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
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 = 1.5xLet'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.
The manger of a water park keeps track of the amount of money collected, M, and the number of tickets,T, each day.
Answer: The variable t us the dependent variable because it affects the amount of money collected, m, each day.
When you purchase a car in the future, what are at least 3 things
you will have to think about first?
Answer:
How much it cost!? Will it fly?! How far will it fly?!
Step-by-step explanation:
The distance between two cities on a map is 6cm. If the scale one the map is 2 cm=50 miles, how many miles apart are the two cities
Work Shown:
2 cm : 50 miles
3*(2 cm) : 3*(50 miles)
6 cm : 150 miles
-X + 2y= -3 and -8x — 3y= -5
Answer:
x=1, y=-1. (1, -1).
Step-by-step explanation:
-x+2y=-3
-8x-3y=-5
----------------
-8(-x+2y)=-8(-3)
-8x-3y=-5
------------------------
8x-16y=24
-8x-3y=-5
-----------------
-19y=19
y=19/-19
y=-1
-x+2(-1)=-3
-x-2=-3
-x=-3+2
-x=-1
x=1
(1, -1)
Answer:
x = 1, y = -1
or as an ordered pair, (1, -1).
Step-by-step explanation:
-x + 2y = -3
-8x — 3y = -5
Multiply first equation by -8:
8x - 16y = 24
Add this equation to the second equation:
-19y = 19
y = -1.
Plug y = -1 into the second equation:
-8x - 3(-1) = -5
-8x + 3 = -5
-8x = -8
x = 1.
find the inverse function f(x)=1/2x+2
Answer:
y=2x-4
Step-by-step explanation:
f(x)=1/2x+2
y=1/2x+2
-----------------
x=1/2y+2
1/2y=x-2
y=2(x-2)
y=2x-4
juliana wrote the terms below. –8, –4, 0, 4, 8, 12 what do these terms represent? an arithmetic series an arithmetic sequence a geometric series a geometric sequence
Answer:
B. an arithmetic sequence
Step-by-step explanation:
hope this helps :)
1. You are planning an extended trip to Mexico. You have a new smartphone to keep in touch with your friends but are concerned about the roaming charges since you will be outside the home network service area. Your plan costs $40.00 per month plus $0.35 per minute for roaming charges. Write a linear model relating your monthly cost, C, and the roaming minutes, t.
A: C = $40 + $0.35t
B: C = $40 $0.35t
C: C = $0.35 + $40t
D: C = $0.35 $40t
What are the steps to convert a number from standard notation to scientific notation?
Answer:
Step-by-step explanation:
The goal in scientific notation is to express a value in terms of a number that contains a single unit before the decimal point.
Examples:
10000: 1.0 x 10^4
23456: 2.3456x10^4
In both cases, the x10^4 is telling us to multiply the first number by 10,000. 10^4 is the same as 10x10x10x10 = 10,000
The justification for scientific notation is that is makes expression large and small numbers much easier, as well as reduces errors due to an incorrectly placed decimal.
An example: Divide 2500000000 by 5000. That would normally require setting up a long-hand division problem that not only wastes paper and pencil, but is also prone to decimal point errors.
Do the same problem with scientific notation:
Count the places you want to move the decimal point backwards to just beyond the 5 in 2500000000. It takes nine steps to move the decimal point to between the 2 and 5: 2.5 followed by 8 zeros. That's a total of next steps to go in front of the 5. This is written 2.5 x 10^9
5000 is represented by 5.0x10^4
Now when we divide the same numbers, but in scientific format, it is easier to see the answer:
(2.5x10^9)/(5.0x10^4)
2.5/5 = 0.5
10^9/10^4 = 10^5 [The exponents are subtracted when dividing with exponents: 9-4 = 5]
Put them together to find the final answer: 0.5x10^5
Then move the decimal point one spot to the right and reduce the exponent by 1:
5.0x10^4
------
Add exponents when multiplying: 10^3 x 10^5 = 10^8 (3+5=8)
Subtract when dividing: 10^7/10^2 = 10^5 (7-2=5)
Multiply when there is an exponent raised to another exponent: (10^4)^3 = 10^12 (4x3 = 12)
Autumn wants to invest $1000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your reasoning. (4 points)
Part B: Autumn wants to invest in an option that would help to increase her investment value by the greatest amount in 7 years. Will there be any significant difference in the value of Autumn's investment after 7 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 7 years for each option if the equation for option 1 is f(x)=100x + 1000 and the equation for option 2 is g(d) = 1000(1.1)d
Answer:
See belowStep-by-step explanation:
Part AAccording the table, the yearly amount increases by 100 dollars in option 1 and 1.1 times in option 2.
