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3 years ago

Write an equation of the circle with center (-7, 4) and radius 8.

Mathematics

1 answer:

Stels [109]3 years ago

7 0

answer

(x+7)^2 + (y-4)^2 = 64

set up equation

the equation of a circle is (x - h)^2 + (y - k)^2 = r^2

where h is the center x coordinate and k is the center y coordinate

values

from the point (-7,4) we know that h = -7 and k = 4

since the radius is 8, r^2 = 8^2 = 64

plug in values

now that we have all the values, we plug them into (x - h)^2 + (y - k)^2 = r^2

(x - h)^2 + (y - k)^2 = r^2

(x - (-7))^2 + (y-4)^2 = 64

(x+7)^2 + (y-4)^2 = 64

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The radius of a sphere is 6 cm what is the volume

spayn [35]

Answer:

904.78

Step-by-step explanation:

A sphere with a radius of 6 units has a volume of 904.78 units

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3 years ago

In the game of roulette, a player can place a $9 bet on the number 11, and have a 1/38 probability of winning. If the metal ba

damaskus [11]

Answer:

1. What is the expected value of the game to the player?

Expected value= -$0.47368

2. If you played the game 1000 times, how much would you expect to lose?

Expected value= -$473.68

Step-by-step explanation:

1. What is the expected value of the game to the player?

Expected value can tell how much you will gain/lose every time you do the game. To find the expected value you need to multiply every value with its chance to occur. There are two types of events here, winning and losing. You have 1/38 chance of winning $315 and 37/38 chance of losing $9.

The expected value will be:

expected value= 1/38 * $315 + 37/38*(-$9) = $8.2894 - $8.7631

expected value= -$0.47368

You are expected to lose $0.47368 every time you play

2. If you played the game 1000 times, how much would you expect to lose?

Expected value calculated for each roll. If you want to know how much you gain/lose by multiple rolls, you just need to multiply the expected value with the number of rolls. The game has negative expected value so you are expected to lose money instead of gaining money. The money you expected to lose will be:

number of roll * expected value

1000 timer * -$0.47368/time= -$473.68

You are expected to lose $473.68 if you play the game 1000 times.

6 0

3 years ago

Show that the points (0.-1).(2, 1).(0.3) and (-2, 1) are the vertices of a square ABCD.

Inessa05 [86]

The diagram is below

A = (0,-1)
B = (2,1)
C = (0,3)
D = (-2,1)

Let's find the distance from A to B using the distance formula.

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-2)^2 + (-1-1)^2}\\\\d = \sqrt{(-2)^2 + (-2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\d \approx 2.828\\\\$

The distance from A to B is exactly $\sqrt{8}$ units or approximately 2.828 units. This is the length of side AB.

Through very similar steps, you should find that the other side lengths of BC, CD and AD are all the same.

Since AB = BC = CD = AD, this means we have a rhombus. Recall a rhombus is any quadrilateral with all four sides the same length.

-----------------------------

Let's find the slope of line AB

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-1)}{2 - 0}\\\\m = \frac{1 + 1}{2 - 0}\\\\m = \frac{2}{2}\\\\m = 1\\\\$

Line AB has a slope of 1.

Through similar steps, you should find the slope of line BC is -1.

Rule: Whenever two slopes multiply to -1, then their corresponding lines are perpendicular.

Based on that rule, lines AB and BC are perpendicular. This means they meet up at a right angle (aka 90 degree angle).

You should find that line CD has a slope of 1, so BC and CD are perpendicular. Lastly, line AD has a slope of -1. So all the slopes mentioned are either +1 or -1. The slopes alternate as you move around the figure. This all shows that any two adjacent sides meet at a 90 degree angle.

Therefore, this figure is a rectangle. Any rectangle has all four angles of 90 degrees.

-----------------------------

The first section showed that we have a rhombus. The second section afterward showed that we also have a rectangle. The combination of a rhombus and a rectangle at the same time leads to a square.

Therefore, quadrilateral ABCD is a square.

5 0

3 years ago

Use the slope formula to fond the slope of the line that passes through the two points.

Nikitich [7]

Answer:

Step-by-step explanation:

Notice that the y-component is the same, -2, in these two points. That means y does not change as x changes, and therefore we conclude that the slope of the line connecting the two points is m = rise / run = 0.

-2 - (-2)

Alternatively, use m = -------------- = 0

3 - 13

The value of the slope in question is zero: m = 0

4 0

3 years ago

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ale4655 [162]

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3 years ago