Line segment MN is shown below. If point P(x,y) partitions the line segment
into the ratio MP:PN = 1:2 then determine the values of x and y.
Line segment:
Point M: (-6,2).
Point N: (9. – 4)

Answers

Answer 1

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

Answer 2
Final answer:

The values of x and y that partition the line segment MN into the ratio 1:2 are x = 3 and y = -4.

Explanation:

To determine the values of x and y that partition the line segment MN into the ratio MP:PN = 1:2, we can use the section formula. The section formula states that the coordinates of a point P(x,y) that partitions a line segment with endpoints M(x1, y1) and N(x2, y2) into the ratio m: n are given by:

x = (nx1 + mx2) / (m + n)

y = (ny1 + my2) / (m + n)

In this case, M(-6, 2) and N(9, -4), and the ratio is 1:2. Plugging these values into the section formula, we get:

x = (2*9 + 1*(-6)) / (1 + 2) = 3

y = (-4*2 + 2*(-4)) / (1 + 2) = -4

Therefore, the values of x and y that partition the line segment MN are x = 3 and y = -4.

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Related Questions

18 times 9 then multiply 1/2??

Answers

Answer:

81

Step-by-step explanation:

18*9=162

162*[tex]\frac{1}{2}[/tex]=81

Answer:

81

Step-by-step explanation:

18 * 9 = 162

162 * 1/2 is 81

Also multiplying by 1/2 is the same as dividing by 2

Hope this helped!

Valeria opened her first bank account at Wells Fargo. she has 80 but she plans to withdraw $5 a week
what is the x?
Equation?
y?
Slope(m)?

Answers

Answer:

x/5=80

Step-by-step explanation:

x=how many months it takes to get all the money out                                              hope it is right or you can google it if not

Solve this equation.
3.5(2.25 + x) = 14

Answers

Answer:

1.75

Step-by-step explanation:

Use the distributive property first.

(3.5 x 2.25) (3.5 x X) = 14

7.875 + 3.5x = 14   Now subtract 7.875 from both sides

3.5x = 6.125  Now divide 3.5 by both sides

x = 1.75

Final answer:

The equation 3.5(2.25 + x) = 14 is solved by first distributing 3.5 through the parentheses, then isolating x on one side, yielding a result of x = 1.75.

Explanation:

In this mathematical equation, the first step is to distribute 3.5 to (2.25 + x). The result is 7.875 + 3.5x = 14. We then subtract 7.875 from both sides to isolate the term with x which gives 3.5x = 6.125. Finally, to solve for x, we divide both sides by 3.5. This gives us x = 1.75.

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Explore the properties of inscribed angles
by following these steps.
1. Move point C and observe how the
angle measures change.
When AC changes,
m ZABC and m ZADC____
and are _____
to each other.

Answers

Answer:they change and are always equal to each other

part 2. they do not change

part 3. 1/2

i just did it on edge 2020

When AC changes, angles ABC and ADC are also changes and are equal to each other.

Inscribed angle :

An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of a circle.

This is different than the central angle, whose vertex is at the center of a circle.

From given figure, It is observed When AC changes, angles ABC and ADC are also change but equal to each other.

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Daniel can eat 15 bowls of Cinnamon Toast Crunch in 60 minutes what is the speed of his cereal eating?

Answers

4 minutes per bowl is the answer because you divide 60/15

Answer:

0.25 (1/4) bowls a minute.

Step-by-step explanation:

If you divide 15 by 60, you get 0.25 (1/4) and then you just add your labels which is bowls a minute.

What is the slope of the line that passes through the points (–9, 2) and (0, 4)?

