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 few days​

Answers

Answer 1

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 = 2xy = 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.


Related Questions

Mrs. Taylor bought 16⅓ yards of material. She used 5¾ yards. How much material does she have left? *

Answers

Answer:

10\frac{7}{12}

Step-by-step explanation:

First thing you want to do is find the common denominator for \frac{1}{3} and \frac{3}{4}. You do this by multiplying to denominators together, so 3*4=12.

Next, multiple the numerators with the opposite denominator. 1*4=4 and 3*3=9.

Now you are left with \frac{4][12] and \frac{9}{12}.

Add those back to your numbers

16\frac{4}{12} - 5\frac{9}{12} = 10\frac{7}{12}

What’s the missing angle of 121 and 29

Answers

Answer:

I am going to guess that shape you are trying to find is an triangle

30˚

Step-by-step explanation:

A triangle angle is 180˚

So add 121 and 29

Which is 150

180 - 150 which is 30

So the missing angle is 30˚

Hope this helps!

Which function represents the following graph? On a coordinate plane, a cubic function has an inflection point at (negative 3, 3) and crosses the x-axis at (0, 4. 5). Y = StartRoot x minus 3 EndRoot 3 y = StartRoot x 3 EndRoot 3 y = RootIndex 3 StartRoot x minus 3 EndRoot 3 y = RootIndex 3 StartRoot x 3 EndRoot 3.

Answers

The function represents the graph is (d) [tex]y = \sqrt[3]{x+3} + 3[/tex]

The points on the graph are given as:

[tex](x,y) = (-3,3)[/tex] --- the inflection point

[tex](x,y) = (0,4.5)[/tex] --- the y-intercept

The function that satisfy the above points is:

[tex]y = \sqrt[3]{x+3} + 3[/tex]

The proof is as follows:

At the inflection point, we have the x value to be -3.

So, the function becomes

[tex]y = \sqrt[3]{x+3} + 3[/tex]

[tex]y = \sqrt[3]{-3+3} + 3[/tex]

[tex]y = \sqrt[3]{0} + 3[/tex]

[tex]y = 0+ 3[/tex]

[tex]y = 3[/tex] ---- the y-value at the inflection point is true for x = -3

Also, at the y-intercept, we have the x-value to be 0

So, the function becomes

[tex]y = \sqrt[3]{x+3} + 3[/tex]

[tex]y = \sqrt[3]{0+3} + 3[/tex]

[tex]y = \sqrt[3]{3} + 3[/tex]

[tex]y = 1.45+ 3[/tex]

[tex]y = 4.45[/tex] ---- the y-value at the y-intercept is true for x = 0

Hence, the function represents the graph is (d) [tex]y = \sqrt[3]{x+3} + 3[/tex]

Read more about graphs and functions at:

https://brainly.com/question/25918641

Answer:

D

Step-by-step explanation:

Please help!
Can someone write out an explanation for how to simplify:
[tex](4x^{-4} )^{-3}[/tex]

I'm having trouble understanding it so a step by step would be helpful!

Answers

First, express x^-4 with a positive exponent. You can do this by putting it in the denominator of a fraction.
(4 • 1/x^4)^-3
Next, multiply the terms in the parentheses.
(4/x^4)^-3
Express ^-3 as a positive exponent by finding the reciprocal of the fraction inside the parenthesis.
(x^4/4)^3
Then, distribute the power into the parentheses. (Numerator and denominator)
x^12/64

Hope this helps!

If cos(θ)= -2/3 and θ lies in quadrant II, find the value of cotθ

Answers

[tex]\text{Given that,}\\\\\cos \theta = - \dfrac 23\\\\\implies \cos^2 \theta = \dfrac 49\\\\\implies 1- \sin^2 \theta = \dfrac 49\\\\\implies \sin^2 \theta =1-\dfrac 49\\\\\implies \sin^2 \theta =\dfrac 59\\\\\\\text{Now,}\\\\\cot^2 \theta = \dfrac{\cos^2 \theta}{\sin^2 \theta} \\\\\\\implies \cot^2 \theta = \dfrac{\tfrac 49}{\tfrac 59}\\\\\\\implies \cot^2 \theta = \dfrac 49 \times \dfrac 95\\\\\\\implies \cot^2 \theta = \dfrac 45\\\\\\[/tex]

[tex]\implies \cot \theta = \pm\sqrt{\dfrac 45} = \pm \dfrac 2{\sqrt 5}\\\\\\\text{Since}~ \theta ~ \text{lies in the second quadrant,} \cot \theta ~\text{will be negative.}\\\\\text{Hence,}~ \cot \theta = - \dfrac{2}{\sqrt 5}[/tex]

