An equation to represent relationship of the weights shown on the scale include the following: 22 + x = 34.
How to write an equation to represent relationship of the weights?Based on the information provided about the weights on this balanced scale, we can logically deduce the following parameters;
Each small square = 1 unit.
Each larger square = 10 units.
The variable x represent the weight of the triangle.
Since there are four small squares and three large squares each labeled ten on one side of this balanced scale, we have:
Total weight = 4(1) + 3(10)
Total weight = 34 units.
Similarly, there are two small squares, two large squares, and a triangle labeled x on the other side of this balanced scale, we have:
Total weight = 2(1) + 2(10) + x
Total weight = 22 + x
By equating the two equations, we have:
22 + x = 34
x = 34 - 22
x = 12
In conclusion, there are 34 units on each side of this balanced scale.
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What is mathematics. why is it important?
Mathematics provides a framework for developing critical thinking, problem-solving, and analytical skills that are valuable in many aspects of life.
What is mathematics?
Mathematics is a fundamental discipline that plays a crucial role in our daily lives and in shaping our understanding of the world.
Mathematics is a field of study that deals with the properties and relationships of numbers, quantities, shapes, and patterns. It involves using logical reasoning, abstraction, and symbolic manipulation to understand and solve problems related to these concepts.
Mathematics is important for many reasons. First and foremost, it is a fundamental tool for understanding and describing the world around us. It plays a crucial role in science, technology, engineering, economics, finance, and many other fields by providing tools for modeling and analyzing complex phenomena.
Mathematics is also essential for making accurate predictions and decisions based on data and evidence, as well as for designing and optimizing systems and processes.
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Create a list of 3 numbers in which the mean is 15
A tank in the shape of a hemisphere has a radius of 8 feet. If the liquid that fills the tank has a density of 98.9 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
848,775 pounds
Step-by-step explanation:
The volume of a hemisphere with radius 8 feet is:
V = (2/3)πr^3 = (2/3)π(8^3) = 268.08 cubic feet
The weight of the liquid is given by:
W = V * ρ * g
where ρ is the density of the liquid and g is the acceleration due to gravity. Plugging in the values, we get:
W = 268.08 * 98.9 * 32.2 = 848,774.7 pounds
Rounding to the nearest full pound, the total weight of the liquid in the tank is 848,775 pounds.
Find the nth term of this sequence:
1,1/4,1/9,1/16,.......
The nth term of the given sequence is 1/n².
What is arithmetic progression?An arithmetic progression (AP) is a sequence of numbers in which each term, starting from the second term, is obtained by adding a fixed constant value to the previous term. This constant value is called the common difference, and it remains the same throughout the sequence.
What is geometric progression?A geometric progression (GP) is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed constant value. This constant value is called the common ratio, and it remains the same throughout the sequence.
In the given question,
The given sequence is of the form:
1, 1/2², 1/3², 1/4², ...
So, the nth term can be written as:
1/n²
Therefore, the nth term of the given sequence is 1/n².
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Use the trapezoid shown to mark each statement below as true or false. If false, rewrite the statement correctly in the space below the statement.
1. The length of line AB can be found using 3^2 + b^2 = 4^2.
2. The perimeter of the trapezoid shown is 22 units.
True. The length of AB can be gotten by 3^2 + b^2 = 4^2.
True. The perimeter of the trapezoid shown is not 22 units.
How to solve for the perimeterThe length of AB can be gotten by 3^2 + b^2 = 4^2.
9 + b^2 = 16
b^2 = 16 + 9
b = 5
Then we have to count the boxes to get the length of the other sides
CD = 4
AD = 8
BC = 5
AB = 5
Then the perimeter would be be 5 + 5 + 8 + 4
= 22
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Assuming that a 390 foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 39°, how far from the base of the tree am I?
Answer:
You can use trigonometry to solve this problem. The distance from the base of the tree to where you are standing forms the adjacent side of a right triangle, with the height of the tree being the opposite side and the angle of elevation being 39°.
