Reason:
Multiply both sides by 5 to undo the division.
w/5 = 3
5*(w/5) = 5*3
w = 15
As a way to check, plug in w = 15
w/5 = 3
15/5 = 3
3 = 3
We get a true statement at the end to confirm w = 15 is indeed the answer.
Given line segment GH is a mid segment of triangle DEF
Find value of x and y
What is the length of line segment DF?
The value of x and y for the triangle is 17 units and 2 units respectively. The length of side DF is 20 units.
What is the midsegment theorem in a triangle?A triangle's midsegment is a line segment that connects the midpoints or centers of two of its opposite or adjacent sides.
According to the midsegment theorem, every line segment joining any two triangle sides' midpoints is parallel to and comprises half of the third side.
DH is the midsegment of the triangle DEF, so the value of x can be given by
(1/2)(28) = x -3
x - 3 = 14
x = 14 + 3
x = 17 units
As given, x - 7 = y + 8. So, put x = 17 in it
17 - 7 = y + 8
10 = y + 8
y = 10 - 8
y = 2 units
The side DF = DH + HF
DF = y + 8 + x - 7
= 2 + 8 + 17 - 7
= 10 + 10
= 20 units
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Sadira estimated the solution of a system of equations is approximately (–3.7, 2.2). What can be concluded of the graph that represents the system of this solution? Check all that apply.
The x-coordinate of the intersection point is between 2 and 3.
The y-coordinate of the intersection point is between 2 and 3.
The y-coordinate of the intersection point is between –3 and –4.
The x-coordinate is closer to –4 than –3.
The y-coordinate is closer to –4 than –3.
Using the solution of system of equations, the y- coordinate of intersection point is between 2 and 3 and the x - coordinate is closer to -4 than -3
System of EquationsIn algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."
In the question given, we are told the system of equation have a solution of (-3.7, 2.2).
What this implies is that the value of x and y are 3.7 and 2.2 respectively.
In the options given;
The y - coordinate of the intersection point is between 2 and 3The x - coordinate is closer to -4 than -3Learn more on system of equations here;
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Answer:
B) The y-coordinate of the intersection point is between 2 and 3.
D) The x-coordinate is closer to –4 than –3.
Step-by-step explanation:
what is the slope of the line?
Answer:
The slope is 2/3
Step-by-step explanation:
y is 4 and x is 6 so it will be 4/6 then divide 2
4:2 = 2
6:2 = 3
2/3
8 Ryan is 5½ feet tall. John is,5½ feet tall.
a Who is taller?
b
How much taller?
John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
Given that,
John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
We have to find who is tall and how much is tall.
A fraction that has the numerator higher than or equal to the denominator is said to be improper.
Take the Ryan,
5 1/4 feet
21/4 feet
5.25 feet tall Ryan.
Take the John,
5 1/3 feet
16/3 feet
5.33 feet tall John.
We can see that John is taller then Ryan.
John is 0.08 feet taller then Ryan.
Therefore, John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
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x+y=8
Let x=6. What is y?
Answer:
y = 2
Step-by-step explanation:
x + y = 8
6 + y = 8 Subtract 6 from both sides of the equation
y = 2
What is the inequality shown?
Answer:
5 is > -4
Step-by-step explanation:
5 is greater than or equal to -4
i think this is the answer
The perimeter of a playing field is 302 yards. It’s length is 7 yards longer than three times its width. What is the area of the playing field?
The area of the field is 4140 square yards.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
Given that, the perimeter of the field is 302 yards.
Let the length and width of the field be l and w respectively.
Given that, the length is 7 yards longer than three times its width, therefore,
l = 7 + 3w
The perimeter of the field is given by:
2(l +w) =302
l + w = 151
w = 151 - l..........(1)
Substitute l = 7+3w into the above equation:
w = 151 - 7 - 3w
w + 3w = 144
4w = 144
w = 36
Substitute w = 36 into equation (1):
36 = 151 - l
l = 151 - 36
l = 115
The area of the field is:
l × w
115 × 36
=4140
Hence, the area of the field is 4140 square yards.
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A sign at the store says 3 orange’s cost 2.25$ how much would one orange cost.
If 3 oranges cost 2.25$ then the cost of 1 orange is $0.83.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A sign at the store says 3 oranges cost 2.25$.
So, The cost of one orange can be obtained by dividing the total cost by the total no. of oranges which is,
= $(2.25/3).
= $0.83.
