All categories

3 years ago

If point P is 4/7 of the distnace frm M to N, what ratio does the point P partiion the directed line segment from M to N

Mathematics

1 answer:

vredina [299]3 years ago

7 0

Answer: 4:3.

Step-by-step explanation:

Given: Point P is $\dfrac{4}{7}$ of the distance from M to N.

To find: The ratio in which the point P partition the directed line segment from M to N.

If Point P is between points M and N, then the ratio can be written as

$\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}$

As per given,

$\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}$

Hence, P partition the directed line segment from M to N in 4:3.

You might be interested in

) There are 8 children in Sophie's preschool class. During free time yesterday, 1 of them

Klio2033 [76]

Using it's concept, it is found that there is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

For an experimental probability, these numbers of outcomes are taken from previous trials.

In this problem, in the previous trial, one out of eight students read a book, hence:

p = 1/8 = 0.125 = 12.5%.

There is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

More can be learned about probabilities at brainly.com/question/14398287

5 0

3 years ago

Can anyone help me plz?

RUDIKE [14]

Answer:

The answer is 37

Step-by-step explanation:

8x8=64

9x3=27

64-27=37

8 0

3 years ago

The length of a rectangle is 4 centimeters more than twice its width of the perimeter of the rectangle is 86centimeters find the

lana66690 [7]

Answer:

$Width= 13 cm$

$length=30cm$

Step-by-step explanation:

Let the length of the rectangle be 'L'

And the width of the rectangle be 'W'

$Perimeter= 86 cm$

According to the statement:

$Length= 2*Width+4\\L=2W+4$

Perimeter of a rectangle= 2(Length+Width)

$86=2(2W+4+W)\\86/2=3W+4\\43=3W+4\\3W=43-4\\3W=39\\W=39/3\\W=13 cm\\\\Length(L)=2W+4\\=2(13)+4=26+4=30 cm\\Length=30 cm$

$Width= 13 cm$

$length=30cm$

6 0

3 years ago

Find the measure of

sergij07 [2.7K]

Answer:

∠ ABC ≈ 137.9°

Step-by-step explanation:

Using the Cosine rule in Δ ABC

cos B = $\frac{a^2+c^2-b^2}{2ac}$

with a = 89, b = 144, c = 65

cos B = $\frac{89^2+65^2-144^2}{2(89)(65)}$ = $\frac{7921+4225-20736}{11570}$ = $\frac{-8590}{11570}$ , thus

B = $cos^{-1}$ ( - $\frac{8590}{11570}$ ) ≈ 137.9° ( to the nearest tenth )

4 0

4 years ago

Constructed Response

Len [333]

Answer:

Check Explanation.

Step-by-step explanation:

Totally, Terrell has 4 protein/meat options and 3 sauce options to pick from.

Meat Options: beef, pork, chicken, or tofu.

Sauce Options: hot, tangy and sweet sauce.

Individually, he could just pick each of the options, but now, the sample space would involve a combination of a protein option and a sauce option. So, the total sample spaces available would be every choice of protein and sauce available.

Using the fundamental counting principle,

A choice of beef meat will be followed by choice of either hot, tangy and sweet sauce giving a sample space of

(beef, hot), (beef, tangy), (beef, sweet)

This can then be repeated across the meat choices

(pork, hot), (pork, tangy), (pork, sweet)

(chicken, hot), (chicken, tangy), (chicken, sweet)

(tofu, hot), (tofu, tangy), (tofu, sweet)

Bringing the total sample spaces to

(beef, hot), (beef, tangy), (beef, sweet), (pork, hot), (pork, tangy), (pork, sweet), (chicken, hot), (chicken, tangy), (chicken, sweet), (tofu, hot), (tofu, tangy) and (tofu, sweet)

Making a total of 12 sample spaces!

Hope this Helps!!!

6 0

3 years ago