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Mila [183]
3 years ago
6

Line segment MN is shown below. If point P(x,y) partitions the line segment

Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0

Answer:

P (-1 , 0)

Step-by-step explanation:

M (-6 , 2)      N (9 , -4)     P (x , y)

horizontal distance of M and N = 9 - (-6) = 15

vertical distance of M and N = 2 - (-4) = 6

1/3 from x coordinate of M (-6): -6 + 15/3 = -1    This is x coordinate of point P

1/3 from y coordinate of M (2): 2 - 6/3 = 0    This is y coordinate of point P

P (x , y)  i.e P (-1 , 0)

check: distance of MP = √(-1 - (-6))² + (0 - 2)² = √29 = 5.385

distance of PN = √(-1 - 9)² + (0 - (-4))² = √116 = 10.77

MP / PN = 5.385 / 10.77 = 0.5 = 1/2

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Using a graphical method, solve the simultaneous equations x+y =4 and y=2x+1
adoni [48]

Answer:

(1, 3)

Step-by-step explanation:

Given the expression

x+y = 4 ... 1

y = 2x+1 ....2

Substitute equation 2 into 1

x + (2x+1) = 4

3x + 1 = 4

3x = 4-1

x = 3/3

x = 1

Since y = 2x + 1

y = 2(1) + 1

y = 3

Hence the solution to the equation is (1,3). This means that the coordinate point on the graph where both lines intersect will be at (1, 3)

7 0
2 years ago
How do i find the slope
Elodia [21]

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

<u>m=</u>\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }<u></u>

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show <u>rise</u>, over the difference in the x points to show <u>run</u>.

Now, to find the slope we insert our values, starting with our second y point:

<u>m=</u>\frac{2-y_{1 } }{x_{2} -x_{1} }<u></u>

Now insert our first y point:

<u>m=</u>\frac{2-4 }{x_{2} -x_{1} }<u></u>

Now we insert our second x point:

<u>m=</u>\frac{2-4 }{-3 -x_{1} }<u></u>

And finally our first x point:

<u>m=</u>\frac{2-4 }{-3 -3 }

Now, we solve:

<u>m=</u>\frac{-2 }{-6}

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

<u>m=</u>\frac{2 }{6}

Now, we simplify our fraction by dividing the top and bottom by 2:

<u>m=</u>\frac{1}{3}<u></u>

So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y=\frac{1}{3}x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

<u>m=</u>\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }<u></u>

Insert our values:

<u>m=</u>\frac{4-1}{2-(-4)}<u></u>

Get rid of the double negative:

<u>m=</u>\frac{4-1}{2+4}<u></u>

Solve:

<u>m=</u>\frac{3}{6}<u></u>

Simplify:

<u>m=</u>\frac{1}{2}

Now that we know our slope, let's plug it in to our slope intercept form equation.

y=\frac{1}{2}x+3

I hope this was helpful! Keep learning! :D

5 0
3 years ago
Please help me with this
Darina [25.2K]
The picture is blank for me. Please take clearer pictures leveled with the question! :)
3 0
3 years ago
Can someone help me with this please
qaws [65]

Answer:

1. Answer is C

4. Answer is G

Step-by-step explanation:

I'm not sure how to explain 1 since I used a calculator.

Number 4 is where you choose a point on the line and count 4 blocks up and 5 blocks left. If it hits another point on the line then that's the graph.

7 0
3 years ago
Explain the level of uncertainties involve in concept of probability. The next generation of miniaturized wireless capsules with
RUDIKE [14]

Answer:

a) the probability that Both motors will operate satisfactorily in the capsule 0.6222

b) the probability that One motor will operate satisfactorily and the other will not is 0.3556

Step-by-step explanation:

Given that;

total number of motors N = 10

number of motors will not operate satisfactory m = 2

number of motors randomly selected n = 2

let X be number of motors will that will not operate successfully

here, X≅Hyper geometric (x; N,n,m)

The probability mass function of x is;

P (X = x)=  { m }   {N - m }

                  {x }    {n - x}

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { N }

                     { n  }

a)

the probability that both motors will operate satisfactorily in the capsule i.e no motor will not operate satisfactory

so

P(X= 0)  = { 2 }    { 10 - 2 }

                 {0 }    { 2 - 0}

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

so

P (X = 0)  = { 2 }   { 8}

              {  0 }   { 2  }

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

p(P= 0)=1×28 / 45 = 28/45 = 0.6222

Therefore the probability that Both motors will operate satisfactorily in the capsule 0.6222

b)

the probability that one motor will operate satisfactorily and the other will not.

P(X=1)  = { 2 }   { 10 - 2 }

              {  1 }    { 2 - 1  }

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

so

P(X=1)  = { 2 }   { 8 }

              {  1 }   { 1  }

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

P(X=1)  = 2×8 / 45 = 16/45 = 0.3556

Therefore the probability that One motor will operate satisfactorily and the other will not is 0.3556

3 0
3 years ago
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