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in a distribution with a mean of 100 and a standard deviation of 15, what is the probability that the score will be 120 or higher
0.0912 is the probability that the score will be 120 or higher .
What is probability explain with an example?
The likelihood that something will occur is the foundation of it. The justification for probability serves as the basic foundation for theoretical probability. A coin is tossed, for instance, and the theoretical likelihood of getting a head is 1 in 2.Zlower = X₁ - μ/σ = 120 - 100/15 = 1.33
the probability is compared as
Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)
= Pr(Z ≥ 120 - 100/15
= Pr( Z ≥ 1.33)
= 0.0912
Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.
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You traveled 300 miles the first day of your trip and then drove 60mph after this day.
Write an equation in slope intercept form to represent the situation.
The slope intercept form of the given situation is:
y = 60x+300
Given,
You traveled 300 miles the first day of your trip and then drove 60mph after this day.
we are asked to determine the slope intercept form of the given situtation.
we know the slope intercept form as:
y = mx+c
we know that at first day we traveled = 300 miles
then after that the graph declines to 60 miles per hour
y = 60x+300
Hence we get the equation as y = 60x+300
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MODELING REAL LIFE The table represents the time x (in minutes) and the distance y (in miles) you bike.
Time, x 30 40 50 60
Distance, y 6 8 10 12
a. Write an equation in point-slope form that represents distance as a function of time.
b. interpret the slope and y-intercept
c. how far can you bike in 4 hours?
justify your answer
a. The equation in a point-slope form that represents distance as a function of time is (y - 6)= (1/5)(x - 30).
b. The slope and y-intercept are (1/5) and 0 respectively.
c. In 4 hours I can bike for 40 miles.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know the equation of a line in point-slope form is (y - y₁) = m(x - x₁).
Given, x represents time in minutes and y represents the distance in miles.
Let us take two ordered pairs (30, 6) and (40, 8).
Slope(m) = (y₂ - y₁)/(x₂ - x₁).
Slope(m) = (8 - 6)/(40 - 30).
Slope(m) = 2/10.
Slope(m) = 1/5.
∴ The equation of the line that represents distance as a function of time
is (y - 6)= (1/5)(x - 30).
Let y = mx + b.
6 = (1/5)30 + b.
6 = 6 + b.
b = 0.
So, y-intercept(b) = 0 and slope(m) is 1/5.
I can bike in 4 hours or (4×60) = 240 minutes is,
y = (1/5)(240) + 0.
y = 48 miles.
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Can someone please fill in blank ASAP
Answer:
The quotient is 48.
Step-by-step explanation:
Estimate the quotient using compatible numbers:
45 (or I guess any number close the answer above, not sure tbh)
Multiply the estimate by 21:
945
45*21
Is the estimate to high or too low?
too low
Adjust and continue until the product is 1008.
1008/21=48
Have a good day/evening! I hope my answer is correct!
A line has a slope of 1/7 and includes the points (0,–4) and (u,–5). What is the value of u?
Answer:
u : -7
So the points are (0,-4) and (-7,-5)
Slope: 1/7
The points (0,g) and (2,10) fall on a line with a slope of 6. What is the value of g?
Answer:
rise/run
(10-g)/(2-0) must equal 6
(10-g)/2 = 6
10-g = 12
-g = 2
g = -2
Estimate each product. then write whether the estimate is greater than or less than the actual product. there are 325 rows of 9 chairs in the theater. there are 102 chairs in the balcony. about how many chairs are there?
Estimate each product then write whether the estimate is greater than or less than the actual product.
= 3027 chairs are there.
There are 325 rows of 9 chairs in the theater.
There are 102 chairs in the balcony.
The total number of chairs there are in the theater and balcony is equal to 3027 chairs.
According to the question;
There are 325 rows in the theater.
Each row contains 9 chairs.
Additionally, there are 102 chairs in the balcony.
In essence, the number of chairs in the theater is;
= 325 × 9
= 2925 chairs.
Additionally, there are 102 chairs in the balcony;
In essence, the total number of chairs is;
= 2925 + 102
= 3027 chairs.
Hence the answer is, = 3027 chairs are there.
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There are 60 books that are either hardcover or softcover. The hardcover books each weigh 26 ounces. The softcover books each weigh 12 ounces. The books weigh 1,056 ounces in all
The number of hardcover books is 24 and the number of the softcover book is 36.
Here we have to find the number of hardcover and softcover.
Here it is given that 60 books are there.
Let x be the number of hardcovers, so the number of software books is 60- x.
