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2 years ago

Write an equation of a line in slope-intercept form that passes through the

Mathematics

1 answer:

Katen [24]2 years ago

8 0

Answer:

y = x - 3

Step-by-step explanation:

First, you need to find the slope from the two given points.

y2 - y1 / x2 - x1

= 3 - (-1) / 6 - 2

= 1

The slope is 1x or simply x.

For the y-intercept, you need to plug one of the coordinates into the equation, which is y = x + b

3 = 6 + b

-3 = b

So the equation is y = x - 3

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A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere

pentagon [3]

Answer:

$V=298.5cm^3$

Step-by-step explanation:

To find the volume of the sphere we need to know its radius.

And the radius can be found with the information we have about the surface area.

The formula for the surface area is as follows:

$SA=4\pi r^2$

from this formula we clear the radius r:

$r^2=\frac{SA}{4\pi}\\ \\r=\sqrt{\frac{SA}{4\pi} }$

and we substitute the known value of the surface area, and also the value of $\pi$ :

$r=\sqrt{\frac{216cm^2}{4(3.1416)} }\\ \\r=\sqrt{\frac{216cm^2}{12.5664} }\\ \\r=\sqrt{17.1887cm^2}\\ \\r=4.146cm$

and now that we know the radius we find the volume:

$V=\frac{4\pi r^3}{3} \\\\V=\frac{4(3.1416)(4.146cm)^3}{3}\\ \\V=\frac{895.521cm^3}{3}\\ \\V=298.5cm^3$

the volume of the sphere is $298.5cm^3$

7 0

2 years ago

Use the table to identify the values of p and q that should be used to factor x2 + 3x – 10 as (x + p)(x + q).

Galina-37 [17]

3 0

2 years ago

A mural inspired by photo graph measures 107 inches by 180 inches.the scale factor is 12.what are the dimensions of the photogra

laila [671]

$\bf \cfrac{mural}{photo}\qquad \cfrac{12}{1}\implies \stackrel{mural}{12}:\stackrel{photo}{1}\qquad \qquad \cfrac{\stackrel{width}{107}}{w}=\cfrac{12}{1}\implies \cfrac{107\cdot 1}{12}=w
\\\\\\
\cfrac{\stackrel{height}{180}}{h}=\cfrac{12}{1}\implies \cfrac{180\cdot 1}{12}=h$

5 0

3 years ago

17. A warehouse has 5 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. All the shelves are full. How many bo

Sav [38]

Answer:

<h3>Total 20 boxes are there. </h3>

Step-by-step explanation:

Total number of shelves in a warehouse = 5 shelves.

Each shelve either can hold maximum 8 boxes with their lengths or can hold 4 boxes with their heights.

So, in that case only 4 boxes could be hold in each of 5 shelves because only 4 boxes could be fit with their heights.

Therefore, total number of boxes = 5 × 4 = 20 boxes .

<h3>Therefore, total 20 boxes are there. </h3>

3 0

3 years ago

Which of the expressions below is equivalent to the expression: 42 + 32 – 13 × 2 + 38? a. 42 + 32 – (26 + 38) b. 42 + 32 – 13 ×

Anika [276]

Using PEMDAS, 42 + 32 - 13 * 2 + 38 can be simplified as,

C. 42 + 32 + 12 = 86

You can check this by inserting the given expression (42 + 32 - 13 * 2 + 38) into a calculator, which should also give you the same answer of 86.

5 0

3 years ago