It means the function is linear in option 1 and exponential in option 2.
Part BCalculate the amount of total value in each case substituting x or d by 7 and compare the amounts:
f(7) = 100*7 + 1000 = $1700g(7) = 1000*(1.1)^7 = $1948.72 (rounded)As we see the option 2 is better choice and the difference is:
$1948.72 - $1700 = $248.72please keep it simple.
Answer:
[tex]z^{2} +\frac{1}{2} +11z[/tex]
Step-by-step explanation:
→ Minus the z² terms
[tex]1\frac{1}{2} z^{2} -\frac{1}{2} z^{2}=1 z^{2}[/tex]
→ Minus the whole numbers
[tex]3\frac{1}{2} -3=\frac{1}{2}[/tex]
→ Add the z terms
11z
Find the equation of the line.
the line go through 2 points ( -4 ; -5 ) and ( 6 ; 4 )
ANSWER: [tex]y=\frac{9}{10}x -\frac{7}{5}[/tex]
ok done. Thank to me :>
If a new car is valued at $26,000 and 10 years later it is valued at $7000, then what is the average rate of change
of its value during those 10 years?
Answer:
The change in value is 19,000 altogether and 1900/year
Step-by-step explanation:
Change in value:
initial value - final value
= $26,000 - $7000
= $19,000
Change in value/year:
change in value/time
= $19,000/10
= $1900/year
PLS HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
R=11cm, r=3cm
Step-by-step explanation:
π(R²-r²) = π(121-9) = 112π cm² = 35.63cm².
hope this helps you.
A piece of timber is
x
cm long.
How long would 3 pieces of timber be put together in a line?
Answer:
3x cm long.
Step-by-step explanation:
If one piece is x cm
and there are 3 together, presumeabley the same length
then you'd just need to multiply the length 3 times, therefore 3x respresents multiplying x 3 times.
Have a good day!
Answer:
3x cm long
Step-by-step explanation:
3 times x is 3x
if 10 apples cost $1 how much would it cost per Apple
Answer:
10 cents per apple
Step-by-step explanation:
1 divided by 10 which is 1. And move the decimal one place to the left, leaving you with .1 or 0.1 or 0.10
pleeeeeeeease help meeeee
Answer:
45
Step-by-step explanation:
First, we have to find the Nth term of this sequence. Since this is linear we can just find the difference to get the n. For example, we can do 3-2 which is one and we can also do 5-4 which is also 1 which confirms that the n is 1. So in other words, 1n However, we don't write the 1 in front of the n because the n itself represents 1n. Next, we have to take away 1 from the first term, which also gives us 1. This is the adjustment to the 1n. So our answer is n+1, which is the nth term for this linear sequence. So now we just substitute 44 into the equation. 44+1=45, which is the 44th term.
Which inequality represents this statement?
A number is no more than 5.
n<5
n≥5
n>5
n≤5
Answer: the last one!! [tex]n\leq 5[/tex]
Step-by-step explanation:
When there is a line under it means no more than!
what is the greatest common factor of 32 and 56
Select all the equations that have {7} as its solution set. 65−2x=6x+9 9−x=14x 3+4x=5x−4 x2+1=8x−5
Answer:
the answer is this hope it helps im not sure if its all right good luck.
Step-by-step explanation:
A. 65-2x=6x+9
B. 9-x=14x
C. 3+4x=5x-4
d is wrong
The first and third equations have {7} as their solution set.
What is an equation?It is a mathematical statement that is made up of two expressions connected by an equal sign.
The first equation is
65−2x=6x+9
Rearranging the above equation gives
8x = 65-9 = 56
i.e x = 7
Consider the second equation,
9−x=14x
i.e x = 9 / 15 = 0.6
The third equation is:
3+4x = 5x−4
i.e x = 7
The last equation is
x^2+1 = 8x−5
Its solution is not equal to 7.