Answers

Answer:

2/9

Step-by-step explanation:

Slope = y2- y1/x2 - x1

Given

x1 = -9

y1 = 2

x2 = 0

y2 = 4

Therefore

Slope = 4 - 2 /0 -(-9)

= 4 - 2/0 + 9

= 2/9

Answer:

2/9 is correct, or just .22

Step-by-step explanation:

Use the formula  [tex]\frac{x^2 - x^1}{y^2 - y^1} = \frac{rise}{run} = \frac{-9 - 0}{2 -4}[/tex]

However, the variables, are not squared, that is meant to be subscript :D

Round your answer to the nearest whole. use Pie as 3.14
Find the volume of a cylinder with a radius of 3 cm and a height of 11 cm.

Answers

To find the volume of a cylinder you must use the formula:


πr^2h

1) Plug in your variables
π(3)^2•(11)

2) Solve
~ 311.01 cm^3

Write an equation for the line that has a slope of 1/2 and passes through the point (-2,5)

Answers

Answer:

y=0.5x+6

Step-by-step explanation:

6 is the y-intercept because you go up 1 over 2.

Answer: The equation of line is [tex]2y - x - 12 = 0[/tex]

Step-by-step explanation:

The formula for finding the equation of a line when slope and a point is gives is :

[tex]y-y_{1}=m(x-x_{1})[/tex]

[tex]x_{1}=-2[/tex]

[tex]y_{1}=5[/tex]

[tex]m = 1/2[/tex]

substituting into the formula , we have :

[tex]y - 5 = 1/2 ( x-(-2) )[/tex]

multiply through by 2 , we have

[tex]2(y-5) = 1(x+2)[/tex]

[tex]2y - 10 = x + 2[/tex]

[tex]2y - x - 10 - 2 = 0[/tex]

[tex]2y - x - 12 = 0[/tex]

Therefore : the equation of line is [tex]2y - x - 12 = 0[/tex]

First, rewrite 13/30 and 9/20 so that they have a common denominator

Answers

Answer:

Must determine the LCD.  Think:  what is the smallest (least) number divisible by both 30 and 20?  You could, of course, just multiply 30 and 20, obtaining 600, but that would not be the LCD.

Note that 30 and 20 share the common factor 10.  Multiplying 3 and 2 together produces 6.  The LCD is 10*6 = 60.  Note that both 30 and 20 divide into 60 with no remainder.

Then  19/30  = 2(19) / 2[30]  = 38/60, and 

13/20 = 3(13) / 3[20]  = 39/60.

Which is larger, 38/60 or 39/60?

Write the relationship between these 2 numbers using the appropriate inequality operator.

Step-by-step explanation:

The fractions 13/30 and 9/20, when rewritten with a common denominator, are 26/60 and 27/60, respectively.

To rewrite the fractions 13/30 and 9/20 with a common denominator, we need to find the least common multiple (LCM) of the denominators, which is the smallest multiple that both 30 and 20 share.

The prime factorization of 30 is 2 * 3 * 5, and the prime factorization of 20 is 2 * 2 * 5. To find the LCM, we take the highest power of each prime factor that appears in either number:

LCM(30, 20) = 2 * 2 * 3 * 5 = 60

Now, let's rewrite the fractions with the common denominator of 60:

13/30 = (13/30) * (2/2) = (13 * 2) / (30 * 2) = 26/60

9/20 = (9/20) * (3/3) = (9 * 3) / (20 * 3) = 27/60

So, the fractions 13/30 and 9/20, when rewritten with a common denominator, are 26/60 and 27/60, respectively.

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luna had $50 when she got to the carnival. After riding 12 rides she had $26 left. What was the price of each ride? Which equation can be used to represent this situation?
26 - 12p = 50
50 + 12p = 26
12p - 50 =26
50 - 12p = 26

Answers

50-12p=26 I believe.
50 - 12p because it says left so you have too subtract

Question 1
Create a circle with center A and a radius of your choice. Create a point B on the circle, and find the coordinates of B. Draw the radius AB. What is
the slope-intercept form (y = mx + b) of the equation of AB? Show your work.

