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.
Noah is making grilled cheese sandwiches for friends. He has 24 ounces of cheese. He plans to split the
cheese evenly between 6 sandwiches.
Write an equation to determine how many ounces of cheese, c, Noah can use on each sandwich
How many ounces of cheese can Noah use on each sandwich?
Answer:
4 ounces
Step-by-step explanation:
6c = 24
c = 4
Answer: Noah can use 4 ounces per sandwich
an equation is c=24/6
Step-by-step explanation:
In order to join a yoga club you have to pay an annual fee and a fee per class. At Yoga For Us the annual fee is $30 and $5 per class. At Stretch Land the annual fee is $60 and
$2 per class. After how many classes would the fees be the same?
After 10
classes the feels the same.
It will take 10 classes for YOGA FOR US & STRETCH LAND to have the same amount of money spent on yoga classes.
For Yoga For Us after 10 classes . You would have spent 50 dollars for the classes,plus our $30 fee is (50+30) which is $80
For Stretch Land after 10 classes. You would have spent 20 dollars for the classes,plus our $60 fee is (60+20) which is $80.
Each yoga studio will have gathered $80 after 10 classes.
Hope this helps <3 & don't forget to drink water!!
Which mixed number is equivalent to the improper fraction 4 2/5?
4 2/5
7 4/5
8 2/5
9 3/5
the answer is 4 2/5, and I don't think others are equivalent to it
The equation y=1/8xrelates proportional quantities x and y. What is the value of x when y is 6?
Answer:
48
Step-by-step explanation:
6 = 1/8x
x = 48
the original price of a jacket was $74.00 .A store manager marked the price down by
25 1/2% . By how much was the price reduced?
Can somebody help me :
Answer:
A
Step-by-step explanation:
Negative numbers are smaller than positive numbers.
Answer:
Your correct 6.55 is a positive number while -6.5 is negitive and positive numbers are always larger then negitive ones
Hope This Helps!!!
How many Match sticks will be In Image 6?
Answer:
19
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
$8.00
Step-by-step explanation:
20% of 44.85=8.97
thats the closest to 8.00
Answer:
the answer is 9 dollars cuz the real answer is $8.97 and round to the nearest whole the answer is 9
Step-by-step explanation:
Given that f(x)=x-5 g(x)=5x and h(x)=-f(x+1)-3g(x-1), then what is the value of h(3)?
please show step by step answer.
Answer:
Step-by-step explanation:
f(x) = x - 5 and g(x) = 5x
- f(x + 1) = - ( x + 1 - 5 ) = 4 - x
- 3g(x - 1 ) = - 3 [ 5 (x - 1)] = 15 - 15x
h(x) = 4 - x + 15 - 15x = 19 - 16x
h(3) = 19 - 16(3) = - 29
do the values in this table represent a proportional relationship? x 2/4 6 8 y 1 2 3 4 yes, and the constant of proportionality is 12. yes, and the constant of proportionality is 2. no. i don't know.
Answer: No
Step-by-step explanation:
Determine the domain and range of the function f(x) = â€""|x| 2. The domain of the function is. The range of the function is.
The domain of the function f(x) = |x|² is the set of all real numbers (-∞ < x < ∞)
The range of the function f(x) = |x|² is the set of all real numbers greater than or equal to zero ( f(x) ≥ 0)
The given function is:
f(x) = |x|²
This can also be expressed as:
f(x) = x²
This is because the square operator cancels the effect of the absolute value
The function f(x) = x² is valid for all real values of x. Therefore, the domain of the function f(x) is -∞ < x < ∞
The range of the function f(x) is all positive real numbers. This is because the square of all numbers gives a positive number.
Range = f(x) ≥ 0
Learn more here: https://brainly.com/question/25915612
Answer:
1. all the real numbers
2. all numbers less than or equal to 2.
Step-by-step explanation:
A certain stock sold for $56.12 on Monday. On Tuesday it sold for $60.19. Find the increase in the price of the stock from Monday to Tuesday
Answer:
$ 4.07
Step-by-step explanation:
The problem is asking for the Increase in the stock price from Monday to Tuesday, meaning they want to know the difference between the stock price on Monday and Tuesday.
So we subtract Monday's price from Tuesday's price.
$60.19- 56.12 = $4.07
Write the quadratic equation whose roots are 1 and -2, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
I = 0
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5
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Save For Later
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Answer:
See belowStep-by-step explanation:
The quadratic equation in factored form:
a(x - α)(x - β), where a- leading coefficient, α and β - rootsWe have:
a = 3, α = 1, β = -2Substitute them to get:
3(x - 1)(x + 2)Converting this into standard form:
3(x - 1)(x + 2) =3(x² + x - 2) =3x² + 3x - 6Dose any one know the answers for geometry A: A semester exam
PLZ I NEED HELP FAST!!
Answer:
Step-by-step explanation:
82 +9=5000 thank me later
PLEASE HELP FAST!!!
3
11
2
Which ordered pair is a solution to the system of linear equations 3 x- y- fo and x+By-to-
10?
O
12
o 5.3
21
o 35
21
3:5
I\ need\ the\ answers\ for\ 6.07\ 8th\ grade\ on\ peak\ fueled
Answer:
what's the question that you need answered?
