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
Simplify<br> Three over five<br> Or three fifths
serg [7]

3/5 cannot be simplified into a smaller fraction.


7 0
3 years ago
Read 2 more answers
Write the expression for when you translate the graph of y = |3x− 5| one unit to the right. Plzz help
AfilCa [17]

Answer:

2<x<4/3

Step-by-step explanation:

Given the equation of a graph to be y = |3x− 5|, if the equation is one unit to the right, this can be expressed as |3x-5| > 1.

Solving the resulting equation

|3x-5| > 1.

Since the function 3x-5 is in a modulus sign, this means that the function can take both negative and positive values.

For positive value of the function;

+(3x-5) > 1

3x > 1+5

3x>6

x>6/3

x>2 ... (1)

For the negative value of the function;

-(3x-5) > 1

On expansion

-3x+5 > 1

-3x > 1-5

-3x > -4

Multiplying through by -1 will also change the inequality sign

x < -4/-3

x < 4/3...(2)

Combining equation 1 and 2, we have;

2<x<4/3

6 0
3 years ago
Read 2 more answers
The volume of a cylinder is 4 pi x3 cubic units and its height is x units.
Rzqust [24]

Answer:

2x

Step-by-step explanation:

The volume of a cylinder, V is given by the formula,

V=\pi r^{2}h

Where, r is the radius and h is the height of the cylinder.

Here, V=4\pi x^{3}, h=x. Plug in these values and solve for radius, r.

This gives,

V=\pi r^{2}h\\4\pi x^{3}=\pi r^{2}x\\r^{2}=\frac{4\pi x^{3}}{\pi x}\\r^{2}=4x^{2}\\

Taking square root both sides, we get

\sqrt{r^{2}}=\sqrt{4x^{2}}\\r=2x

Therefore, the radius of the cylinder can be expressed as 2x.

6 0
3 years ago
A mosaic at the art museum is divided into 6 sections that each contain about the same number of tiles. There are 2,889 tiles to
AlexFokin [52]

Answer

Find out the how many tiles are in each section .

To prove

Let us assume that the number of tiles are in section are be x.

As given

A mosaic at the art museum is divided into 6 sections that each contain about the same number of tiles.

There are 2,889 tiles total in the mosiac .

Than the equation becomes  

6 × x = 2889

x = \frac{2889}{6}

x = 481.5

Therefore the total number of tiles in each sections are 481.5 .


7 0
3 years ago
What is a polynomial function
kakasveta [241]
Polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
5 0
3 years ago
Read 2 more answers
Other questions:
  • Beth's team raised $4,239 in a fundraiser. When Beth sends in the information for the
    14·1 answer
  • Please answer 7 and 8 for mark as brainliest
    9·1 answer
  • The binomial formula has two parts. The first part of the binomial formula calculates the number of combinations of X successes.
    6·1 answer
  • FIND THE VALUE OF X PLEASE HELP PLEASE AND THANK U
    14·1 answer
  • What are the multiples of the factors of 15
    6·1 answer
  • Consider the statement : Congruent triangles are always similar. Which of the following statements is an example of the statemen
    6·1 answer
  • There is a brick patio around a fire pit, as shown. Use 3.14 for pi.
    11·1 answer
  • Please help ASAP. Will give brainliest!
    5·1 answer
  • 6th grade math plz help?
    14·2 answers
  • What is ACB on the diagram below?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!