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
mash [69]
3 years ago
6

Three points have coordinates A (0 , 7) , B (8 , 3) and C (3k , k)

Mathematics
2 answers:
SashulF [63]3 years ago
5 0

9514 1404 393

Answer:

  k = 2.8

Step-by-step explanation:

Segments AB and AC are on the same line, so have the same slope. Using the slope formula, we have ...

  m = (y2 -y1)/(x2 -x1)

  (3 -7)/(8 -0) = (k -7)/(3k -0)

Multiplying by 6k gives ...

  -3k = 2(k -7)

  -5k = -14 . . . . . . subtract 2k

  k = 14/5 = 2.8 . . . . divide by -5

AfilCa [17]3 years ago
4 0

Answer:

k=14/5

Problem:

Three points have coordinates A (0 , 7) , B (8 , 3) and C (3k , k)

Find the value of the constant k for which C lies on the line that passes through A and B

Step-by-step explanation:

The slope of a line containing points (a,b) and (c,d) is found by computing (b-d)/(a-c). This is just the change in y divided by the change in x.

The slope of a line containing points (0,7) and (8,3) is (7-3)/(0-8)=4/-8=-1/2.

The slope of a line containing points (0,7) and (3k,k) and (8,3) is still -1/2 because it doesn't matter what two points on a line you use to calculate the slope. The slope will remain the same no matter the pair of points on the line you choose for it's calculation.

So lets pretend the question is now find the point (3k,k) such that a line with slope -1/2 goes through (3k,k) and (0,7).

We want to solve the equation:

(k-7)/(3k-0)=-1/2

Simplify denominator

(k-7)/(3k)=-1/2

Cross multiple

(k-7)(2)=(-1)(3k)

Distribute or multiply

2k-14=-3k

Subtract 2k on both sides

-14=-5k

Divide both sufes by -5

-14/-5=k

Simplifying fraction

14/5=k

You might be interested in
There are 32 homes on Willis Street 1/4 of the homes Street have gas heat. How many homes on Willis Street have gas heat?
ycow [4]
8 houses have gas heat.
Hope this helps!
5 0
3 years ago
Read 2 more answers
What is 79.623 rounded to the nearest hundred??
kondaur [170]
79.623 rounded to the nearest whole would be 80 
8 0
3 years ago
Determine the domain of (f/g) (x) when f(x)=1/x and g(x)= sqrt x+5
ra1l [238]

Answer:

all work is answer and shown and pictured

7 0
3 years ago
Read 2 more answers
Compute 41, 42, 43, 44, 45, 46, 47, and 48. Make a conjecture about the units digit of 4n where n is a positive integer. Use str
padilas [110]

Answer:

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

Step-by-step explanation:

4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

To prove this conjecture

4^1 = 4\\4^2 = 16 unit digit = 6

hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1  to 8 )

8 0
3 years ago
Find the center of the equation 4x2 + y2 + 8%-5= 0.<br> O (-1,0)<br> (1,0)<br> (2.0)
balu736 [363]
Vertex: 0,4.92
focus: 0,4.8575
axis of symmetry: x = 0
directrix: y = 4.9825
3 0
3 years ago
Other questions:
  • Can someone explain the snake method, I don't understand how to do it
    13·2 answers
  • If an inequality uses the phrase at most, it will require a greater than symbol
    6·2 answers
  • Solve the system of equations 3r – 4s = 0 and 2r + 5s = 23.
    8·1 answer
  • On November 7, 2013, Twitter began to sell shares of its company and Naomi purchased 20 shares for $26 each. It went up $3.15 ev
    8·1 answer
  • I don’t understand Help please???!!
    15·1 answer
  • A store owner determined 80% of customers bought a drink and 30% of customers bought a snack. If the store sold 120 snacks that
    13·1 answer
  • Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of f
    15·1 answer
  • PLEASE HELP! 43 POINTS
    12·2 answers
  • PLS HELP I DONT UNDERSTAND :( WILL GIVE BRAINLIEST + 25 POINTS!!
    12·1 answer
  • The figure is made up of a semicircle and a triangle. Find the perimeter. Round your answer to the nearest hundredth. 25 ft 7 ft
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!