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
Juliette [100K]
3 years ago
14

points a,b and c are collinear on AC, and AB:BC=3/4. A is located at (x,y), B is located at (4,1), and c is located at (12,5). w

hat are the values of x and y?
Mathematics
2 answers:
inn [45]3 years ago
7 0

Answer:  The required values are  x = 2  and  y = 2.

Step-by-step explanation:  Given that the points A, B and C are collinear on AC and AB : BC = 3 : 4.

Also, A is located at (x, y), B is located at (4, 1) and C is located at (12,5).

We are to find the values of x and y.

We know that

the co-ordinates of a point that divides a line segment with endpoints (a, b) and (c, d) in the ratio m : n are given by

\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).

According to the given information, we get

4=\dfrac{3\times 12+4\times x}{3+4}\\\\\\\Rightarrow 4=\dfrac{36+4x}{7}\\\\\Rightarrow 36+4x=28\\\\\Rightarrow 4x=8\\\\\Rightarrow x=\dfrac{8}{4}\\\\\Rightarrow x=2

and

1=\dfrac{3\times5+4\times y}{3+4}\\\\\\\Rightarrow 1=\dfrac{15+4y}{7}\\\\\Rightarrow 15+4y=7\\\\\Rightarrow 4y=8\\\\\Rightarrow y=\dfrac{8}{4}\\\\\Rightarrow y=2.

Thus, the required values are  x = 2  and  y = 2.

olga_2 [115]3 years ago
5 0
We have two unknowns: x and y. Now, we have to formulate 2 equations. The first would come from the use of the given ratio:

We use the distance formula to find the distance between coordinates:

3/4 = √[(x-4)²+(y-1)²] / √[(4-12)²+(1-5)²]
√[(x-4)²+(y-1)²]  = 3√5
(x-4)²+(y-1)² = 45
x² - 8x + 16 + y² - 2y + 1 = 45
x² - 8x + y² - 2y = 28  --> eqn 1

The second equation must come from the equation of a line:
y = mx +b
m = (5-1)/(12-4) = 1/2

Substitute y=5 and x=12 for point (12,5)
5 = (1/2)(12) + b
b = -1

So, the second equation is

y = 1/2x -1 or x = 2 + 2y --> eqn 2

Solving the equations simultaneously:
(2 + 2y)² - 8(2 + 2y) + y² - 2y = 28 
Solving for y, 
y = -2
x = 2+2(-2) = -2

Therefore, the coordinates of point A is (-2,-2).

You might be interested in
A circle is centered on point B, Points A, C and D lie on its circumference. if ABC measures 122 degrees, what does ADC measures
iren2701 [21]

Answer:

61°

Step-by-step explanation:

Angle extended to the circumference is half the angle at the centre

ADC = ½ ABC = ½ × 122 = 61

5 0
3 years ago
A nest of ants has been growing exponentially in such a way that its population, P, as a function of w weeks is given by P(w)=24
Hunter-Best [27]

Answer:

0.9%

Step-by-step explanation:

Given that:

A nest of ant is represented by the exponential growth function :

P(w)=24,000(1.063)^w

Where w = number of weeks

Recall :

Growth function is generally represented as :

P(t) = A(1 + r)^t

Where ; A is the initial population figure; r = growth rate and t = time

Hence, the growth rate per week of the function given is :

(1 + r) = 1.063

r = 1.063 - 1

r = 0.063

Number of days in a week = 7

Hence, growth rate per day = r /7

0.063 / 7

= 0.009

(0.009 * 100%) = 0.9%

8 0
3 years ago
Is this statement true or false?
Sloan [31]

Answer:

True

Step-by-step explanation:

A down payment is mostly for deposit reasons with insurance. It also let's the landlord know you will be moving in soon. They will use that money for repairs when you move out. You have a chance of getting it pack if they find no damages :D

3 0
3 years ago
Read 2 more answers
Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.
fredd [130]

\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}

\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}

so the ODE is indeed exact and there is a solution of the form F(x,y)=C. We have

\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)

\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)

f'(y)=0\implies f(y)=C

\implies F(x,y)=x^2y^3+\ln(x+y^2)=C

With y(1)=2, we have

8+\ln9=C

so

\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}

8 0
3 years ago
Alicia borrowed $15,000 to buy a car. She borrowed the money at 8% for 6 years. What is the interest rate she will pay for the l
Likurg_2 [28]
First convert the rate into a decimal.
8/100=0.08
Next put all those numbers 15,000, 0.08, and 6 into the equation A=P(1+(rt)).
This is how you do it.
A=15,000(1+(0.08*6))
A=15,000(1+0.48)
A=15,000(1.48)
A=22,200
7 0
3 years ago
Other questions:
  • The probability of getting a 1 is 0.3
    8·1 answer
  • What is the volume of this pyramid
    11·1 answer
  • Drag the operator to the correct location on the image. Which operation results in a trinomial?
    11·1 answer
  • HELPPP PLEASE ANSWER FAST CLASS IS ALMOST OVER!!!
    14·1 answer
  • Q.2*
    14·1 answer
  • You have two choices at a sales job. The first is that you can make a monthly salary of $3,000 or you could make $1,000 a month
    11·1 answer
  • Find the area of the square.<br> A<br> 25.0<br> B<br> 20.0<br> с<br> 15.0<br> D<br> 10.0
    8·2 answers
  • How many degrees does the minute hand of a clock travel in one minute
    15·2 answers
  • Ten times the sum of three and number is -21. what is the number?
    12·2 answers
  • 8w^2+8w+9 <br> what's the value if w=2
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!