MATHEMATICS MIDDLE SCHOOL

Hi. Please help with this question.Workings would be appreciated. Find the equations of the following line :
perpendicular to 3x-2y =3 and passing through (3,-7)
Note : For perpendicularism , M1 = -1/M2
M2 =-1/M1

Answers

Answer 1

Answer:

Answer:

$y = -(2)/(3)x - 5$

2x + 3y + 15 = 0

2x + 3y = -15

Step-by-step explanation:

We are given an equation in standard form. To find the slope, we can convert it to slope-intercept form, which is y = mx + b.

"m" will be the slope.

Isolate "y":

3x - 2y = 3

-2y = -3x + 3

$y = (-3)/(-2)x + (3)/(-2)$

$y = (3)/(2)x - (3)/(2)$

The slope is 3/2.

m = 3/2

To find the slope of a perpendicular line, find the negative reciprocal by flipping the fraction and changing the negative/positive.

m⊥ = -2/3 which is: $-(2)/(3)$

Substitute the coordinates (3, -7) and the slope into slope-intercept form.

y = mx + b Start with the general formula.

$-7 = -(2)/(3)(3) + b$

-7 = -6/3 + b Multiply -2/3 by 3

-7 = -2 + b Add 2 to both sides to isolate "b"

-5 = b

b = -5 Keep the variable on the left side

Now we know for our new equation:

m = -2/3

b = -5

Substitute the new information into slope-intercept form.

y = mx + b

$y = -(2)/(3)x - 5$ This is the equation

You might need to convert this is standard form, which is:

ax + by = c or ax + by + c = 0

Use the form where "c" will be positive, or what your teacher prefers.

$y = -(2)/(3)x - 5$

$y + (2)/(3)x= -(2)/(3)x - 5 + (2)/(3)x$ Add $(2)/(3)x$ to both sides

$y + (2)/(3)x= - 5$

$y + (2)/(3)x +5= - 5 + 5$ Since "c" is negative, add 5 to both sides.

$y + (2)/(3)x + 5= 0$

To get rid of the fraction, multiply the whole equation by "3".

$3y + (3)((2)/(3)x) + (3)(5)= 0$

3y + 2x + 15 = 0

2x + 3y + 15 = 0 Rearrange to follow ax + by + c = 0

2x + 3y = -15 Or rearrange to follow ax + by = c

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What is the area of the equilateral triangle?

Answers

the area of an equilateral triangle is A= 3/4a squared.

If a plant manufacturing carpet backing has a cylindrical tank that is 3 meters high and is 6 meters in diameter, what is the volume of the tank? Assume 3.14 for pi. A)28.3 m3 B)37.7 m3 C)56.5 m3 D)84.8 m3

Answers

the equation to find the volume of a cylinder is π∗r2∗h so if you plug in the correct values, you should have an equation of π∗32∗3 which is equal to π∗27 which equals approximately 84.823 meters^3

Hope this helps.

a cylinder has a volume of 321 cubic units. if a cone has the same height and radius as the cylinder, what is its volume in cubic units

Answers

1. First, let us write out the formula for the volume of a cylinder:

V = πr^(2)h

Now, given that the cylinder has a volume of 321 cubic units, we can rewrite the above formula with this new information:

321 = πr^(2)h

2. The volume of a cone is given by the following formula:

V = (1/3)πr^(2)h

Now, we can substitute 321 = πr^(2)h into the formula above to find the volume of the cone (this will work as the cone and cylinder have the exact same radius and height). Thus we get:

V = (1/3)πr^(2)h

V = (1/3)*321

= 107 cubic units

Note that there is another method that is perhaps more intuitive and can be used quite effectively in multiple choice questions, where working isn't required. What you should notice from the general formulas for the volume of a cone and a cylinder is that the volume of a cone is actually 1/3 of the volume of a cylinder (given that they have the same radius and height). Thus, if we know that the cone in our situation has the exact same radius and height as the cylinder, we can use this method as such:

Volume of cone = (1/3)*Volume of cylinder

Volume of cone = (1/3)*321

= 107 cubic units

Identify and equation in point slope form for the line perpendicular to y= -3x+7 that passes through 2,-4

Answers

perpendicular slope: 1/3

y + 4 = 1/3(x - 2)

y + 4 = 1/3x - 2/3

y + 12/3 = 1/3x - 2/3

y = 1/3x - 14/3

The volume of a rectangular pyramid is 1.32 cubic inches. The height is 1.1 inches. The length of the base is 1.2 inches. What is the width of the base of the pyramid?

Answers

To find the volume of a prism, you must multiply the length, width and height. To work out the width, you must work backwards. 1.32 divided by 1.1= 1.2 (Volume divided by height). 1.2 divided by 1.2= 1 (Answer divided by 1.2= Width of the base) The answer is 1 cm.

Please show steps to:

6(g+3)=-12

Thank you!! <3