In the given simplex tableau with basic variables 23, x4, and x5, the entries α, β, γ, δ, and η are unknown parameters. To find the conditions of the parameter values that will make the following statements true:
1. For the optimization problem to be unbounded, the objective function's coefficients corresponding to the non-basic variables in the tableau should be negative or zero. In this case, the non-basic variables are x1, x2, and x6. Therefore, we need to have 4α - 3δ ≤ 0 and -γ + 3η ≤ 0 for the problem to be unbounded.
2. For the current solution to be feasible but not optimal, we need to have all coefficients in the bottom row of the tableau to be non-negative except for the value in the last column (which is the objective function value). Therefore, we need to have δ > 0 and 3γ < 0.
3. For the current solution to have the optimal objective value and multiple sets of basis that achieve the same objective value, we need to have all coefficients in the bottom row of the tableau to be non-negative except for the value in the last column (which is the objective function value). In addition, we need to have at least two coefficients in the bottom row to be zero. Therefore, we need to have δ = 0 and 3γ ≥ 0, and at least one of the following conditions must hold: 4α - 3δ > 0, -γ + 3η > 0, or -4α + 3δ + γ - 3η = 0.
Explanation: The conditions for the given statements are based on the properties of the simplex method and the standard form of the linear programming problem. The simplex method seeks to maximize or minimize the objective function while satisfying the constraints of the problem. The standard form requires all variables to be non-negative and the constraints to be written as linear equations or inequalities. The simplex tableau is used to keep track of the current basic variables, their coefficients, and the objective function value. The conditions for the given statements are derived by analyzing the coefficients in the tableau and their relationships with the objective function value.
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What is the value of y in the triangle? a 30-60-90 triangle with long leg length y and hypotenuse length 6 a. B. C. D.
The value of y in the right triangle is found to be 3√3 units.
Explain the term trigonometric ratios?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their abbreviations.Given data:
Right triangle with angles:30-60-90.Long length = y.Hypotenuse length = 6So, apply trigonometric ratios:
cos 30 = y / 6
y = cos 30 * 6
y = √3 / 2 * 6
y = 3√3
Thus, the value of y in the triangle is found to be 3√3 units.
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Can you spot any mistakes below?
Q1. Make y the subject of the formula:
k=y(squared)+a
√k =y+a
√k - a=y
y=√k-a
Q2. Express in terms of t
t=v/4+1
t-1+v/4
t-1/4=v
Please help I do not know if there are any mistakes
In Q1, The equation k = y² + a is correct,
To make y the subject of the formula, √k = y + a is incorrect, it should be √k = y + √a
√k - √a = y
In Q2, t = v/4 + 1 is correct
t - 1 + v/4 is incorrect, it should be t - 1 = v/4
t - 1/4 = v
so the correct answer is t-1/4=v
A line passes through the point (1, -9) and has a slope of 5.
Write an equation in slope-intercept form for this line.
Answer:
y = 5x - 14
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
Given that the line passes through the point (1, -9) and has a slope of 5, we can use the point-slope form of a line, which is y - y1 = m(x - x1)
Substituting the point and slope we have:
y - (-9) = 5(x - 1)
y + 9 = 5x - 5
Now we can solve for y by adding 9 to both sides of the equation:
y = 5x - 14
So the equation in slope-intercept form for the line that passes through the point (1, -9) and has a slope of 5 is:
y = 5x - 14
Answer:
y = 5x - 14
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
Given that the line passes through the point (1, -9) and has a slope of 5, we can use point-slope form to write the equation of the line. Point-slope form is written as: y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
We know that the line passes through the point (1, -9) and has a slope of 5, so we can substitute these values into the point-slope form:
y - (-9) = 5(x - 1)
Simplifying, we get:
y + 9 = 5x - 5
Now we can add 9 to both sides to get:
y = 5x - 14
So the equation of the line in slope-intercept form is y = 5x - 14
We can confirm that the point (1,-9) belongs to the line by substitute the values x =1 and y = -9 into the equation y = 5x - 14, if the equation holds true then the point belongs to the line.
Amanda bought a dektop computer and a laptop computer. Before finance charge, the laptop cot more than the dektop. She paid for the computer uing two different financing plan. For the dektop the interet rate wa per year, and for the laptop it wa per year. The total finance charge for one year were. How much did each computer cot before finance charge?
The desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.
The discipline of finance is the study of money, money systems, and capital assets. It is associated with economics, which is the study of the production, distribution, and consumption of money, assets, products, and services, but is not the same thing
Let x be the cost of the desktop computer before finance charges.