Using the tangent function: tan(θ) = opposite/adjacent
tan(39°) = 390 / adjacent
Adjacent = 390 / tan(39°)
Adjacent ≈ 496.4 feet
So you are approximately 496.4 feet away from the base of the tree.
Step-by-step explanation:
Can someone please help me!!!
The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).
What is vertex?Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.
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2 1/4-6/7=
2 5/12-blank=2/3
7 1/12-5 3/8=
blank+7/10=2 9/20
To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:
9/4 - 24/28
= 63/28 - 24/28
= 39/28
Therefore, 2 1/4 - 6/7 = 39/28.
To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:
2 5/12 = (2*12 + 5)/12 = 29/12
Then we can subtract 2/3 from both sides:
2 5/12 - 2/3 = blank
To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:
29/12 - 8/12
= 21/12
= 7/4
Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.
To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:
7 1/12 = (712 + 1)/12 = 85/12
5 3/8 = (58 + 3)/8 = 43/8
Then we can subtract:
85/12 - 43/8
= 85/12 - (433)/(83)
= 85/12 - 129/24
= 5/24
Therefore, 7 1/12 - 5 3/8 = 5/24.
To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:
2 9/20 = (2*20 + 9)/20 = 49/20
Then we can subtract 7/10 from both sides:
blank + 7/10 - 7/10 = 49/20 - 7/10
Simplifying the right side:
49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4
Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:
blank = 7/4
Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.
Please helpppp it’s urgent!!! Assume you have a balance of $3000 on a credit card with an APR of 24 %, or 2 % per month. You start making monthly payments of $200, but at the same time you charge an additional $100 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. How long does it take to pay off the credit card debt? Round your numbers to the nearest cent?
It will take around 3.72 months to pay off the credit card debt.
Explain about the annual percentage rate APR?The annual rate of interest that a person must pay on a loan or receives on a bank account is known as the annual percentage rate (APR).APR is utilized for everything, including credit cards, auto loans, and mortgages.The formula for APR is:
A = P * [tex](1 + r/n)^{nt}[/tex]
In which,
A = amount after compounding.
P = balance amount
r = rate of interest.
n = number of time compounded.
Initial balance: $30,000.
Payments per month = $200.
Expenses = $100
Balance amount = 30,000 - 12 *(200 - 100)
Balance amount = $28800
So, time taken for paying off credit card debt.
30,000 = 28800 [tex](1 + 0.24/1)^{1*t}[/tex]
[tex](1.24)^{t}[/tex] = 30,000 / 28800
[tex](1.24)^{t}[/tex] = 1.04
Solve by using logarithmic function.
t = ln (1.04) / 1.24
t = 0.31 year
t = 3.72 months
Thus, it will take around 3.72 months to pay off the credit card debt.
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Pls help meee!!!
Anybody pls!!
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
58 points please urgent super urgent
4x=16
what is x
Answer:4? Think
Step-by-step explanation:
Hi please help me with this question
115° is the value of external angle.
Where is exterior angle?
Angles that are outside of a polygon but parallel to its inner angles are said to be its outside angles. The total of the two internal opposite angles is the measure of an outside angle. A triangle's one side is extended to form the triangle's exterior angle.
Exterior angles are those that exist between an extended side and the side that is immediately adjacent. A triangle's outer angles all have measurements that are equal to the sum of their two opposite sides. inner perspectives.
AD ║EG
∠BFC= 75°
∠EFB = 40°
∠FCD = ( 40+75)
= 115°
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Find the midpoint of AB if A located at (1, 4) and B is located at (3, -6).
Answer:
The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:
[(x1 + x2) / 2, (y1 + y2) / 2]
In this case, A is located at (1, 4) and B is located at (3, -6). So the midpoint M of AB is:
[(1 + 3) / 2, (4 + (-6)) / 2]
= [2, -1]
Therefore, the midpoint of AB is at the point (2, -1).
The coordinates of the midpoint of the line AB is [2, -1]
What is section formula?Section formula is used to find the ratio in which a line segment is divided by a point internally or externally.
It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc.