Answer:

yysywywyyw7e7eueuuwuwuuwueu3u3

The price of a package of 4 pens is $8.00. The same pens are sold at $2.50 each. If Alex bought three packages of pens rather than buying 12 pens individually, the amount he saved on 12 pens is the percent of the amount he paid is

Answers

Answer:

25%

Step-by-step explanation:

alex paid:

8x3 = 24

he saved:

2.50x12-24 = 30 - 24 = 6

percent:

(6/24)x100 = 25%

Solve for x.
(x+16)
(4x-5)°
11
7
9
13

Answers

Answer:

4

3

+

5

9

2

8

0

Step-by-step explanation:

mathmatic equation
solve y:
7=4(3y-3)

Answers

Answer:

y=1.58

Step-by-step explanation:

7=4(3y-3)

Simplify the distributive property.

7=12y-12

Add 12 to both sides.

19=12y

Divide 12 on both sides.

1.58=y

-hope it helps

Use the distributive property
12y-12=7
-12 goes to the other direction by changing its sign
12y=7+12
12y=19
Divide
Y=19/12

A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. He collects data for 15 randomly selected students and determines the value for s was 0.67.

Answers

The interpretation of the value of s being 0.67 is that: the typical distance between the observed grade points and predicted grade points was about 0.67 points.

The given parameters are:

n = 15s = 0.67

Variable s

In regression, the variable s represents the average distance that the observed values fall from the regression line

The grade points

In this case, we have:

The observed grade points and The predicted grade points

Hence, 0.67 represents the typical distance between the observed grade points and predicted grade points.

Read more about regression at:

https://brainly.com/question/25472374

The U.S. Energy Department states that 60% of all U.S. households have ceiling fans. In addition, 29% of all U.S. households have an outdoor grill. Suppose 13% of all U.S. households have both a ceiling fan and an outdoor grill. If a U.S. household is randomly selected, the probability that the household has neither a ceiling fan nor an outdoor grill is

Answers

Answer:

Very sorry if this is no help

Step-by-step explanation:

PLEASE HELP I"LL GIVE BRAINLIST

Every week, Fred deposits $84 into his savings account, which is 20% of his weekly income. How much income does Fred make each week?

$480

$420

$510

$505

Answers

Answer: 420 dollars.

Step-by-step explanation:

Answer:

Total income, $420.

Step-by-step explanation:

if $84 is 20% of freds income, then freds income could be modeled by the equation

Income = 84/.2 which equals $420 ((((ganggang)))

to check this, you can take his total income (420) and multiply it by 20%, and if we get 84, we are correct, 20% of freds income($420) IS in fact $84.

420*.2 = $84 proving ourselves to be correct.

3/4 of analisa's friends came to her birthday party. express this fraction as a percant and a decimal.

Answers

Answer:

0.75 And 75%

Step-by-step explanation:

If 3/4 came then 25, 50, 75, 100 what is the 3rd number of of those 4

the average weight of 6 boys is 40 kg .Two boys weighing 40kg and 20kg left the group.Find the average weight of the remaining four boys​

Answers

the average weight of 4boys 39.6 is Wight

A class has 6 boys and 14 girls. What is the ratio in simplest form that compares number of boys to total number of students?
A. 6:14
B. 6:20
C. 3:7
D. 3:10

Answers

C) 3:7
hope this is helpful!

Find the sum of 4+3x and 5-4x+2x 2

Answers

Answer:

[tex]\huge\color{green}\boxed{\colorbox{black}{Answer ☘}}[/tex]

To find - sum of the given two terms.

[tex](4 + 3x) + (5 - 4x + 2x {}^{2} ) \\ 4 + 3x + 5 - 4x + 2x {}^{2} \\ = > 2x {}^{2} - x + 9[/tex]

—————————————————

[tex]\color{purple}\boxed{\colorbox{black}{Additional Information♡}}[/tex]

Here ,

we basically added the like terms together..

like, the terms ( 3x and -4x ) will be added together.. and the terms ( 4 and 5 ) will be added together...

since there's none other term having "" as the coefficient.. so 2x² will be left as it is!

hope helpful~

~ExhaustedZombie

The sum of the expression 4+3x and 5-4x+2x² is 2x² + 7x + 9

How to find sum of expressions

Given:

4+3x

5-4x+2x²

Sum means addition of expressions

(4+3x) + (5-4x+2x²)

= 4 + 3x + 5 - 4x + 2x²

= 2x² + 3x - 4x + 5 + 4

= 2x² + 7x + 9

Therefore, the sum of the expression is 2x² + 7x + 9

Learn more about sum:

https://brainly.com/question/11562149

Angela is following this recipe to make biscuits.
Angela uses 1.1 litres of syrup.
How much sugar is needed in kg?