We know that the laptop cost 150 more than the desktop, so the cost of the laptop is x+150
We also know that the total finance charge for one year is $303 and the interest rate of the desktop is 7% and the interest rate of the laptop is 9.5%
So we can set up the following equations using the information provided:
(x*0.07) + ((x+150)*0.095) = 303
Simplifying and solving for x:
0.07x + 0.095x + 14.25 = 303
0.165x = 288.75
x = $1750
Therefore, the desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.
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which is larger 7/12 or 2/3 with explanation
Answer:
2/3
Step-by-step explanation:
First divide the numerator by the denominator.
You then get the percentage and then you can judge from there.
Answer:
2/3
Step-by-step explanation:
first we have to equalise the denominators
we know 3 × 4 = 12 so we multiply both the denominator and the nominator by 4 which would give us 8/12
so the answer would be 2/3 since 8/12>7/12
Help with geometry similar triangles. Given AB || CD Find the length of BE.
Answer:
BE = 24
Step-by-step explanation:
These triangles are similar because of AA (Angle, Angle)
The given gives us a pair of parallel sides, allowing us to see that angles C and B are congruent due to being alternate interior angles.
Furthermore, we see that <AEB = <CEB due to vertical <'s being =
Next, we must set up a proportion;
If we create a proportion between the triangles, we must divide corresponding sides;
52/26 = 5x -7 / 2x+2 because we divided both triangles by using the same corresponding sides divided by the same corresponding side.
Simplify 52/26 to 2 and we get that 2 = 5x-7 / 2x+2
Multiply both sides by 2x+2 to get 4x+4 = 5x-7
Subtract 4x from both sides and add 7 from the right side to isolate x and get x=11
Finally, substitute the value of 11 for x into BE 2(11) + 2 and get 22 + 2 =24
aidan is going to buy movie tickets for his friends. matinee tickets are $5 each and evening tickets are $10 each. aidan can spend at most $50 dollars. write and graph an inequality to represent the number of matinee tickets, x, and evening tickets, y, Aiden can buy
The inequality to represent the number of matinee tickets, x, and evening tickets, y, Aiden can buy is,
⇒ 5x + 10y ≤ 50
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Aidan is going to buy movie tickets for his friends. matinee tickets are $5 each and evening tickets are $10 each. Aidan can spend at most $50 dollars.
Now, Let the number of matinee tickets Aiden can buy = x
And, The number of evening tickets Aiden can buy = y
So, We can formulate;
The correct inequality is,
⇒ 5x + 10y ≤ 50
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The future amount due on a compound interest loan of $12,000 at 7% compounded semiannually for four years is approximately ____. If the compounding period is increased to monthly, the amount due on the loan would be approximately ____
Part a: Future amount due on a compound interest loan is $12271.78.
Part b: The amount due on the loan would be $12033.64, if the compounding period is increased to monthly.
Explain the term compounding?Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."The formula for compounding is:
A = P(1 + r/100n)∧nt
P = $12,000
r = 0.07
Part a: compounded semiannually.
t = 4 years.
n = 2
A = 12000(1 + 0.07/100*2)∧2*4
A = 12000*1.00280
A = 12271.78
Thus, future amount due on a compound interest loan is $12271.78.
Part b:
t = 4 years.
n = 12
A = 12000(1 + 0.07/100*12)∧12*4
A = 12000*1.0028038
A = 12033.64
Thus, if the compounding period is increased to monthly, the amount due on the loan would be $12033.64.
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Answer: $15,802
$15,865
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIST!
What is the length of the square’s side?
Answer:
x = 6 / sqrt(2)
Step-by-step explanation:
We are given the diagonal of a square
The side length is x
Using the Pythagorean theorem
x^2 + x^2 = h^2 where h is the length of the hypotenuse which is 6
x^2+x^2 = 6^2
2x^2 = 36
x^2 = 18
Taking the square root of each side
sqrt(x^2) = sqrt(18)
x = 3 sqrt(2)
This can be rewritten as
x = 3 sqrt(2) * sqrt(2)
------------------------
sqrt(2)
x = 3*2
-------
sqrt(2)
x = 6 / sqrt(2)
What is an algebraic expression for this word phrase? 7 more than the product of 5 and n
a. 5 + 7n is the algebraic expression for 7 more than the product of 5 and n
How is this determined?The expression needed to indicate the value of 5 added to the product of 7 and n is "5 greater than the product of 7 and n."
The equation 7n represents the product of 7 and n, and the expression 5 + 7n is obtained by adding 5 to 7n.
This is the proper algebraic expression for the phrase that was given.
It follows that 5 + 7n = 5 + 21 = 26, which is 5 more than the sum of the products of 7 and 3. As an illustration, if we substitute a value of 3 for n, the expression 7n would equal 21.