Given that, we need to find the midpoint of AB if A located at (1, 4) and B is located at (3, -6).
The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:
[(x1 + x2) / 2, (y1 + y2) / 2]
In this case, A is located at (1, 4) and B is located at (3, -6).
So the midpoint M of AB is:
= [(1 + 3) / 2, (4 + (-6)) / 2]
= [2, -1]
Hence, the midpoint of AB is at the point (2, -1).
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Need help with number 10.
Answer:
Width = 12
Length = 19
Step-by-step explanation:
They multiply to 228 and 19in is 7in larger than 12in.
A particle moves along the x-axis so that its velocity at any time t ≥ 0 is given by
v(t) = (2(pi) − 5)t − sin(t(pi))
A. Find the acceleration at any time t.
B. Find the minimum acceleration of the particle over the interval [0, 3].
C. Find the maximum velocity of the particle over the interval [0, 2].
Answer:
A. To find the acceleration, we need to take the derivative of the velocity function with respect to time:
a(t) = v'(t) = 2(pi) - cos(t(pi))
B. To find the minimum acceleration, we need to find the critical points of the acceleration function in the interval [0, 3].
a'(t) = sin(t(pi))
The critical points occur when sin(t(pi)) = 0, which means t = 0, 1, 2, 3. We need to evaluate the acceleration function at these points and at the endpoints of the interval:
a(0) = 2(pi) - cos(0) = 2(pi)
a(1) = 2(pi) - cos(pi) = pi + 2
a(2) = 2(pi) - cos(2pi) = 2(pi)
a(3) = 2(pi) - cos(3pi) = pi - 2
The minimum acceleration occurs at t = 3, with a minimum value of pi - 2.
C. To find the maximum velocity, we need to find the critical points of the velocity function in the interval [0, 2].
v'(t) = 2(pi) - cos(t(pi)) = 0
The critical points occur when cos(t(pi)) = 2(pi). We can solve for t as follows:
cos(t(pi)) = 2(pi)
t(pi) = arccos(2(pi))
t = arccos(2(pi))/pi ≈ 1.58
We need to evaluate the velocity function at these points and at the endpoints of the interval:
v(0) = -sin(0) = 0
v(1.58) ≈ 1.69
v(2) = (2(pi) - 5)(2) - sin(2(pi)) = 4(pi) - 10
The maximum velocity occurs at t = 1.58, with a maximum value of approximately 1.69.
a restaurant menu offers tomato, broccoli, and potato soups. customers order potato soup 50% of the time, broccoli 30% of the time, and tomato 20% of the time the chef designs a simulation to estimate how many of her next 10 customers will order broccoli soup. she labels five index cards p, three cards b, and two cards t. she shuffles the cards and randomly chooses a card from the pile. she records the letter, returns the card, and draws another. she repeats this process for a total of 10 draws. she completes this simulation five times. based on the simulations, how accurate is the chef's estimation regarding broccoli soup orders?
The simulation suggests that the chef's estimation of 30% broccoli soup orders is reasonable, but actual orders will vary from one set of customers to the next.
The chef's estimation of 30% broccoli soup orders seems reasonable based on the probabilities given, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next. To estimate the accuracy of the chef's estimation, she conducts a simulation by shuffling cards representing the soup choices and randomly selecting one for each of the 10 customers. She repeats this process five times.
Based on the simulation results, we can see that the actual number of broccoli soup orders varies quite a bit from the expected value of 1.5. However, this is to be expected due to the random nature of the simulation.
To further estimate the accuracy of the chef's estimation, we could calculate the mean and standard deviation of the results to get a better sense of the distribution of possible outcomes.
Overall, the simulation suggests that the chef's estimation of 30% broccoli soup orders is a reasonable estimate, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next.
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Pregunta 6. Una de les bases de un recipiente para guardar la gasolina se ha roto y es necesario
comprar un nuevo. El diámetro del recipiente es de 10 cm. ¿Qué área debe tener la base del
recipiente que se compre?
a. A == -10²
b.
A=2-m-5
C. A = -5²
d.