Step-by-step explanation:
?
can someone plz help me I need the answer asap
Answer:
no. c is the correct answer
Share 120 in the ratio 3:5:7
Answer:
24:40:56
Step-by-step explanation:
3+5+7=15
120/15=8 1 Ratio is 8
3x8=24
5x8=40
7X8=56
i dont know if its the easiest method
What is m<6
A.80
B. 100
C.70
D.110
Step-by-step explanation:
to fully answer we would need to see at least one specific size (segment lengths, angle sizes).
but there is not one in the whole visible picture. so, everything just stays relative.
just be the presentation in the picture, angle 6 is larger than 90 degrees. so, B or D would be right.
if it helps you, it is clear that 6 = 1 = 9 = 14 = 180-2 = 180-5 = 180-10 = 180-13.
a computer artist created a rectangular image measuring 55 125 scale factor of 2.5 what are the dimensions of the dilated image? quick!!
Answer:
sex
Step-by-step explanation:
69
NEED HELP NOW!!!
Properties of Perpendicular Bisectors Properties of Both Perpendicular Bisectors and Angle Bisectors Properties of Angle Bisectors
The bisector passes through the midpoint of a segment
The bisector is equidistant from the endpoints of the segment
The bisector can only exist if the original figure is a line segment.
The bisector cuts the original figure into two congruent parts.
The bisector is equidistant from portions of the figure.
Only one of each type of bisector exists in a plane.
The bisector passes through the interior of an angle.
The bisector creates a right angle with the figure.
The bisector is equidistant from the sides of the angle.
Which piece of information is incorrectly placed in the table?
A. The bisector cuts the figure into two congruent parts.
B. The bisector is equidistant from portions of the figure.
C. The bisector passes through the midpoint of a segment.
D. The bisector creates a right angle with the figure.
D.
Explanation:
a landscape of farmland bisected by long straight roads"
divide into two parts.
hope I help you ☺️❤️
:) :>
What would be the equation of the midline of this graph?
Answer:
Step-by-step explanation:
Vertices of the quadrilateral ABCD are,
A → (-5, 2)
B → (-3, 4)
C → (-2, 4)
D → (-1, 2)
By reflecting the given quadrilateral ABCD across x-axis to form the image quadrilateral A'B'C'D',
Rule for the reflection of a point across x-axis is,
(x, y) → (x , -y)
Coordinates of the image point A' will be,
A(-5, 2) → A'(-5, -2)
From the picture attached, point E is obtained by translation of point A'.
Rule for the translation of a point by h units right and k units up,
A'(x+h, y+k) → E(x', y')
By this rule,
A'(-5 + h, -2 + k) → E(1, -1)
By comparing coordinates of A' and E,
-5 + h = 1
h = 6
-2 + k = -1
k = 1
That means
Rule for the translation will be,
[(x + 6), (y + 1)]
read what on the image then answer
Fraction 10/12 would be greater than 3/4
Will mark brainly!
What is the inverse of [tex]f(x)=\frac{2}{x-1} +6?[/tex]
[tex]f^{-1} (x)=\frac{2}{x-1} +6[/tex]
[tex]f^{-1} (x)=\frac{2}{x} +7[/tex]
[tex]f^{-1} (x)=\frac{2}{y-6} +1[/tex]
[tex]f^{-1} (x)=\frac{2}{x-6} +1[/tex]
Answer:
[tex] {f}^{ - 1} (x) = \frac{2}{x - 6} + 1[/tex]
Step-by-step explanation:
we will subistitute f(x) by y and solve the equation in order to get the value of x,
then we subistitute x by y and y by x and y=f^-1(x)
On a certain hot summer's day, 421 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $788.50. How many children and how many adults swam at the public pool that day?
There were _ children at the public pool.
There were _ adult at the public pool
Answer:
214 children and 207 adults
Step-by-step explanation:
214 x 1.75=374.5
207 x 2 = 414
414 + 374.5 = 788.5
2. What is the x-intercept for the equation -2x + 5y = -10?
Answer:
Step-by-step explanation:
X intercept occurs when y = 0
-2x + 5(0) = -10
x = -10/-2
x = 5
Express the perimeter of the following
rectangle in terms of n.
3n-7
n + 5
1. O 4n - 2
2. O 8n - 14
3. O 8n - 4
4. O 6n - 14
FAM I NEED YOU HELP POR FAVOR:
You purchase two bottles of sunscreen and a hat. The hat costs $6.50. You pay 6% sales tax. You pay a total of $16.43. How much does one bottle of sunscreen cost?
Answer:
I got you fam dont worry
Step-by-step explanation:
if you want me to show my work I dont mind at all but the answer is 4.50
how to find the domain and range of a piecewise function without a graph
Answer:
Step-by-step explanation:
The x component of a function is domain and the y component is range of a function . For example - R1={(3,4),(5,6),(7,9)} The domain of R1 ={3,5,7} The range of R1={4,6,9}
Why does demand for a product or service play a significant role in starting a new business?
Answer:
Basic economics like demand should important to you whether you run a seasonal business, buy a vacation property for passive income, or run a more traditional firm.