The weight of each hardcover is 26 ounces and of softcover is 12 ounces.
The total weight is 1056 ounces.
So we get:
26x + ( 60 -x) 12 = 1056
26x - 12x + 720 = 1056
14x = 336
x = 24
60-x = 60 -24 = 36
Therefore the number of hardcovers is 24 and the number of softcovers is 36.
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The complete question:
There are 60 books that are either hardcover or softcover. The hardcover books each weigh 26 ounces. The softcover books each weigh 12 ounces. The books weigh 1,056 ounces in all. Find the number of hardcover and softcover books are there.
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 60 lbs. The maximum capacity of the elevator is 1110 lb. How many boxes of books can the delivery person bring up at one time?
The number of boxes that the delivery person can carry at a time is less than or equal to 15.
Given,
The weight of the delivery person = 160 lb
The weight of one box of books he carries = 60 lbs
The maximum capacity of the elevator = 1110 lb
We have to find the number of boxes of books can the delivery person bring up at one time;
Let x be the number of boxes;
Then,
The number of boxes that the delivery person can carry at a time;
160 + 60x ≤ 1110
60x ≤ 1110 - 160
x ≤ 950/60
x ≤ 15.8
That is,
The number of boxes that the delivery person can carry at a time is less than or equal to 15.
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Which statement explains whether 0.1515 is rational?
A Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
B Yes, because 0.1515 is a terminating decimal, so it can be expressed as a ratio of integers.
(c) No, because 0.1515 is a repeating decimal, so it cannot be expressed as a ratio of integers.
D No, because 0.1515 is a terminating decimal, so it cannot be expressed as a ratio of integers.
A statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
The correct answer is an option A
We need to select a correct statement that explains whether 0.1515 is rational.
We can observe that 0.1515 is the recurring decimal 0.15
This decimal can be written as a ratio of two integers.
Consider numerator = 5 and the denominator = 33.
So, 5/33 = 0.1515..
This means, 0.1515 can be expressed as p/q where p, q are integers with q ≠ 0
Therefore, a statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
The correct answer is an option A
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Match the correlation coefficients with the scatterplots shown below! Will give brainliest to correct answer!
The scatterplot and their corresponding correlation coefficient are as follows;
Scatterplot [tex]{}[/tex] Correlation coefficient
Scatterplot A [tex]{}[/tex] r = -0.42
Scatterplot B [tex]{}[/tex] r = -0.85
Scatterplot C [tex]{}[/tex] r = 0.64
Scatterplot D [tex]{}[/tex] r = 0.86
What is a correlation coefficient?The correlation coefficient is an indication of the strength of a linear relationship that is used to model an observed dataset.
The value of the correlation coefficient ranges from -1 to 1, with a positive correlation indicating that both variables increases proportionately, and a negative correlation indicating that as one variable increases the other decreases.
A low value of the correlation coefficient indicating that there is a weak relationship between the variables such that the prediction of the output from the input has a low reliability.
The scatterplot D shows the strongest correlation, which indicates that it has the highest correlation coefficient of 0.86The scatterplot B also has a strong negative correlation such that as the input variable increases, the output decreases corresponding to r = -0.85The scatterplot A has a weak relationship as the points are scattered on the graph, however, as the output values increase, the input decreases indicating a negative correlation coefficient, which corresponds to the option, r = -0.42The scatterplot C has a week positive correlation, therefore, the scatterplot C corresponds to the option, r = 0.64Learn more about the correlation coefficient here:
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The correlation coefficients that matches the scatterplots are as follows;
Scatterplot A; r = -0.42
Scatterplot B; r = -0.85
Scatterplot C; r = 0.64
Scatterplot D; r = 0.86
How to interpret the correlation coefficient?The correlation coefficient is defined as a statistical measure of the strength of a linear relationship that exists between two variables. Its' values can range from -1 to 1.
Now, a correlation is considered to be a positive correlation when both variables increases or decreases in tandem which is the same direction. Meanwhile, a negative correlation is defined as on whereby one variable increases as the other decreases.
Now, the farther away the data points are from each other the greater the value of the correlation coefficient and vice versa.
