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
ycow [4]
3 years ago
12

Point A is located at (5, 6) and point B is located at (8, −2) . What are the coordinates of the point that partitions the direc

ted line segment AB¯¯¯¯¯ in a 1:3 ratio?
Mathematics
2 answers:
spayn [35]3 years ago
6 0

Answer:

(6;3.33)

Step-by-step explanation:

To find the coordinates of the point that partitions in a 1:3 ratio, we use:

x=x_{1}+k(x_{2}-x_{1})\\y=y_{1}+k(y_{2}-y_{1})

Where k is the ration of partitions, \frac{1}{3} in this case.

Now, we replace all values:

x=x_{1}+k(x_{2}-x_{1})\\x=5+\frac{1}{3}(8-5)=5+\frac{1}{3}3=6

<em>So, the horizontal coordinate is 6.</em>

y=y_{1}+k(y_{2}-y_{1})\\y=6+\frac{1}{3}(-2-6)=6+\frac{1}{3}(-8)=3.33

<em>The vertical coordinate is 3.33.</em>

<em />

Therefore, the coordinates of the point that partitions the directed line segment AB in a 1:3 ratio is (6;3.33)

alekssr [168]3 years ago
5 0

Answer:

(6, 3 1/3)

Step-by-step explanation: Split this problem into x and y parts. In x direction, the length of the AB is (8-5)=3. So 1/3 from A would be 5+1/3(8-5)=6

In y, AB goes from 6 to -2, so the coordinate changes by (-2-6)=-8 units.

1/3 along this ling will be 6 + 1/3 (-2-6)=6-2 2/3=3 1/3

You might be interested in
Choose an appropriate metric unit of a typical house cat
valentina_108 [34]
Your answer is gram hope this helps that is what unit to use  :)
8 0
3 years ago
What is the greatest common factor of 9 21 60?
nordsb [41]
The greatest common factor (GCF) of 9, 21 and 60 is: 3

Factors of 9: 1, 3, 9
Factors of 21: 1, 3, 7
Factors of 60: 1, 2, 3, 4, 5, 6

The common factors between the three numbers are 1 and 3, but since 3 is the highest number, it is considered the GCF.
8 0
3 years ago
Select the one answer. 2x+3x3
gulaghasi [49]

Answer:

2 times x plus 3 times x cubed.

Step-by-step explanation:

2x = 2 * x = two times (multiplied) by x.

+ = plus.

3x^3 = 3 * x^3 = three times (multiplied) by x cubed.

~

7 0
3 years ago
I need help with all of them
lara [203]
Click on the picture! This is the explanation in accident I deleted it hope it helps!

6 0
3 years ago
The Johnson twins were born eleven years after their older sister. This​ year, the product of the three​ siblings' ages is exact
vodka [1.7K]
So there are 3 siblings: the first twin, the second twin, and their older sister.

Since the sister is older by 11 years, you can represent their relationship with the following equation;
age of twin = age of older sister - 11
t = s - 11

Representing this next part may be a little hard to show, but i'll do my best :)

Adding the ages together can be represented like this;
total age = t + t + s
If the product of their ages ( t * t * s ) is 1181 more than the sum, you can show it like this:
t * t * s = (t + t + s) + 1181
Now you substitute in (s - 11) for t because s = t - 11.
t * t * s = (t + t + s) + 1181\\&#10;(s-11) * (s-11) * s = ((s-11) + (s-11) + s) + 1181\\&#10;(s^{2}-22x+121)*s=s+s-11-11+1181\\&#10;s^{3}-22s^{2}+121s-2s=1159\\&#10;s^{3}-22s^{2}+118s-1159=0
Factor:
Since it's a third-degree equation, I just entered it into a polynomial solver in my calculator. There was only one factor listed, x = 19. Using (s - 19) = 0 as a factor, the equation becomes the following:
s^{3}-22s^{2}+118s-1159=0\\&#10;(s-19)(s^{2}-3s+61)=0
Using the quadratic formula, you get:
s= \frac{-b(+-)\sqrt{b^{2}-4ac}}{2a}\\&#10;s= \frac{-(-3)(+-)\sqrt{(-3)^{2}-4(1)(61)}}{2*1}\\&#10;s= \frac{3(+-)\sqrt{(9)-244}}{2}\\&#10;s= \frac{3(+-)\sqrt{-235}}{2}

Since you have a square root of a negative number, the answer will be imaginary. You cannot have an age that is imaginary, so the age of the older sister (s) is 19 years.

Because t = s - 11, that means that t = (19) - 11 = 8.
t is the age of the twins, so the twins are 8 years old.
8 0
3 years ago
Other questions:
  • In a circle a chord 10 inches long is parallel to a tangent and bisects the radius drawn to the point of tangency. How long is t
    15·1 answer
  • The great owlet moth has a wingspan of 12.13 inches.write this number as a mixed number.
    10·2 answers
  • Question: What are two steps in solving the inequality 5(x - 2) &lt; 9? Choose all that apply.
    5·1 answer
  • Last winter, the Kranepool family used 431 gallons of heating oil at a price of $4.12
    9·1 answer
  • You originally draw a design for an art contest on a 2 in. x 5 in. card. The second phase of the contest requires the drawing to
    7·2 answers
  • A square is inscribed in a circle. If the area of the square is 9 in2, what is the ratio of the circumference of the circle to t
    15·1 answer
  • Howard is laying an oak wooden floor in his house. The measurements of the floor are 14.5 feet by 40 feet. The wood is packaged
    11·1 answer
  • Claire climbs 555 feet to the top of a monument. She looks down and sees her friend, who is standing at point B in
    11·2 answers
  • Kylie is birdwatching and has seen 9 thrushes so far, as well as 24 other birds. Considering this data, how many of the next 88
    9·1 answer
  • Solve the following system of equations.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!