Answers

Answer: I couldn't find the answer but I did find the formula? Sorry if this doesn't help much :(

Update:

Center at (-3,0)

Radius = 1

Step-by-step explanation:

(x-x1)^2 + (y-y1)^2 = r^2

(x-x2)^2 + (y-y2)^2 = r^2

Answer:

If point A = (4,4) and B = (8,7)

The slope of M would be 3/4.

Step-by-step explanation:

m = y^2 - y^1/x^2 - x^1 = 7 - 4/ 8 - 4 = 3/4. m = 3/4.

y = mx + b

y = 3/4 x + b

4 = (3/4)(4) + b

b = 4 - 3 = 1

The equation of line AB is y = 3/4 x + 1.

I hope this helps and that it is easy to understand and read! :)

what is the area of the base of a square pyramid whose side is length 17 m​

Answers

Answer:

289

Step-by-step explanation:

Base of the square pyramid is square

Formula: Length × Width

17 × 17 = 289

Does 2, square root of 5, 3 form a right triangle

Answers

Answer:

yes

Step-by-step explanation:

since [tex]3^2=5+2^2[/tex]

yes it does from a right triangle

which expression is equivalent to (1/4)m + (3/4)m - (3/8)(m+1)?

1. (5/8)m + (3/8)
2. (5/8)m - (3/8)
3. (3/8)m + (5/8)
4. (3/8)m - (5/8)

Answers

Answer:

2. (5/8)m - 3/8.

Step-by-step explanation:

(1/4)m + (3/4)m - (3/8)(m + 1)

=   m - (3/8)m - 3/8

= (5/8) m - 3/8.

Find the leg of each isosceles right triangle when the hypotenuse is given the measure 12 cm

Answers

Answer:16.97cm

Step-by-step explanation:

To find the hypotenuse side of an isosceles of side 12cm each

Using pythagoras theorem

hyp^2=opp^2+adj^2

hyp^2=12^2+12^2

Hyp^2=144+144

hyp=√288

Hyp=16.97cm

HELPPP PLEASE❗️❗️❗️❗️

Answers

Answer:

33

Step-by-step explanation:

You find the measure of B, which is 180 - (93 + 58) = 29 degrees

You use the law of sines which is 16/sin(29) = (BC)/sin(93)

You multiply both sides by sin(93) and get:

sin(93)*16/sin(29) = BC

You plug this into a calculator and get:

32.9574164555, which is approx. 33

What is the measure of angle c In degrees?

Answers

c = 64
73 + 43 = 116
180 - 116 = 64

Answer:

64⁰

Step-by-step explanation:

By angle sum property :

A + B + C = 180⁰

C = 180 - 73 - 43

C = 180 - 116

C = 64⁰

75 books represent 10% of total books at library 4.

Answers

Answer:

750 books

Step-by-step explanation:

10% .............75 books

100% .............x books

x = 100×75/10 = 7500/10 = 750 books

Plz help me out ASAP

Answers

Answer:

68

Step-by-step explanation:

cos22=sinx

sin^-1(cos22)=x

x= 68

(02.04 LC)
What is the equation of a line that contains the points (5,0) and (5,-2)?
x = 5
Ox=0
Oy=0
Oy=5

Answers

Answer:

oy=5

Step-by-step explanation:

t golf DJ o frick vet gn hf hi

What is the missing constant term in the perfect square that starts with x squared minus 8x ?

Answers

Answer:

16

Step-by-step explanation:

[tex] {x}^{2} - 8x + 16 = (x - 4) ^{2} \\ [/tex]

The volume of the figure is 168 cubic meters.
What is the height of the figure, in meters?
3.5
7
10.5
14

Answers

Answer:

3.5

Step-by-step explanation:

This is because 12 times 4 is 48 and if you divide 168 by 48 you get 3.5 . 3.5 times 12 times 4 is 168.

What is the period of the function shown in the graph?

