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s2008m [1.1K]
2 years ago
10

Please help me solve this geometry problem:)

Mathematics
1 answer:
yarga [219]2 years ago
8 0

Given:

The endpoints of a line segment are (-5,12) and (-5,0).

To find:

The coordinates of a points which divides the line segment in 2:1.

Solution:

Section formula: If a point divides a line segment in m:n.

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

Let point P divides the given line segment in 2:1. They, by using section formula, we get

P=\left(\dfrac{2(-5)+1(-5)}{2+1},\dfrac{2(0)+1(12)}{2+1}\right)

P=\left(\dfrac{-10-5}{3},\dfrac{0+12}{3}\right)

P=\left(\dfrac{-15}{3},\dfrac{12}{3}\right)

P=\left(-5,4\right)

Therefore, the coordinate of the point that partitions the given segment in the ratio 2:1 are (-5,4).

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A car trip from New York to Cincinnati took 12.5 hours. The return trip by the same route took 1 hour longer because the average
zhenek [66]

A car trip from New York to Cincinnati took 12.5 hours. The return trip by the same route took 1 hour longer.

Let x be the speed of the car

Car trip from New York to Cincinnati

We know Distance D = speed * time

time = 12.5 hours and speed =x

D = 12.5x

Return trip

The return trip by the same route took 1 hour longer. So 12.5+1 = 13.5 hours

he average rate of speed was 4 mph less. So speed is x-4

Distance D = speed * time

time = 13.5 hours and speed =x-4

D = (x-4)*13.5

D= 13.5x-54

The distance of ongoing trip and return trip are same

So we equate both the distance equations D= 13.5x-54  and D= 12.5x

12.5x = 13.5x-54    

Subtract  13.5 on both sides

-1x = -54

x=54

speed of ongoing trip = 54 miles per hour

Distance D = 12.5x = 12.5 * 54=675 miles

The length of the route = 675 miles



4 0
3 years ago
The common ratio in a geometric series is 0.50.50, point, 5 and the first term is 256256256.
V125BC [204]

Answer:

504

Step-by-step explanation:

I think the correct question is like:The common ratio in a geometric series is 0.50 ( point 5) and the first term is 256.  

Find the sum of the first 6 terms in the series.

If it's right, then

Sₙ = (a₁ * (1 - rⁿ)) / (1 - r)

S₆ = (256 * ( 1 - 0.5⁶)) / (1 - 0.5) = (256 * 0.984375) / 0.5 = 504

6 0
2 years ago
Given the function defined below, what is the value of the 4th term?
MakcuM [25]

Answer:

The 4 t h term is   f(4)   = 143

Step-by-step explanation:

<em>Explanation</em>:-

Given  function f(1) = -4

Given 'nth' term is  f(n) = -3f(n-1) +5

Put n =2         <em> f(2) = -3 f(2-1) +5</em>

                             = -3 f(1) +5

                             = -3 (-4) +5

                             = 12 +5

                       f(2) = 17

put n= 3      

                         f(n) = -3f(n-1) +5  

                      <em>   f(3) = -3 f(3-1) +5</em>

                            = -3f(2) +5

                           = -3(17) +5

                           = -51+5

                      f(3) = -46

Put n=4

                  f(n) = -3f(n-1) +5

               <em>  f(4)  = -3f(4-1) +5</em>

<em>                  f(4)  = -3f(3)+5</em>

                f(4)   = -3(-46)+5

                f(4)   = 138 +5

                f(4)   = 143

<u><em>Final answer</em></u>:-

<em>The 4 t h term is   f(4)   = 143</em>

         

6 0
2 years ago
If a consumer takes out a $100 payday loan, his total cost will be higher because of
Zolol [24]

Answer:

being smart

Step-by-step explanation:

4 0
2 years ago
What can be constructed from polygons alone?
UkoKoshka [18]

Cone (not including the vertex)

Cylinder

4 0
2 years ago
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