The scatterplot A is a negative correlation because the output increases as the input decreases and vice versa. This is more scattered than the other negative correlation; r = -0.42
The scatterplot B also has a stronger negative correlation than scatter plot A since r = -0.85
The scatterplot C has a positive correlation, but not so strong as seen by the spacing of the scatter dot points. Thus, the scatterplot C has a correlation coefficient of r = 0.64
The scatterplot D has a stronger positive correlation coefficient than C as seen in the dot scatter points and as such its' correlation coefficient is 0.86
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What is the area of a rectangle ABCD with vertices at
A(-1, 11)
B(7, 9)
C(10, 13)
D(2, 7)
The Area of the rectangle is 32 square units
Finding the Area of Rectangle with vertices:The area of the rectangle can be defined as 'the region covered by the rectangle in a 2-D plane. The formula for the area of the Rectangle or the Quadrilateral with vertices is given below
Area of Quadrilateral
= (¹/₂) | x₁y₂+ x₂y₃+ x₃y₄ +x₄y₁ - (x₂y₁ +x₃y₂ +x₄y₃ +x₁y₄) |
Where (x₁, y₁); (x₂, y₂); (x₃, y₃) and (x₄, y₄) are vertices of the quadrilateral
Here we have
Vertices of rectangle are A(-1, 11), B(7, 9), C(10, 13) and D(2, 7)
If we draw the given vertice in a graph then the order of the sides will be 'ACBD' [ For more understanding observe the given figure ]
From the above formula,
Area of rectangle
= (¹/₂) | (-1)(13) + (10)(9) + (7)(7) + (2)(11) - [ (10)(11)+(7)(13) +(2)(9) +(-1)(7) ] |
= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |
= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |
= (¹/₂)(64)
= 32 Square units
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In expression (-6)4 what is the power and exponent?
In the expression (-6)⁴, the power and exponent is 4
What is an exponent?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the power or exponents us the number of times the number is raised which is 4.
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can someone pls helppp!!!!!!
Answer:
(a) 2x + x + 39 = 90
(b) m<1 = 34°; m<2 = 56°
Step-by-step explanation:
Use the angle addition postulate. Angles 1 and 2 add to a right angle. A right angle has a measure of 90°.
(a) m<1 + m<2 = 90
2x + x + 39 = 90
(b)
Solve the equation for x.
2x + x + 39 = 90
3x = 51
x = 17
Use the value of x to find the angle measures.
m<1 = 2x = 2(17) = 34
m<2 = x + 39 = 17 + 39 = 56
Answer:
a.) 3x+39=90
b.) ∠1=34°
∠2=56°
Step-by-step explanation:
According to the graph, ∠1 + ∠2=90°.
∠1=2x and ∠2=x+39
So,
[tex]2x+(x+39)=90\\2x+x+39=90\\3x+39=90\\3x=51\\x=17[/tex]
Rewrite the equations for the two angles substituting 17 for x.
∠1=[2(17)]°=34° and ∠2=[(17)+39]°=56°
Find the value of r so the line that passes through the pair of points has the given slope.
(12, 10), (−2, r), m=−4
Based on the concept of the slope intercept form, the value of r is 66.
Slope intercept form:
The general formula to calculate the slope intercept form equation is written as,
y = mx + c
where
(x, y) represents the point
m represents the slope
c represents the y-intercept.
Given,
Here we know the pair of points (12, 10), (−2, r) and the value of slope which is m = -4.
And we need to find the value of r.
We know that the formula for of the slope intercept form is
y = mx + c
So, we have to use the slope and the point (12, 10), to find the intercept of the line,
When we apply the value on the formula, then we get,
=> 10 = -4(12) + c
=> 10 = -48 + c
=> c = 58
Therefore, the slope intercept form equation is written as
=> y = -4x + 58
Now, we have to find the value of r, by apply the point (-2,r) on the equation, then we get,
=> r = -4(-2) + 58
=> r = 8 + 58
=>r = 66
Therefore, the value of r for the given pair of points is 66.
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Line g pae through point (9, 9) and (1, 4). Line h i parallel to line g. What i the lope of line h?
Line g pae through point (9, 9) and (1, 4) and the slope of line h is 0.68.
The coordinates of line g are (9,9) and (1,4).
Substitute the values in the slope formula with (x1, y1) = (9,9) and (x2, y2) = (1, 4).
m = (y2-y1)/(x2-x1)
m = (4-9)/ (1-9)
m = (-5)/ (-8)
m = 0.68
the slope of the line g is 0.68
line h is parallel to line g so parallel lines have the same slope
slope of line h is 0.68
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I need help pls this is due soon
30 points pls don't guess I really need help
Answer: x ≈ 2.67
Step-by-step explanation:
To solve, we will isolate the variable with reverse operations.
