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2 years ago

Write an equation of the line that passes through (2 -5) and is parallel to the line 2y=3x+10

Mathematics

1 answer:

andrey2020 [161]2 years ago

8 0

Step-by-step explanation:

Given equation is

2y = 3x + 10

3x - 2y + 10 = 0 .....i)

Any line parallel to line I) is

3x - 2y + k = 0 ......ii)

As the line two passes through the point ( 2 , - 5 ) Now substituting the values

3 * 2 - 2 * ( - 5) + k = 0

6 + 10 + k = 0

16 + k = 0

k = - 16

Now putting the value of k in equation two

3x - 2y + 16 = 0 is the required equation.

Hope it will help :)❤

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A regular square pyramid has base edges of length 16 and its lateral faces are inclined 30° to the base of the pyramid. What is

Helga [31]

Answer:

1) $h=\frac{8\sqrt{3}}{3}\ units$

2) $V=\frac{2,048\sqrt{3}}{9}\ units^3$

Step-by-step explanation:

Part 1) Find the height of the pyramid

we know that

$tan(30^o)=\frac{h}{(b/2)}$

where

h is the height of the pyramid

b is the length side of the square base

we have

$tan(30^o)=\frac{\sqrt{3}}{3}$

$b=16\ units$

substitute

$\frac{\sqrt{3}}{3}=\frac{h}{(16/2)}$

$\frac{\sqrt{3}}{3}=\frac{h}{8}$

$h=\frac{8\sqrt{3}}{3}\ units$

Part 2) Find the volume of the pyramid

we know that

The volume of the pyramid is equal to

$V=\frac{1}{3} Bh$

where

B is the area of the square base

h is the height of the pyramid

we have

$B=(16^2)=256\ units^2$

$h=\frac{8\sqrt{3}}{3}\ units$

substitute

$V=\frac{1}{3} (256)(\frac{8\sqrt{3}}{3})$

$V=\frac{2,048\sqrt{3}}{9}\ units^3$

8 0

3 years ago

What is the measure of (3y + 27)<br> What is the measure of (5y - 3)

saw5 [17]

Answer:

Angle A: 72°

Angle B: 108°

Step-by-step explanation:

Opposite angles are equal

Adjacent angles add up to 180

5y - 3 = 3y + 27

2y = 30

y = 15

Angle A:

5(15) - 3 = 72°

Angle B:

180 - 72 = 108°

4 0

3 years ago

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Angelina_Jolie [31]

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