Recipe: Makes 14 biscuits
110 g margarine
100 g sugar
275 ml syrup
200 g oats
50 g sultanas

Answers

Answer:

  0.4 kg

Step-by-step explanation:

A proportion can be used to find the amount of sugar.

  x/(1.1 L) = (0.1 kg)/(0.275 L)

  x = (1.1)(0.1)/0.275 kg = 0.4 kg

Angela needs 0.4 kg of sugar for her biscuits.

What is a bond and how do you make money from it?

Answers

Answer:

Bonds are among a number of investments known as fixed-income securities. They are debt obligations, meaning that the investor loans a sum of money (the principal) to a company or a government for a set period of time, and in return receives a series of interest payments (the yield).

Step-by-step explanation:

65,754.59 round it to the nearest tenth

Answers

Answer:

65,754.6

Step-by-step explanation:

When rounding, the last digit is number you need to observe. If the digit is less than 5 (4,3,2,1), then round down. If it is 5 or greater, then round up.

A scale drawing of AJ’s room shows the length as 5 cm and the width as 8 cm. Using a scale of 1 cm = 10 ft, find the area of the room.

Answers

Answer:

4000 sqft

Step-by-step explanation:

you multiply 5*10 which equals 50 then 8*10 which equals 80 then to find area you multiply 50*80 which equals 4000 sqft


I really need help!!

Answers

Answer:

Red: y=4

Green: x=-1

Yellow: x=6

Blue: x=-2

Step-by-step explanation:

The lines are all passing through the Axis, so there is no slope for each line.

Can someone pls help I’m trying to solve for x

Answers

Answer:

x = 2.3

Step-by-step explanation:

x = 5*(13-12.54) = 2.3

Answer:

127.7

Step-by-step explanation:

you do 12.54 + 13 = 25.54

then 25.54 x 5 = 127.7

I need help with this

Answers

Answer:

5 + 5 = 10

10 + 10 = 20

20 + 20 = 40

40 + 40 = 80

80 is the answer.

if a customer spent $60, how many people did they buy food and beverages for?

Answers

They could have spent $10 on each person of a group of 6

tASAP HELP + 50 POINTS
Find the value of x. Show all the work

Answers

Answer:

7

Step-by-step explanation:

im pretty sure at least. since x is on a midpoint, it'd half of 14.

See those similar lines

The line.of length x passes through midpoint of the traingles on opposite sides

At this case according to BPT theorem

2x=14x=14/2x=7

levi is a salesperson who sells computers at an electronics store he makes a base pay of $60 each day and then is paid a $5 commission for every computer sale he makes make a table of values and then write an equation for p in terms of x representing Levi's total pay on a day on which he sells x computers​

Answers

Answer:

equation : P(x) = 5x+60

Table :

If x (levi sells this many computers)

then y (levi makes this much money)

x : 0 ; 1 ; 2 ; 3 ; 4 ; 5 so on...

y : 60 ; 65 ; 70 ; 75 ; 80 ; 85 so on...

Step-by-step explanation:

This equation can be modeled by P(x) = 5x+60

P= levi's total pay

x = number of computers sold

This equation can be input into a graphing calculator to find a table of the corresponding x and y values for this equation. To solve without using a calculator, plug in a certain value for x in the equation and solve for y to get its corresponding value.

Someone please help me with this question And you can get 20 points

Answers

[tex]\text{Consider the slope - intercept form} ~y = mx +c,\\\\ \text{where m is the slope and and c is the y-intercept.}\\\\(a) \\\\y = -\dfrac 12 x +8 \\\\\text{This is in a form of y = mx +c, so}\\\\\text{Slope, m =}-\dfrac 12 ~ \text{and}~ \text{y - intercept , c =8}\\\\(b)\\\\y = 9x -2 \\\\\text{This is in a form of y = mx +c, so}\\\\\text{Slope, m =9}~ \text{and}~ \text{y - intercept ,}~ c =-2\\\\[/tex]

Suppose that n is a positive number and Log10 n = q. Which expression always equals the value of Log10 n^2?