A = 2-m-10
The area should the base of the new container must have option D that is, A = 2m-10.
What is area?In mathematics, area is a measurement of the size of a two-dimensional surface or shape, usually measured in square units such as square meters, square centimeters, or square feet. It is the amount of space inside the boundary of a flat object or shape.
Here,
To calculate the area of the base of the new container, we need to find the radius of the container first. Since the diameter is given as 10 cm, the radius would be half of that, which is 5 cm. The formula for the area of a circle is A = πr², where A is the area and r is the radius. So, substituting the values, we get:
A = π(5 cm)²
A = π(25 cm²)
A = 25π cm²
However, the answer choices are not in this format. To simplify the answer, we can use the value of π as approximately 3.14 (rounded to two decimal places). So, the area of the base would be:
A = 25π cm²
A ≈ 25(3.14) cm²
A ≈ 78.5 cm²
Now, we need to choose the answer option that represents this area in terms of variables. The only option that matches is:
d. A = 2m-10
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Complete question:
Question 6. One of the bases of a container for storing gasoline has broken and it is necessary to buy a new one. The diameter of the container is 10 cm. What area should the base of the new container have?
a. A = -10²
b. A = 2m-5
c. A = -5²
d. A = 2m-10
Abe laid three shortest worms together end to end what is the total length of these three worms
Based on the information provided, the total length of the worms would be 6 1/2 inches.
How to calculate the length of the worms?The graph presented shows the length of the worms Abe measured, based on the graph we know that the shortest worm was 2.125 inches, while the longest worm was 2.875 inches. Using this information, let's now add the three shortest worms together:
2.125 inches + 2.125 inches + 2.25 inches = 6.5 inches in total, which can be expressed ad 6 1/2.
Based on this, the total length of the three shortest worms would be 6 1/2.
Note: This question is incomplete; here is the complete question:
Abe measured the lengths of several worms. He made this line plot to display his measurements. Abe laid the three shortest worms together end to end. What is the total length of these three worms?
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what is the perimeter for a 141 by 234
Step-by-step explanation:
the width is 23.5ft and the length is 47ft
The train conductor made sure to count the number of passengers on each train.
Passengers per train
Stem Leaf
1
23456799
8
90
trains
8888
5
6
0
How many trains had exactly 48 passengers?
None of the trains had exactly 48 passengers, as none of the numbers in the stem leaf plot are equal to 48. The closest numbers are 45 and 49, but neither are exactly 48.
What is passenger?Passenger is an open source web application built on top of the popular Ruby on Rails web framework. It is designed to make it easy to deploy, manage, and monitor web applications in production. Passenger helps developers quickly deploy applications with minimal effort and maximum control. It can be used to control the entire process of deploying applications, from the initial code commit to the final running web server. Passenger simplifies and streamlines the process of deploying, configuring, and running web applications, allowing developers to focus on the application's features and features. Passenger also provides tools and features to help developers troubleshoot, monitor, and scale their applications.
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calculate the total distance that the water tanker has covered in March 2022
The total distance that the water tanker has covered in March of 2022 is given as follows:
1860 kilometers.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The parameters for this problem are given as follows:
Velocity of 60 kilometers a day.Time of 31 days, as the month of March has 31 days.Hence the total distance is then obtained as follows:
d = v x t
d = 60 x 31
d = 1860 kilometers.
Missing InformationThe complete question is:
"Assuming that the water tanker travels an average of 60 kilometers a day, calculate the total distance that the water tanker has covered in March 2022".
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I am struggling to correct numbers 1, 3, 4, 5, and 7. I have been working for hours on this.
Answer:
Step-by-step explanation:
1. sinL = 3/5
3. cosL = 4/5
4. sinN = 4/3
5. cos32 = x/14
x = 14(cos32) = 11.9
7. tan75 = 17/x
x = 17/tan75 = 4.56 ≈ 4.6
Question 8 Suppose the graph of rectangle ABCD shows the scale drawing for a safety fence that Kenny is setting up around a construction area. Each unit on the graph represents 25 feet. After studying the scale drawing, Kenny decides to build a fence that encloses a larger area. If Kenny dilates rectangle ABCD by a scale factor of 2.5, and fencing costs $5.25 per foot, how much will he spend on fencing?
