1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sveta_85 [38]
3 years ago
6

What is the ratio in which the point P(3/4,5/12) decides the line segment joining points A(1/2,3/2) and B(2,-5)

Mathematics
1 answer:
timama [110]3 years ago
6 0

Given:

The point P\left(\dfrac{3}{4},\dfrac{5}{12}\right) divides the line segment joining points A\left(\dfrac{1}{2},\dfrac{3}{2}\right) and B(2,-5).

To find:

The ratio in which he point P divides the segment AB.

Solution:

Section formula: If a point divides a segment in m:n, then the coordinates of that point are,

Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)

Let point P divides the segment AB in m:n. Then by using the section formula, we get

\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)

\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)

On comparing both sides, we get

\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}

\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}

Multiply both sides by 4.

3(m+n)=2(4m+n)

3m+3n=8m+2n

3n-2n=8m-3m

n=5m

It can be written as

\dfrac{1}{5}=\dfrac{m}{n}

1:5=m:n

Therefore, the point P divides the line segment AB in 1:5.

You might be interested in
You have 400 feet of fencing to enclose a rectangular plot. Find the length and width of the plot that will maximize the area. W
3241004551 [841]
Well, we can denote L and W for the length and width respectively. Lets say the A is the area, we have: 1. A=(L × W) as well as 2. 2(L+W)=400. We rearrange the second equation to get 3. W=200-L. From this, we can see that 0<L<200. Substitute the third equation into the first to get A=(200L-L²). put this formula into the scientific calculator and you will find a parabola with a maximum. That would be the maximum area of the enclosed area. Alternatively, we can say that L is between 0 and 200 when the area equals 0. (The graph you find will be  area against length). As the maximum is generally found halfway, we substitute 100 into the equation and we end up with 10000.

Hope this helps.
6 0
3 years ago
Is this right? I chose 15.
daser333 [38]

Answer:

Correct, it is 15

Step-by-step explanation:

Because 3 turns into 9, you also want to multiply the other by 3, so you’d do 5x3 to get 15

7 0
3 years ago
Read 2 more answers
Simplify (18x^4 – 3x^3 – 2x^3 + x^2 – 10 + 6), showing how you got your answer would be preferable!
Crazy boy [7]

Answer:

1

8

4

−

3

3

−

2

3

+

2

−

1

0

+

6

18

x

4

−

3

x

3

−

2

x

3

+

x

2

−

10

+

6

18x4−3x3−2x3+x2−10+6

1

8

4

−

3

3

−

2

3

+

2

−

4

18

x

4

−

3

x

3

−

2

x

3

+

x

2

−

4

18x4−3x3−2x3+x2−4

2

Combine like terms

Solution

1

8

4

−

5

3

+

2

−

4

Step-by-step explanation:

7 0
3 years ago
Clair has250 pennies some pennies are in a box the rest are in her bankthere are more then 100 pennies in each place how many pe
9966 [12]

Answer:

In each place there must be more 100 pennies, but as the total 250 pennies, there are several ways that the money is distributed.

Because there may be 101 pennies in the box and 149 pennies in the bank, but it can also be the opposite; in the box 149 pennies and in the bank 101 pennies.

Therefore, there are many options to answer the question, as long as it is met that there are more than 100 pennies in one place.

8 0
3 years ago
A skateboard ramp at the skate park is in the shape of a triangular prism. What is the lateral surface area of the ramp? (SA = P
rodikova [14]

Answer:

Step-by-step explanation: i dont know

3 0
3 years ago
Other questions:
  • Bertha buys electricity from a company that offers a choice of two tariffs. Both have a daily charge of $0.20 regardless of how
    5·1 answer
  • In the diagram, how many circles are there for each square?
    8·2 answers
  • Solve 3x2 18x 15 = 0 by completing the square.
    15·1 answer
  • In​ 2000, the population of a country was approximately 5.99 million and by 2069 it is projected to grow to 12 million. Use the
    10·1 answer
  • kate has 4 3/8 of fabric and needs 2 7/8 yards to make a skirt. how much extra fabric will she have left?
    10·1 answer
  • Which postulate or theorem proves that A CFE and ADFE are congruent? o OSSS Congruence Postulate O SAS Congruence Postulate O AA
    7·1 answer
  • What is the surface area of a sphere with a radius of 30m?
    15·1 answer
  • 0.000009 in scientific notation.
    5·2 answers
  • Using the data from the theoretical probability table, what is the probability of the spinner landing only once on yellow in two
    14·1 answer
  • Use the coordinate plane below (PLEASE HELP FIRST TO ANSWER AND ANSWER ALL WILL GET BRAINIEST)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!