Answers

Answer:

  4 units

Step-by-step explanation:

A function is periodic with period P when it can be shifted P units left or right and its graph will map to itself. Here, rising "edges" of the function cross grid lines that are 4 units apart, so the period is 4 units.

SOME ONE PLZZZZZZZZZZZ HELP FREEE BRAINLIST!!

Answers

Answer:

22.6 mi

Step-by-step explanation:

The shortest route is to go from bloomington to seaside to westminster. Simply add up the distances along this route.

Answer:

22.6

Step-by-step explanation:

13.2+9.4=22.6

Given f(x)=3x2+7 and g(x)=2x2-x-1 find (f+g)(x)

Answers

Answer: (f+g)(x)=5x2-x+6

Step-by-step explanation:

I hope this helps

Find one value of x that is a solution to the equation (x^2+3)^2=4x^2+12

Answers

Answer:

[tex] {( {x}^{2} + 3) }^{2} = {4x}^{2} + 12[/tex]

[tex] \bf \purple{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} } [/tex]

[tex] {( {x}^{2}) }^{2} + 2({x)}^{2} (3) + {(3)}^{2} = {4x}^{2} + 12[/tex]

[tex] {x}^{4} + {6x}^{2} + 9 = {4x}^{2} + 12[/tex]

[tex] {x}^{4} = {4x}^{2} - {6x}^{2} + 12 - 9 [/tex]

[tex] {x}^{4} = { - 2x}^{2} + 3[/tex]

[tex]( {x}^{2} \times {x}^{2}) = { - 2x}^{2} + 3[/tex]

[tex]2 \times {x}^{2} = { - 2x}^{2} + 3[/tex]

[tex] = \frac{ { - 2x}^{2} + 3 }{ {2x}^{2} } [/tex]

[tex] = 3[/tex]

The graph shows the speed of a ball in free fall for 10 seconds. Which is the constant of proportionality shown in the graph?

Answers

Given:

The graph shows the speed of a ball in free fall for 10 seconds.

We need to determine the constant of proportionality for the given graph.

Constant of proportionality:

The constant of proportionality can be determined using the formula,

[tex]\frac{y}{x}=k[/tex]

Where k is the constant of proportionality.

Let us consider any of the coordinate from the graph and substitute in the formula.

Consider the coordinate (4,40) and substitute in the above formula.

Thus, we have;

[tex]\frac{40}{4}=k[/tex]

[tex]10=k[/tex]

Thus, the constant of proportionality is 10 meters per second squared.

Answer:

10 meters per second squared

Step-by-step explanation:

help please now 20 points

Answers

Answer:

2/5

Step-by-step explanation:

The theoretical probability of getting blue is TOTAL BLUE SPUN/ TOTAL SPINS

There were 12 blue spins out of 30 total spins, making the probability equal to 12/30 = 2/5

What is the length of AB?
А. 8
В. 2
С. 6
D. 4

Answers

Answer:

C

Step-by-step explanation:

63° =63°

CB = AB

3x = 4x - 2

Answer:

Answer C is correct

=6

Step-by-step explanation:

[tex]3x = 4x - 2 \\ 2 = 4x - 3x \\ 2 = x \\ \\ ab \: \: \: length = 3x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3 \times 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6[/tex]

Angle 1 is 100 degrees. What is the measure of angle 3?

Answers

Answer:

Angle 3 is also 100

Step-by-step explanation:

They are vertical angles and vertical angles are always congruent.

The angle 3 is in the given figure is ∠3 = 100°.

What are parallel lines?

The parallel lines are a group of straight lines that never intersect with one another. The distance between two parallel is always the same.

The measure of angle 1 is given as ∠1 = 100°.

When two lines intersect each other, the pair of vertically opposite angles are equal.

Since, angle 1 and angle 3 are vertically opposite, they are equal.

Thus, ∠3 = 100°.

Hence, the measure of angle 3 is 100°.

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