of visitors that are student to art museum = 60%

Total number of students to museum = 144

We have to find the total number of visitors to the museum.

Let x be the total number of visitors to the museum.

Thus, we can write the equation:

$60\%\times x = 144\\\\\dfrac{60}{100}\times x = 144\\\\\Rightarrow x = 144\times \dfrac{100}{60}\\\\\Rightarrow x = 240$

Thus, there were 240 visitors to the art museum on that day.

6 0

3 years ago

Find the missing sides. (Help me)

slavikrds [6]

Answer:

2nd one

Step-by-step explanation:

when it's a 45 45 and 90 triangle, it's 1, 1, sqrt 2, but now since the 1 is sqrt 2, v is sqrt 2, and u and sqrt 2 times sqrt 2, which is 2

3 0

3 years ago