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3 years ago

Write an equation of the line that passes through a pair of points: (2, 3), (4, -2)

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

5 0

Answer:

C. y = -5/2x +8

Step-by-step explanation:

To solve first find the slope using the slope formula which is m= $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ . To find the slope simply plug in the points, $\frac{-2-3}{4-2}$ which equals -5/2. Next, put the equation into slope-point form, which is $y-y_{1} = m(x-x_{1})$ . I will use the point (2,3). y-3=-5/2(x-2), then solve for y which equals y=-5/2+8.

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,

omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

Pyramid A

$s = 4$ -- base sides

$V = 36$ -- Volume

Pyramid B

$s = 6$ --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

$B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}$

$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

This gives:

$36 = \frac{1}{3} * 4\sqrt 3 * h$

Make h the subject

$h = \frac{3 * 36}{4\sqrt 3}$

$h = \frac{3 * 9}{\sqrt 3}$

$h = \frac{27}{\sqrt 3}$

To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

Since the heights of both pyramids are the same, we can make use of:

$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where

$s = 6$

So:

$B = \frac{1}{2} * 6^2 * sin(60)$

$B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}$

$B = 9\sqrt 3$

So:

$V = \frac{1}{3} * B * h$

Where

$B = 9\sqrt 3$ and $h = \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

$V = 81$

6 0

3 years ago

Read 2 more answers

HELP! HELP!

alexgriva [62]

Answer:

The answer should be C. By combining like terms you can find the answer. 1.75a+2.75a = 4.5a

2.25b + 1.75b = 4b

2.25c + 1.25c = 3.5c

Step-by-step explanation:

8 0

3 years ago

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An old house has a basement stairway that has steps with 7.25 inch vertical risers and 7 inch horizontal treads. What is the slo

svlad2 [7]

Answer:

1.04 inch

Step-by-step explanation:

Given: Old house has a basement stairways with 7.25 inch vertical riser and 7 inch horizontal treads.

Remember; horizontal treads is known as run in steps.

Now, calculating the slope of the stairways.

Formula: $Slope= \frac{Rise}{Run}$

Rise= 7.25 inch

Run= 7 inch.

Subtituting the value in the formula

Slope= $\frac{7.25}{7}= 1.0357 \approx 1.04$ (∵ Round to two decimal)

∴ Slope of stairways is 1.04.

4 0

3 years ago

A chemist is using 342 milliliters of a solution of acid and water. If 14.4% of the solution is acid, how many milliliters of ac

Irina-Kira [14]

Answer:

47.88milliliters

Step-by-step explanation:

Given data

Total amount of the solution= 342 milliliters

14% is acid

Hence the amount of acid

=14/100* 342

=0.14* 342

=47.88milliliters

Therefore there are 47.88milliliters of acid

8 0

3 years ago

Please solve for g!!!!

laiz [17]

The answer to the question

3 0

3 years ago

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