Kenny will spend $4,593.75 on fencing the dilated rectangle.
What is rectangle ?
A rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides of equal length. It is a type of parallelogram in which both pairs of opposite sides are parallel and congruent (of equal length). The opposite sides of a rectangle are also perpendicular (form a right angle) to each other. The area of a rectangle is equal to the product of its length and width, while its perimeter is equal to the sum of the lengths of all its sides. Rectangles are commonly used in geometry, architecture, engineering, and many other fields.
According to the question:
Since each unit on the graph represents 25 feet, the dimensions of the original rectangle ABCD are:
AB = 4 units, which represents 4 x 25 = 100 feet
BC = 3 units, which represents 3 x 25 = 75 feet
Therefore, the perimeter of ABCD is 2(AB + BC) = 2(100 + 75) = 350 feet.
When dilating by a scale factor of 2.5, each dimension of ABCD will be multiplied by 2.5. Therefore, the dimensions of the dilated rectangle A'B'C'D' are:
A'B' = AB x 2.5 = 100 x 2.5 = 250 feet
B'C' = BC x 2.5 = 75 x 2.5 = 187.5 feet
The perimeter of A'B'C'D' is 2(A'B' + B'C') = 2(250 + 187.5) = 875 feet.
Therefore, Kenny will need to fence a perimeter of 875 feet. At a cost of $5.25 per foot, the total cost of fencing will be:
875 feet x $5.25/foot = $4,593.75
Therefore, Kenny will spend $4,593.75 on fencing the dilated rectangle.
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Part B: create your own cube root function.
Come up with the equation of 2 different cube root functions. None of these can be the parent function y=^3 squared root of x. For each, find the domain, range, x- and y-intercepts, and describe any transformation for each. Also, give the coordinates of 3 points that you known are on the function (coordinates must be exact values).
plSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
2 wholes 3 tenths and 5 hundredths
Step-by-step explanation:
The customer service department of a company found that the relationship between the number of minutes a customer spends on hold when telephoning and the customer's level of satisfaction on a 10-point scale can be approximated by the equation y=10−0.1x
, where x
is the number of minutes on hold and y
is the level of satisfaction. What does 0.1 represent in the equation?
In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.
Define slopeit represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.
In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.
In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.
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If m∠ A=5x+6 and m∠ B= 7x-18 Find m∠C
Answer:
We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:
m∠A + m∠B + m∠C = 180
Substitute the given values:
5x+6 + 7x-18 + m∠C = 180
Combine like terms:
12x-12 + m∠C = 180
Add 12 to both sides:
12x + m∠C = 192
Subtract 12x from both sides:
m∠C = 192 - 12x
Therefore, m∠C is equal to 192 minus 12 times x.
Please help me asap:}
Simultaneous equations are a set of equations that are solved together to determine the values of the variables that satisfy both equations.
