30 POINTS PLEASEE HELP 8TH GRADE MATH PLEASEE

WILL GIVE BRAINLIEST!

Nataly [62]

Answer:

The equation the circle is given by

${\bf 4x}^{\bf 2}+{\bf 4y}^{\bf 2}-{\bf 8x+0y-60}={\bf 0}$

Step-by-step explanation:

The general form of the circle is

$x^2+y^2+Dx+Ey+F=0\hfill (1)$

Given points are (5,0) , (0,4) and (2,4)

Let the points (5,0) , (0,4) and (2,4) be (x_1,y_1) , (x_2,y_2) and (x_3,y_3) respectively

The equation of the circle passes through given points (5,0) , (0,4) and (2,4)

Substituting the point (5,0) in (1)

$(-5)^2+(0)^2+D(5)+E(0)+F=0$

$25-5D+F=0$

$5D-F=25\hfill (2)$

Substituting the point (0,4) in

$(0)^2+(4)^2+D(0)+E(4)+F=0$

$16+4E+F=0$

$4E+F=-16\hfill (3)$

Substituting the point (2,4) in

$(2)^2+(4)^2+D(2)+E(4)+F=0$

$4+16+2D+4E+F=0$

$2D+4E+F=-20\hfill (4)$

By solving the equations (2) ,(3) and(4) we get the values of D,E and F as below

$D=-2$ , $E=0$ and $F=-15$

substituting the values of D,E and F in (1) we get

$x^2+y^2-2x+(0)y-15=0$

Now multiplying the above equation into 4 we get

$4x^2+4y^2-8x+(0)y-60=0$

6 0

3 years ago

Find the complete solution of the system 5x+3y+11z=37 3y+z=12 5x+9y+13z=61

valkas [14]

Answer:

$y = \displaystyle\frac{12-z}{3}\\\\x = -2z + 5$

Step-by-step explanation:

We are given a system of equation:

$5x+3y+11z=37\\3y+z=12\\5x+9y+13z=61$

To find a solution to the given system, we follow the given steps.

1. Subtracting second equation from first and third equation, we get:

$5x+3y+11z-3y-z=37-12\\5x+10z = 25\\5x+9y+13z-3(3y+z) = 61 - 36\\5x + 10z = 25$

2. After eliminating z to obtain two equations in two variable, we observe that the two equations obtained were same.

So we have three equations that will all graph in the same plane.

Thus, there are infinite number of solution to the given system of equation.

We can write the values of x and y in the form of z:

$y = \displaystyle\frac{12-z}{3}\\\\5x + 12 - z + 11z = 37\\5x = -10z + 25\\x = -2z + 5$

3 0

3 years ago

What is the probability of getting zero heads in six tosses? What is the probability of getting exactly two heads in six tosses?

alexira [117]

Answer:

The probability of getting zero heads in six tosses is 0.015625.

The probability of getting exactly two heads in six tosses is 0.234375.

Step-by-step explanation:

Using the Minitab software for computing the desired probabilities.

We take n=6 and p=1/2 because we have six tosses and in binomial distribution the probability of success p remains constant in each trial whereas the probability of success in this case is getting heads.

When a coin is tossed then there are two possible outcomes head or tail.

So,

p= P(heads)=1/2=0.5

The probability of getting zero heads in six tosses is computed by considering the following steps:

In Minitab

Calc >Probability Distributions > Binomial

Select n=6 and p=0.5 and select input constant=0 and bubble the probability and by clicking OK we get the following output:

Probability Density Function

Binomial with n = 6 and p = 0.5

x P( X = x )

0 0.015625

So, the probability of getting zero heads in six tosses is 0.015625.

The probability of getting exactly two heads in six tosses is computed by considering the following steps :

In Minitab

Calc >Probability Distributions > Binomial

Select n=6 and p=0.5 and select input constant=2 and bubble the probability and by clicking OK we get the following output:

Probability Density Function

Binomial with n = 6 and p = 0.5

x P( X = x )

2 0.234375

So, the probability of getting exactly two heads in six tosses is 0.234375.

7 0

4 years ago

BRAINLIEST

fomenos

The answer is C (Length=32 feet and Width=24 feet)

5 0

3 years ago

PLEASE HELP TY show all work

aksik [14]

Answer:

36 cm

Step-by-step explanation:

$V= \frac{4}{3} \pi r^{3}$

$3V= 4\pi r^{3}$

$r^{3}=\frac{3V}{4\pi }$

$r= 3\sqrt{\frac{3V}{4\pi } }$

$r=3\sqrt{\frac{3* 24429 cm^{3} }{4\pi } }$

r=18 cm

diameter= d= 2r

d= 2(18cm)= 36 cm

5 0

4 years ago