All categories

3 years ago

What is the slope of the line?

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

8 0

Answer:

The slope of the line must be 3

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

step 1

we know that

The volume of a rectangular prism is equal to

$V_r_p=Bh$ ----> equation A

where

B is the area of the base of the prism

h is the height of the rectangular prism

step 2

The volume of a square pyramid is equal to

$V_s_p=\frac{1}{3}Bh$ -----> equation B

where

B is the area of the square base of pyramid

h is the height of the pyramid

step 3

substitute equation A in equation B

$V_s_p=\frac{1}{3}V_r_p$

Find the relationship between the volume of a rectangular prism and the volume of a square pyramid

$\frac{V_r_p}{V_s_p}=3$

therefore

The slope of the line must be 3

let's check it

To solve for the slope of the line, you must choose two coordinates first and use the formula

$m=\frac{y2-y1}{x2-x1}$

Choosing the points (2,6) and (3,9)

substitute

$m=\frac{9-6}{3-2}=3$ ----> is correct

You might be interested in

Why is the greatest common factors with 2 numbers sometimes 1

OverLord2011 [107]

The greatest common factor of two numbers, one of which is 1, will always be 1.

5 0

3 years ago

William invested $2,300 in an account paying an interest rate of 2 1/8% compounded quarterly. Nolan invested $2,300 in an accoun

shusha [124]

Answer:

$478

Step-by-step explanation:

After 20 years, William will have a total of $3,513.94

After 20 years, Nolan will have a total of $3,991.93

Difference = $478

William:

2300[1 + (.02125 ÷ 4)]^4 · 20

2300 · (1 + .0053125)^80

2300(1.5278)

$3,513.94

Nolan:

2300[1 + (.0275 ÷ 12)]^12 · 20

2300 · (1 + .0023)^240

2300(1.7356)

$3,991.93

6 0

3 years ago

Read 2 more answers

Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). What are the possible coordina

grandymaker [24]

Important question. No menu of choices given so we'll just have to figure it out.

It's not possible in two dimensions for all three vertices of an equilateral triangle to be lattice points, i.e. points with integer coordinates.

Since A(-2,1) and B(4,1) have integer coordinates, our other point won't. There will be a √3 involved, the algebraic tell that there's a 30/60/90 triangle lurking somewhere in the problem.

Here the given side is parallel to the x axis which makes things easier.

|AB| = 4 - -2 = 6

The x coordinate of the third vertex will be the same as that of the midpoint of AB, let's call it M,

M = ( (-2 + 4) / 2, (1 + 1)/2 ) = (1, 1)

We're making some progress. Whatever our height h is our two candidates for the third vertex C are (1, 1 ± h).

Since |AB|=6, we get |AB|=|BC|=|AC|=6 because it's an equilateral triangle.

The altitude CM bisects the triangle into 2 30/60/90 triangles. Let's take one of them, AMC. Angle AMC is a right angle, so we have a right triangle with legs |AM|=3 and |CM|=h, and hypotenuse |AC|=6. The Pythagorean Theorem tells us:

3² + h² = 6²

9 + h² = 36

h² = 27

h = 3√3

Answer: C is (1, 1 + 3√3) or (1, 1 - 3√3)

4 0

3 years ago

The interarrival time of nuclear particles in a Monte Carlo simulation of a reaction is designed to have a uniform distribution

jekas [21]

Answer:

Incomplete question, but you can use the formulas given to solve it.

Step-by-step explanation: