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3 years ago

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Mathematics

1 answer:

8_murik_8 [283]3 years ago

6 0

Answer:

1/6

Step-by-step explanation:

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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

Quadrilateral ABCD quadrilateral WXYZ. If AD = 12, DC = 6, and ZY = 36, find WZ.

valentinak56 [21]

If they're similar it would be 72, 36x2=72.

8 0

3 years ago

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There are 100m of ribbon. 1 1/2m are needed to make a bouquet. How man can be made? How many m of ribbon are left over ?

Umnica [9.8K]

Answer:

66 can be made

1m left

Step-by-step explanation:

$100 \div 1.5 = 66.667(5s.f.)$

Ribbons that can be made= 66

$66 \times 1.5 = 99m$

length used= 99m

length remaining= 100m- 99m= 1m

8 0

3 years ago

HELP PLS!!!!! What is 1+1

GREYUIT [131]

Answer:

1+1=2 i think

Step-by-step explanation:

3 0

3 years ago

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Find the Area of the shaded part.

Westkost [7]

To find the area of the shaded part we have to subtract the rectangle area from the triangle area :

$s = \frac{1}{2} \times (8x + 2)(6x) - (x)(3x + 1) \\$

$s = \frac{1}{2} \times (48 {x}^{2} + 12x) - (3 {x}^{2} + x) \\$

$s = \frac{48}{2} {x}^{2} + \frac{12}{2} x - 3 {x}^{2} - x \\$

$s = 24 {x}^{2} + 6x - 3 {x}^{2} - x$

$s = 24 {x}^{2} - 3 {x}^{2} + 6x - x$

$s = 21 {x}^{2} + 5x$

And we're done

Have a great day ♡

4 0

2 years ago

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