What are Simultaneous equations?1) 4x + 5y = 3 ---(1)
y - 3x = -7 ----(2)
Using the substitution method;
y = -7 + 3x ----(3)
Thus
4x + 5(-7 + 3x) = 3
4x -35 +15x = 3
19x - 35 = 3
19x = 3 + 35
x = 2
Then
4(2) + 5y = 3
8 + 5y = 5
y = 13/5
y = 2 3/5
2) 2x - 4y = 24 ----- x 3
-3x + 2y = -48 ----- x 2
6x - 12 y = 72 ---- (3)
-6x + 4y = -96 ---- (4)
Add 3 and 4
16y = -24
y = -24/16
Substitute y = -24/16 into (1)
2x - 4(-24/16) = 24
2x + 6 = 24
x = 15
3) -x + y = 13 --- 1
3x - 4y = 46 ---- 2
y = 13 + x ---- 3
Substitute 3 into 2
3x - 4(13 + x) = 46
3x - 52 - 4x = 46
-x - 52 = 46
x = 98
Substitute x = 98 into (1)
-98 + y = 13
y = 13 + 98
y = 111
Let C be x and D be y
x + y = 180
x = 33 + 6y
x - 6y = 33
x = 180 - y
Substitute and obtain;
180 - y - 6y = 33
180 - 7y = 33
y = 33 - 180/-7
y = 21
Then
x + 21 = 180
x = 180 - 21
x = 159
Lastly
Let small = x , medium = y
x + y = 150
4x + 6y = 764
x = 150 - y
4(150 - y) + 6y = 764
600 - 4y + 6y = 764
600 + 2y = 764
2y = 764 - 600
y = 82
Then;
x + 82 = 150
x = 68
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The solutions to the simultaneous equations are:
1) x = 2 and y = -1
2) x = 18 and y = 3
3) y = -7 and x = 6
How to Solve the System of simultaneous Linear Equations?There are three main methods in solving simultaneous equations and they are:
1) Elimination Method
2) Substitution Method
3) Graphical Method
1) 4x + 5y = 3
y = 3x - 7
Substitute 3x - 7 for y in the first equation to get:
4x + 5(3x - 7) = 3
4x + 15x - 35 = 3
19x - 35 = 3
19x = 35 + 3
19x = 38
x = 38/19
x = 2
Thus:
y = 3(2) - 7
y = -1
2) 2x - 4y = 24
-3x + 2y = -48
Multiply eq 2 by 2 and eq 1 by 1 to get:
2x - 4y = 24 -----(3)
-6x + 4y = -96 -----(4)
Add eq 3 to eq 4 to get:
-4x = -72
x = 18
2(18) - 4y = 24
36 - 4y = 24
36 - 24 = 4y
4y = 12
y = 3
3) -x + y = -13
3x - 4y = 46
From eq 1, x = y + 13
Thus:
3(y + 13) - 4y = 46
3y + 39 - 4y = 46
39 - y = 46
y = 39 - 46
y = -7
x = -7 + 13
x = 6
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Find the derivative of the following, using differentiation from first principles. f(x) = 2x²-1/x
The required derivative of [tex]f(x) = \frac{2x^3 - 1}{x}$[/tex] is [tex]$f'(x) = 4x + \frac{1}{x^2}$[/tex].
What is differentiation?A technique for determining a function's derivative is differentiation. Mathematicians use a method called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.
The function [tex]f(x) = \frac{2x^3 - 1}{x}$[/tex] can be written as [tex]f(x) = 2x^2 - \frac{1}{x}$[/tex].
The derivative of f(x) can be found using the power rule and the derivative of 1/x, which is[tex]-\frac{1}{x^2}$[/tex].
Therefore, we have:
[tex]$f'(x) = 4x + \frac{1}{x^2}$$[/tex]
So the derivative of [tex]f(x) = \frac{2x^3 - 1}{x}$[/tex] is [tex]$f'(x) = 4x + \frac{1}{x^2}$[/tex].
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Complete question:
Find the derivative of the following, using differentiation from first principles. f(x) = 2x²-1/x.
Suppose you are a ladybug on the “outer” surface of the Klein bottle. Describe a path on the surface of the bottle that you can travel that would get you to the “inside” where a special gentleman bug is waiting.
As a ladybug on the outer surface of the Klein bottle, there is no direct path to the inside. However, you can travel along a specific type of curve called a "cross-cap curve" to reach the inside. and using topology.
To do this, start by moving along the outer surface of the Klein bottle until you reach the point directly opposite to your starting position. Then, imagine folding the surface of the bottle in half along a line that runs through this point.
This folding will create a new surface that intersects with the original surface of the bottle along a cross-cap curve. Follow this curve until you reach the inside of the Klein bottle, where the special gentleman bug is waiting for you.
It's important to note that the Klein bottle is a non-orientable surface, which means that there is no "inside" or "outside" in the traditional sense. However, the concept of inside and outside can still be useful for navigation purposes.
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