What are the coordinates of the point on the directed line segment from (−7,−5) to (8,−10) that partitions the segment into a ratio of 3 to 2?

Answers

Answer 1

Answer:

let's say P(−7,−5) and Q(8,−10) gets partitioned on a 3 : 2 ratio from P to Q by point R, so

$\textit{internal division of a line segment using ratios} \n\n\n P(-7,-5)\qquad Q(8,-10)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{3:2} \n\n\n \cfrac{P\underline{R}}{\underline{R} Q} = \cfrac{3}{2}\implies \cfrac{P}{Q} = \cfrac{3}{2}\implies 2P=3Q\implies 2(-7,-5)=3(8,-10)$

$(\stackrel{x}{-14}~~,~~ \stackrel{y}{-10})=(\stackrel{x}{24}~~,~~ \stackrel{y}{-30}) \implies R=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-14 +24}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-10 -30}}{3+2} \right)} \n\n\n R=\left( \cfrac{ 10 }{ 5 }~~,~~\cfrac{ -40}{ 5 } \right)\implies R=(2~~,~-8)$

Related Questions

Ushma and her friends went to a movie that started at 7:35 p.m. The movie ended at 9:20 p.m. Ushma got home 50 minutes after the movie ended. What time did Ushma get home? Explain how you found your answer?
20=8+v i dont know how to do this
Marika and Freddy sold 70 homes for Ron Realty. If Marika sold 2.5 times as many homes as Freddy, how many homes did each sell?
The monthly cost of a certain long distance service is given by the linear function y=0.08x+ 8.95 where Y is in dollars and X is the amount of time in minutes called in a month. Find and interpert the slope and y-intercept of the linear equation
Hy! (√2+1)²+(3-√3)²-(√5+1)²=???Thank yours!:*

A rectangular stage set up in a theater has an area of (15x^2+3x-12) square feet. Factor the polynomial completely.

Answers

15x²+3x-12
=3(5x²+x-4)
=3(x²+x-20)
=3(x+5)(x-4)
=3(5x+5)(5x-4)
=3(x+1)(5x-4)

If h(x) = −4x − 10, find h(−5).

−30
1.25
10
−1

Answers

The value of function h (-5) will be;

⇒ h (-5) = 10

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is,

⇒ h (x) = - 4x - 10

Now,

Here, The function is,

⇒ h (x) = - 4x - 10

So, To find the value of h (-5) as;

Substitute x = - 5 in above equation as;

⇒ h (x) = - 4x - 10

⇒ h (-5) = - 4 × -5 - 10

⇒ h (-5) = 20 - 10

⇒ h (-5) = 10

Thus, The value of function h (-5) will be;

⇒ h (-5) = 10

Learn more about the substitution method visit:

brainly.com/question/26094713

#SPJ2

$h(x)=-4x-10\n\nh(-5)\to x=-5\n\nsubtitute\ the\ value\ of x=-5\ to\ the\ formula:\n\nh(-5)=-4(-5)-10=20-10=\boxed{10}$

I need help to simplify

Answers

The ones i know are 9 and 10 and those are
9.)Z/x3y4
10.) X/ z5y4
you subtract them from each other and whichever one has the bigger number goes on the bottom.
Hope this helped :)

divide until a number or both numbers are at their smallest point or they are an odd number.

A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point. The motorboat has a speed of 22 mi/h relative to the water. In what direction should the boat be headed?

Answers

The direction should the boat be headed is 60 degrees north 30 degrees west and this can be determined by using the trigonometric functions.

Given :

A straight river flows east at a speed of 11 mi/h.
A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point.
The motorboat has a speed of 22 mi/h relative to the water.

The following steps can be used in order to determine the direction should the boat be headed:

Step 1 - The trigonometric function can be used in order to determine the direction should the boat be headed.

Step 2 - The mathematicalexpression of the cosine function is given by:

$\rm cos\theta=(base)/(hypotenuse)$

where $\theta$ is the direction should the boat be headed.

Step 3 - Now, substitute the known values in the above formula.

$\rm cos\theta=(11)/(22)$

Step 4 - Simplify the above expression.

$\rm cos\theta=(1)/(2)$

$\theta = 60^\circ$

Step 5 - So, the angle from the west axis is given by:

$90-60=30^\circ$

The direction should the boat be headed is 60 degrees north 30 degrees west.

For more information, refer to the link given below:

brainly.com/question/11709244

Answer:

N 30 degree W

Step-by-step explanation:

We are given that

Speed of river flows=11 mi/h(East)

Speed of motorboat relative to water=22mi/h

We have to find the direction in which the boat should be headed.

Let direction of the boat = $\theta$

We know that

$Cos\theta=(Base)/(hypotenuse)$

Using the formula

$Cos\theta=(11)/(22)=(1)/(2)$

$Cos\theta=Cos60^(\circ)$

Because $Cos60^(\circ)=(1)/(2)$

$\theta=60^(\circ)$

Angle from the west axis= $90-60=30^(\circ)$ W

Hence, the direction of boat should be headed in N 30 degree W

Rewrite 4/6:1/3 as a unit rate. A: 2/1 B: 12/6 C: 2/9 D: 12/1

Answers

Answer:

2/1

Step-by-step explanation:

get the first part of each fraction to something divisible by the second part

4· 3=12/6

1· 3=3/3

12÷2= 23÷3= 1

2/1

Answer:

Correct answer is A 2:1

Step-by-step explanation:

When writing a unit rate the denominator is always 1

If you want to obtain a unit rate you divide both quantities by the second one.

what is a unit rate?

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Use the cubic model y=5a^3-2a^2+a-45 to find the value of y when x=4.