As a result of the preceding equations, we can conclude that only the first and third equations have "7" as their solution set.
To learn more about equation, use the link given below:
https://brainly.com/question/29538993
#SPJ2
The angle measures of an isosceles triangle are shown. Find the value of w.
Answer:
[tex]w=7[/tex]
Step-by-step explanation:
Using the Angle Sum Theorem which states that all the interior angles in a triangle add up to 180 degrees you can use that to solve for w with the following:
[tex]62 +9w-1+8w=180[/tex] First combine like terms
[tex](62-1)+(9w+8w)=180[/tex]
[tex]61+17w=180[/tex] Then subtract 61 from both sides.
[tex]17w=180-61[/tex]
[tex]17w=119[/tex] Now divide by 17
[tex]w=119/17[/tex]
[tex]w=7[/tex]
I need help eeeeeeeee
Answer:
one left so they all shift by 1
In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has?
A. x + y = 16. 0.10 x + 0.25 y = 2.95.
B. x + y = 16. 0.05 x + 0.25 y = 2.95.
C. x + y = 2.95. 0.10 x + 0.25 y = 16.
D. x + y = 16. 0.01 x + 0.25 y = 2.95.
Answer:
A. x + y = 16; 0.10x + 0.25y = 2.95Step-by-step explanation:
Given:
Dime is $0.10, number of dimes is x, total of dimes = 0.10xQuarter is $0.25, number of quarters is y, total of quarters is 0.25yNumber of coins is 16:
x + y = 16Total amount is $2.95:
0.10x + 0.25y = 2.95Correct choice is A
The table shows the relationship between the two variables. Which selection describes the relationship?
The table and options are below!
Answer:
D.
Step-by-step explanation:
It's not linear but it is decreasing.
Answer: Firstly, we take a look at the Y numbers to figure out if we're increasing or decreasing. Obviously, the numbers are going into the negatives so we know it's decreasing. After plotting the graph you'll see it's constant and in a straight line making it linear. So, your answer would be decreasing; linear.
Will give thank,brainly and 5 stars!
The second and last one.
The second one multiplies the cost of each type of ticket by two, therefore saying that you wanted to buy two of each type of ticket.
The last one multiplies the cost of a single ticket of all three types and multiplies it by 2.
Answer:
The second and last one
Step-by-step explanation:
Hope this helps and have a good day!
Jorge has 2% + 1 saved in his piggy bank. Lou Ellen has X-2 saved in the bank. What is
the minimum amount Jorge will have in savings for them to have $163 together. Letj
represent Jorge,
Answer:
yeyeyeeyeyeeyeey
Step-by-step explanation:
y=x−4
y=4x+2
Find x and y
Answer:
x = -2
y = -6
Step-by-step explanation:
x - 4 = 4x + 2
-4 = 3x + 2
-6 = 3x
x = -2
y = -2 - 4; y = -6
How many different terms are in the expression? 28s + 3t+ 6b + 21f
Answer:
4
Step-by-step explanation:
In math, the word difference is the result of subtracting one number from another. It refers to the difference in quantity between two numbers. In math, we get the difference between two numbers by subtracting the subtrahend (the number being subtracted) from the minuend (the number being subtracted from).
[tex] \huge \red{\boxed{ \colorbox{black}{ \color{gold}{question}}}}[/tex]
Need help~
[tex] \sqrt{3 + 3 + 3 + 3 + 3 + 3} [/tex]
Answer:
3√2
Step-by-step explanation:
First, combine all the numbers in the square root, and then square root the number provided:
√(3 + 3 + 3 + 3 + 3 + 3) = √18
When square rooting, first, find prime factors of the number, 18. If there are pairs, they will be combined into a whole number:
√18 = √(3 * 3 * 2) = 3√2
3√2 is your answer.
~
Which sequence shows the numbers in order from least to
greatest?
1
2
-3
4
3
-3
OA) 2 3
} }
OB) Ź. *.
oc) * * Ź
OD) * *
4
Answer:
-3 1 2 3 4
Step-by-step explanation:
Answer:
-3 1 2 3 4
Step-by-step explanation: