All categories

3 years ago

If point P is 4/7 of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

Mathematics

2 answers:

Ket [755]3 years ago

8 0

Answer:

4:3

Step-by-step explanation:

Given that P divides segment MN into 4/7, let MN to be x units in length then

MP = 4/7 x =4x/7 --------(i)

But MN =MP+PN so;

x=4x/7 +PN

x- 4X/7 =PN

3x/7 =PN ----------(ii)

To get the ratio of MP:PN

MP: PN

4x/7:3x/7

MP/PN = 4x/7 / 3x/7

MP/PN =4/3

MP:PN = 4:3

miskamm [114]3 years ago

8 0

Answer: 4:3

Step-by-step explanation:

Given : A point P is 4/7 of the distance from M to N.

∴ Let the distance between M to N be d.

$\Rightarrow\ MP=\dfrac{4}{7}\times d=\dfrac{4d}{7}$

Also, the point P partition the directed line segment from M to N .

Thus , MN = MP+PN

$\Rightarrow\ d=\dfrac{4d}{7}+PN\\\\\Rightarrow\ PN= d-\dfrac{4d}{7}=\dfrac{7d-4d}{7}\\\\\Rightarrow\ PN=\dfrac{3}{7}d$

Now, the ration of MP to PN will be :-

$\dfrac{MP}{PN}=\dfrac{\dfrac{4d}{7}}{\dfrac{3d}{7}}=\dfrac{4}{3}$

∴ Point P partitioned the line segment MN into 4:3.

You might be interested in

the piggybank had 25.65 in dimes and quarters if there were 20 more quarters than dimes, how many dimes were in the piggybank

Nadusha1986 [10]

X = number of dimes
y = number of quarters
---
10x + 25y = 2565
y = x + 20
---
put the system of linear equations into standard form
---
10x + 25y = 2565
x - y = -20
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = 59
y = 79

4 0

3 years ago

Which of these equations shows a proportional relationship between x and y

Vesna [10]

Answer:

it is H any help I'm glad to help

7 0

3 years ago

Given the slope is -5 and the y-intercept is -2, what is the equation of the line in slope-intercept form? A y = 5x + 2 B y = -5

Law Incorporation [45]

Answer:

B. y = -5x -2

Step-by-step explanation:

Fill in the given values in the form ...

y = (slope)x + (y-intercept)

y = -5x +(-2)

y = -5x -2 . . . . simplify; matches choice B

8 0

3 years ago

What number must you add to complete the square?<br> x^2 + 2x = -1

Andru [333]

$\large\begin{array}{l} \textsf{You must add 1 to complete the square.}\\\\ \textsf{There is a very common special product: (square of a sum)}\\\\ \mathsf{(a+b)^2=a^2+2ab+b^2}\\\\\\ \textsf{Take the given equation:}\\\\ \mathsf{x^2+2x=-1\qquad(i)}\\\\\\ \textsf{The first term is a square (x squared)}\\\\ \textsf{The second term is a product of 2, x and 1.} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{We need to find a proper value for b, so that if we add it to}\\\textsf{the left side of the equation, we get a perfect square.}\\\\ \textsf{So,}\\\\ \begin{array}{cccccccccc} \mathsf{a^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{a}&\!\!\!\cdot\!\!\!&\mathsf{b}&\!\!\!+\!\!\!&\mathsf{b^2}&=\mathsf{(a+b)^2}\\\\ \mathsf{\downarrow}&&&\!\!\!\!\!&\downarrow&\!\!\!\!\!&\downarrow&&\downarrow\\\\ \mathsf{x^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{x}&\!\!\!\cdot\!\!\!&\mathsf{1}&\!\!\!+\!\!\!&\mathsf{1^2}&=\mathsf{(x+1)^2} \end{array}\\\\\\ \textsf{Just by comparing the expressions above, we can conclude that}\\\textsf{b must be equal to 1, so we get a perfect square:}\\\\ \mathsf{(x+1)^2=x^2+2x+1} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{Back to (i), adding 1 to both sides:}\\\\ \mathsf{x^2+2x+1=-1+1}\\\\ \boxed{\begin{array}{c} \mathsf{(x+1)^2=0} \end{array}} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{If you want to solve this equation for x, you will find}\\\\ \mathsf{x+1=0}\\\\ \mathsf{x=-1}\quad\longleftarrow\quad\textsf{(solution)} \end{array}$

If you're having problems understanding the answer, try seeing it through your browser: brainly.com/question/2112248

$\large\begin{array}{l} \textsf{Any doubt? Please, comment below.}\\\\\\ \textsf{Best regards! :-)} \end{array}$

6 0

3 years ago

Read 2 more answers

Find the slope from points (9,-13), (7,-11)? <br> That’s what my question is

k0ka [10]

Answer:

Step-by-step explanation:

The entered points belong to an increasing, linear function.

Equation: y = 1x + 4.

4 0

3 years ago