Given:
[tex]\displaystyle x^2=\frac{521}{73}[/tex]
Square root both sides of the equation:
[tex]\displaystyle x=\sqrt{\frac{521}{73}}[/tex]
Evaluate:
x = 2.6715138 ... ≈ 2.67
What’s 55 divided by 50,325?
Answer:
Step-by-step explanation:
0.0010928961748634
but 50,325 divided by 55 is 915
An orange grower harvested oranges from 4 acres of land and collected 720 bushels of oranges. The next day, the farmer harvested oranges from 7 acres of land and collected 1,260 bushels of oranges.
Is there a proportional relationship between the number of bushels of oranges collected and the number of acres harvested over the two days? Explain.
No, it is not proportional because both variables cannot be zero at the same time.
No, it is not proportional because all ratios between the number of bushels collected and the number of acres harvested are not equivalent.
Yes, it is proportional because the farmer collected 18 bushels for every 1 acre harvested.
Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Answer:
(d) Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Step-by-step explanation:
You want to know if the ratios 4 acres : 720 bushels and 7 acres : 1260 bushels represent a proportional relationship.
ProportionA relationship is proportional if the ratio of the dependent variable to the independent variable is a constant. We can check this for the numbers given:
(720 bu)/(4 ac) = 180 bu/ac
(1260 bu)/(7 ac) = 180 bu/ac
The ratios are the same, 180 bushels for each acre, so the relationship is proportional.
Answer:
(d) Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Step-by-step explanation:
I took the exam and got it right
Find the component form of the vector that translates A(-4,8) to A'(7,-9)
The component form of the vector that translates A to A' is (11, -17)
A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
In translation, the shape of the figure does not change but its size may change.
Other transformation processes are reflection and rotation.
The component form of the vector is governed by the rule; A' - A
so we subtract corresponding x- coordinates and corresponding y- coordinates
A' - A = (7, -9) - (-4, 8)
= ( 7 - - 4, -9 - 8)
-= ( 11, -17)
In conclusion, the vector that translates A to A' is ( 11, -17 )
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Yani buys a certain brand of cereal that cost you $10 per box. Yani changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand. Y= 7x
Part A: How many more dollars is the price of a box if Yanis original of cereal than the price of a box of super-saving cereal? Show your work.
Part B: how much money does Yani save each month with the change In cereal brand if he buys 5 cereal boxes each month? Show your work.
Answer:
part A= 3
Part B= 15$
Step-by-step explanation:
Part A= 10-7=3
Part B = 5*10 =50 7*5= 35 50-35= 15$
The Collin Freight Company has an order for three products to be delivered to a
destination. Product I requires 10 cubic feet, weighs 10 pounds, and has a value
of $100. Product II requires 8 cubic feet, weighs 20 pounds, and has a value of $20.
Product III requires 20 cubic feet, weighs 40 pounds, and has a value of $200. If the
carrier can carry 6,000 cubic feet, 11,000 pounds, and is insured for $36,900, how
many of each product can be carried?
A , B, C are the amounts of each product
10A + 8B + 20C = 6000 <--- volume constraints
10A + 20B + 40C = 11000 <---- weight constraints
100A + 20B + 200C = 36900 <---- $$$$
What is product?Byproducts are things created in a process, typically one that is industrial or biological, in addition to the main result. A byproduct of the sugar refining process is sulfured molasses.
the first two equations together:
10A + 8B + 20C = 6000
10A + 20B + 40C = 11000
first is subtracted from second: 12B + 20C = 5000 3B + 5C = 1250 —- identifies this equation. ALPHA
Connect the second and third equations:
10A + 20B + 40C = 11000
100A + 20B + 200C = 36900
The top equation is multiplied by 10:
100A + 200B + 400C = 110000 —— Weight restrictions
100A + 20B + 200C = 36900 <—— $$$$
takes them away:
180B + 200C = 73100
18B + 20C = 7310
9B + 10C = 3655 —- identifies this equation. ALPHA BETA: BETA: 9B + 10C = 3655 3B + 5C = 1250
ALPHA is multiplied by 3:
9B + 15C = 3750
9B + 10C = 3655
takes them away:
5C = 95\s C = 95/5 = 19
Plugging into BETA yields the following results: 9B + 10(19) = 3655 9B = 3655 - 190 B = 385
Adds to the initial first equation:
10 A + 8(385) + 20(19) = 6000 A=254\s A=254\sB=385\sC=19
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