Answers

2q

Answer:

solution given:

[tex]log_{10} n=q[/tex]

now

[tex]  Log_{10 }n^2=?[/tex]

by using property of logarithms

[tex]log_{a} n^p=p log_{a}n [/tex]

now

[tex]  Log_{10 }n^2=2 Log_{10 }n[/tex]

=2q

since [tex]log_{10} n=q[/tex]

Step-by-step explanation:

Evaluate the expression when a=-2 and x=7.
-2a+x

Answers

Step-by-step explanation:

-2a + x

Putting values of a = - 2 and x = 7

-2(-2) + 7

4 + 7

= 11

The answer is 11 bc -2*-2 =4+7=11

Which functions are invertible
Select each correct answer

Answers

Answer:

  the top two

Step-by-step explanation:

For a function to be invertible, it must pass the "horizontal line test." That is, there can be no horizontal line that will intersect the graph in more than one place. The bottom two graphs fail this test, so do not represent invertible functions.

The two top graphs show invertible functions.

Two​ trains, Train A and Train​ B, weigh a total of 378 tons. Train A is heavier than Train B. The difference of their weights is 210 tons. What is the weight of each​ train?

Answers

Answer:

Train A is 294 tons and Train B is 84 tons

Step-by-step explanation:

You can create a system of equations

A+B=378

A-B=210

Adding both would get

2A=588

2A/2=588/2

A=294

Now plug that in to the second equation (either is fine)

294-B=210

B=84

Check

294+84=378

Step-by-step explanation:

Let,

Weight of train A = x

Weight of train B = y

x + y = 378 (1)

x - y = 210 (2)

Now,

On adding 1 and 2

x + y + x - y = 378 + 210

2x = 588

x = 588/2

x = 294 tons

From 1

294 + y = 378

y = 378 - 294

y = 84 tons

Other Questions
What is 6 percent of 200 plz show your work thirty tickets were sold for a concert, some at 60 cent and the rest is at $1. If the total was raised to $22, how many had the cheaper tickets. Find the 75th term of the arithmetic sequence16, 15, 14, Emilio borrows $1200 from a bank with 8% simple interest per year. How much is the interest What factors led to the rise of Americas first political parties? Why was the Albany Plan of Union less successful than the Iroquois Confederacy?A. It started a war between the southern and northern colonies.B. It was rejected by the colonists, so they remained separated.C. It split on whether to support the British or the French.D. It set up a government in which lawmakers were appointed, not elected. 1/2 of a bowl of cereal is divided equally between 4 bowls. how much cereal is in each bowl Why were people near the Yellow River able to grow enough food to support a civilization? aTwo taxi companies have different pricing systems. Company A charges a flat fee of $8 plus $0.10per mile driven. Company B does not charge a flat fee, but charges $0.60 per mile driven. At whatdistance do both companies charge the same amount? How to get a fever in 10 mins or less 2. What characteristics of bougainvilla plant makes animals to be afraid? A. It has spores on its stem C. It has thorns on its stem B. It has spreading, feathery root stem D. It has light rounded waxy leavesPLEASE HELP ME I REALLY NEED THE CORRECT ANSWER RIGHT NOW!!!! A regular hexagon is rotated 360 about its center. How many times does the image of the hexagon coincide with the pre image during the rotation?A. 1 timeB. 3 timesC. 12 timesD. 6 times A passive eruption that primarily forms lava flows and minor scoria is termed a __________________ eruption.a.Hawaiianb.Vulcanianc.Plineand.Strombolian X=-2y,x-y=9 solve by substitution SHOW ALL WORK 0. CHARITY Cain collects money on the weekends for his favorite charity. Thepast four weekends he collected $105, $170, $132, and $165. How muchdoes he have to collect on the fifth weekend to average at least $150 forthe five weekends? who was the first person to study the embryos of different species QUESTION 19 PLEASE HELP ME ASAP explain different users of computer in briefly? A merchant buys a television for $125 andsells it after a 60% mark-up. How much doeshe sell the television for? THIS IS FOR THE BOOK " THE RED UMBRELLA" *I WILL GIVE BRAINLIST TO THE BEST and QUICKEST ANSWER!3. Knowing the conflict your character faces, what will the turning point be for him or her? Begin outlining the plot by starting with the climax.How does he or she get to that point? (That's the exposition and rising action. How is he or she changed as a result of the turning point?(That's the falling action and resolution.).4. Outline the plot of your narrative by recording at least three events in all stages except the climax, where you will have just one event. Thenplan your character's response to the events. What will he or she say, think, or do in light of the events you have planned?What happens in this stage of the story?Character's Response