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
Soloha48 [4]
2 years ago
9

X/2 = Y/3 = Z/4. prove that :2X-Y+5Z / 3Y-X =3. note :: (/) is for a fraction aka divide. help pls I've been stuck on it for a f

ew days​
Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
5 0

The given equation

x/2 = y/3 = z/4

can be broken into three separate equations which I'll call equations (A), (B) and (C)

  • x/2 = y/3 ..... equation (A)
  • y/3 = z/4 .... equation (B)
  • x/2 = z/4 .... equation (C)

We'll start off solving for z in equation (C)

x/2 = z/4

4x = 2z ... cross multiply

2z = 4x

z = 4x/2 ... divide both sides by 2

z = 2x

Now let's solve for y in equation (A)

x/2 = y/3

3x = 2y

2y = 3x

y = 3x/2

y = (3/2)x

y = 1.5x

The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.

We won't be using equation (B) at all.

---------------------

The key takeaway from the last section is that

  • z = 2x
  • y = 1.5x

Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:

(2x-y+5z)/(3y-x)

(2x-y+5(2x))/(3y-x) ..... plug in z = 2x

(2x-y+10x)/(3y-x)

(12x-y)/(3y-x)

(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x

(12x-1.5x)/(4.5x-x)

(10.5x)/(3.5x)

(10.5)/(3.5)

3

We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.

You might be interested in
Calculate 2/3 of 27<br><br> Plssss help solve....
natali 33 [55]

Answer:

18

Step-by-step explanation:


5 0
3 years ago
PLEASE help! this is so difficult! i literally cannot solve it to save my effing life.
jeka57 [31]

For the first question

The image grew bigger the new triangle is bigger than the original one

The scale factor is 3 by finding the length of

CA prime divided by Regular CA

8 0
3 years ago
Please help I'll give brainiest
Komok [63]
For the first is 3864
The second is 1320
A=3.14(which is pie) x 20.5^2
A=420x pie
A=1320
For the third is 2544
3864-1320=2544
Sorry if this is wrong too.
8 0
2 years ago
Read 2 more answers
A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of m
posledela

Answer:

Check the attached document for the solutions, cheers

Step-by-step explanation:

Download docx
7 0
3 years ago
PLEASE HELP WILL MARK BRAINLY
mash [69]

Answer:

250 girls

Step-by-step explanation:

Please let me know if you want me to write an explanation for my answer :)

8 0
3 years ago
Other questions:
  • The markings of a standard ruler
    5·1 answer
  • Which of the following is a subset of {1,2,3}<br><br> {0}<br> {0,1}<br> {1,2,3}<br> {1,2,3,4}
    6·1 answer
  • Solve for x. x3 = 216
    14·2 answers
  • Alejandro was asked to solve a system of linear equations by using the substitution method. What is the error in his work below?
    9·2 answers
  • If the volume of a cube is 12,167 cubic inches, what is the length of a side of the square?
    6·1 answer
  • Find the distance between the points (5/2,3) and (3/2,8)
    13·1 answer
  • Anybody know the answer?
    9·1 answer
  • Find the area of the polygon:
    13·1 answer
  • I will give you a brainlyist if you salve and 50 points and 5 stars plz help
    7·1 answer
  • If 15 baseballs cost $9 how much would 30 cost
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!