What is the exact volume of a sphere with a diameter of 36 in.?

Part 1

Dmitrij [34]

Answer:

a) A n (B' n C') = {3, 9}.

b) (AUB) n (BUC) = {2,4,5,6,7,8}

Step-by-step explanation:

a) Rewriting C ; C = {4,5,6,7,8}

B' = {3,5,7,9} and C' = {2, 3, 9}

so (B' n C') = {3, 9}

and A n (B' n C') = {3, 9}.

b) {A U B} = { 2,3,4,5,6,7,8,9} and {B U C} = {2,4,5,6,7,8}

so (AUB) n (BUC) = {2,4,5,6,7,8}

4 0

3 years ago

Write the equation of the line in fully simplified slope-intercept form.

Bad White [126]

Answer:

$y = -\frac{2}{5} x-6$

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula $m =\frac{y_2-y_1}{x_2-x_1}$ . Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):

$m = \frac{(-6)-(-4)}{(0)-(-5)} \\m = \frac{-6+4}{0+5} \\m = \frac{-2}{5} \\$

So, the slope of the line is $-\frac{2}{5}$ .

2) Next, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the $m$ , $x_1$ and $y_1$ into the formula.

Since $m$ represents the slope, substitute $-\frac{2}{5}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form:

$y-(-6) = -\frac{2}{5} (x-(0))\\y + 6 = -\frac{2}{5} x\\y = -\frac{2}{5} x-6$

6 0

3 years ago

Find the missing length

SashulF [63]

Answer:

c = 37

Step-by-step explanation:

Pythagorean thm formula:

a² + b² = c²

Given:

a = 12

b = 35

Work:

a² + b² = c²

12² + 35² = c²

144 + 1225 = c²

c² = 1369

$\sqrt{c^2} =\sqrt{1369}$

c = 37

6 0

3 years ago

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Find the coordinates of the orthocenter for XYZ with X(-5,-1) Y(-2,4), Z(3,-1)

V125BC [204]

9514 1404 393

Answer:

(-2, 2)

Step-by-step explanation:

The orthocenter is the intersection of the altitudes. The altitude lines are not difficult to find here. Each is a line through the vertex that is perpendicular to the opposite side.

Side XZ is horizontal, so the altitude to that side is the vertical line through Y. The x-coordinate of Y is -2, so that altitude has equation ...

x = -2

__

Side YZ has a rise/run of -1/1 = -1, so the altitude to that side will be the line through X with a slope of -1/(-1) = 1. In point-slope form, the equation is ...

y -(-1) +(1)(x -(-5))

y = x +4 . . . . . . . . subtract 1 and simplify

The orthocenter is the point that satisfies both these equations. Using the first equation to substitute for x in the second, we have ...

y = (-2) +4 = 2

The orthocenter is (x, y) = (-2, 2).

4 0

3 years ago

Which situations can be represented by isometric transformations? Check all that apply. A photo is projected from a computer int

Romashka-Z-Leto [24]

Answer:

The correct options are;

A circular game piece is moved three squares forward

The flag on a mailbox is turned up

Step-by-step explanation:

An isometric transformation also known as isometry, is the rigid motion transformation or movement that preserves the shape, angles, and distances between of a pre-image (object) and the final image.

Rotation, reflection, translation (parallel motion), glide deflection (transformation involving translation and reflection) such as snow footprints are forms of isometric transformation.

6 0

4 years ago

Read 2 more answers