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3 years ago

Find all points on the x-axis that are a distance 5 from P(-8,3)

1 answer:

8 0

On the x axis means that the y value is 0 or the point is (x,0)

distance formula

D= $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$
we know that distance is 5
the first point is (x1,y1)
the (x2,y2) is (x,0)

so
D=5
x1=-8
y1=3
x2=x
y2=0

5= $\sqrt{(-8-x)^2+(3-0)^2}$
5= $\sqrt{(-8-x)^2+(3)^2}$
5= $\sqrt{64+16x+x^2+9}$
5= $\sqrt{x^2+16x+73}$
square both sides
25= ${x^2+16x+73}$
minus 25 both sides
0=x^2+16x+48
factor
0=(x+4)(x+12)
set each to zero

x+4=0
x=-4

x+12=0
x=-12

the points are

(-4,0) and (-12,0)

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James is selecting a marble. James chooses a marble at random and then replaces it. He then selects a second marble at random. W

tresset_1 [31]

Answer:

The probability of selecting a solid black marbles both times;

P = 9/100

Attached is the completed question;

Step-by-step explanation:

Number of solid black marbles = 3

Total number of marbles = 10

The probability of selecting a solid black marble;

P1 = 3/10

With the assumption that the marbles are replaced before next selection.

The probability of selecting a solid black marbles both times;

P = P1 × P1 = 3/10 × 3/10 = 9/100

P = 9/100

7 0

3 years ago

a student reads at a rate of 16 pages per day which ordered pair would be on a graph of its relationship

mojhsa [17]

I found the choices that should have been included in this problem.
a) (1.5,26)
b) (2.25,30)
c) (5.5,88)
d) (7.25,110)

y = 16x
choice a. y = 16(1.5) = 24
choice b. y = 16(2.25) = 36
choice c. y = 16(5.5) = 88
choice d. y = 16(7.25) = 116

The correct answer is choice c. (5.5, 88)

8 0

3 years ago

Evaluate the line integral c y3 ds,<br> c.x = t3, y = t, 0 â‰¤ t â‰¤ 3

Temka [501]

$\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\int_{t=0}^{t=3}t^3\sqrt{1^2+(3t^2)^2}\,\mathrm dt=\int_0^3t^3\sqrt{1+9t^4}\,\mathrm dt$

Take $u=1+9t^4$ so that $\mathrm du=36t^3\,\mathrm dt$ . Then

$\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\frac1{36}\int_{u=1}^{u=730}\sqrt u\,\mathrm du=\frac{730^{3/2}-1}{54}$

7 0

3 years ago

PLEASE HELP

katrin2010 [14]

The game that is used for the scenario above in terms of fair play is using a balloon. Here, the player will hit the balloon.

<h3>What is the scenario under the balloon game?</h3>

The rule of play are:

This is a classic game with simple rules which are:

Each player to hit the balloon up and it bonce into the air but when one should not allow it to touch the ground.,
Players would be tied together in twos and they will juggle a lot of balloon and it have to be more than 1 balloon with one of their hands tied to their back.

A scenario of the worksheet game whose expected value is 0 is given below:

Assume that it costs about $1 for a player to play the billon game and as such, if the player hits a balloon, they will be given $3. what can you say. Can you say that it this game is fair or not? and who has the biggest advantage.

Solution

Note that a game is ”fair” if the expected value is said to be 0. When a player is said to hits a balloon, their net profit often increase by $4. So when the player do not hit a balloon, it drops to $1.

(4)(0.313) + (-1)(0.313)

= 0.939 approximately

Thus, the expected value is $0.939 which tells that the game is fair.

Learn more about fair play from

brainly.com/question/24855677

#SPJ1

4 0

2 years ago

Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about th

irina [24]

The coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)

<h3>How to determine the image of point B?</h3>

The complete question is added as an attachment

From the attached image, we have the following coordinate

B = (-2, 4)

When the triangle is rotated by 270 degrees, the rule of rotation is:

(x, y) ⇒ (y, -x)

For point B, we have:

B' = (4, 2)

Hence, the coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)