Because option b is a product of 5 and (7+n), which is not equivalent to 5 greater than the product of 7 and n, the other choices are incorrect.
The product of option c and (5+n) is 7, but it also does not equal 5 greater than the product of 7 and n.
A sum of 5, 7, and n makes up option d, which also does not equal 5 greater than the result of the product of 7 and n.
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There are x sparrows in a tree. There are 50 sparrows on the ground beneath the tree. Let y represent the total number of sparrows in the tree and on the ground.
A. Express y in terms of x
B. Make a table to show the relationship between y and x. Use values of x=10,20,30,40, and 50 in your table
We can write the linear equation:
y = x + 50
And evaluating it on the given values of x, we will get the table:
x y
10 60
20 70
30 80
40 90
50 100
How to express y in terms of x?We know that there are x sparrows in a tree, and there are 50 sparrows on the ground beneath the tree.
y represents the total number of sparrows, then y is equal to the number of sparrows on the tree (x) plus the ones beneath (50) then we will get:
y = x + 50
B) Now we want to make a table. To make that table, we need to evaluate the linear equation in different values of x.
if x = 10
y = 10 + 50 = 60
if x = 20
y = 20 + 50 = 70
if x = 30
y = 30 + 50 = 80
if x = 40
y = 40 + 50 = 90
if x = 50
y = 50 + 50 = 100
Then the table will be:
x y
10 60
20 70
30 80
40 90
50 100
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A box contains twelve 16 GB pen drives and eighteen 32 GB pen drives. Two 16 GB pen drives are defective, and four 32 GB pen drives are defective. If a pen drive is picked at random, what is the probability that it is a 16 GB pen drive or defective?
Therefore , the solution to the given problem of probability comes out to be P =0.6.
How are probabilities determined?Probability theory, a subfield of mathematics, calculates the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where 1 denotes certainty and around 0 denotes how probable the event is to occur. A likelihood is a numerical representation of the likelihood that a particular event will occur. Probabilities may alternatively be stated as percentages with a range of 0% to 100% or as a number between 0 and 1. the percentage of events over a wide range of comparably likely outcomes that happen in comparison to all other conceivable outcomes.
Here,
Given :
Twelve 16 GB and 18 32 GB pen drives are packaged together in a box.
To find the probability of 16gb pen drive is defective:
Thus,
Total pendrive = 30
Event = 16gb pen drive or defective:
The probability of it is 16gb pendrive = 12/30 = 0.4
The probability of it is defective pendrive = 6/30 = 0.2
thus,
total probability (16gb pen drive or defective) = 0.4 +0.2 =0.6
Therefore , the solution to the given problem of probability comes out to be P =0.6.
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What is the result of dilating a figure using a scale factor of 1?
When a figure is dilated using a scale factor of 1, the resulting figure is the same as the original figure.
This is because a scale factor of 1 means that the dimensions of the original figure are not changed in any way.
Mathematically, this is represented by the equation:
Original Length x Scale Factor = Resulting Length
For a scale factor of 1, the equation simplifies to:
Original Length x 1 = Resulting Length
Therefore, the resulting length is equal to the original length.
For example, if a line had a length of 5 units before dilating, the resulting length would be 5 units after dilating.
5 units x 1 = 5 units
This is because the scale factor of 1 does not change the length of the line in any way.
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Which of the following triangles is congruent to triangle PQR?
Third triangle is congruent to triangle PQR.
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
For triangles, there are five primary congruency rules:
Side-Side-Side is an SSS criterion.
The side-angle-side SAS criterion.
Angle, Side, Angle is an ASA criterion.
Angle-Angle-Side is an AAS criterion.
Right Angle Hypotenuse Side (RHS) Criteria
As Height of the triangle PQ is similar to triangle third
Angle 90° ≈ Angle 90° of third triangle
Angle 67° ≈ Angle 67° of third degree
So, By ASA, both the triangles are congruent.
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42
1. Solve for the missing angle measures.
1)
a = 75⁰
d
b
2)
a
b
d=1040
The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.
How do you find an angle measure?With a protractor, you can determine how large an angle is. Alternatively, the congruent angles could be indicated on the figure by an arc. Supplementary angles are two angles whose combined measurements are 180°, such as two right angles since 90° + 90° Equals 180°. the measurement of an angle wherein 1 degree equals 1/360 of a circle.
An angle (created by perpendicular lines) that is exactly 90 degrees is called a right angle. Less than 90 degrees is considered an acute angle. Revolutions, degrees, and radians are the three types of angles that can be measured. Degrees serve as a more widely used measurement unit. In order for a right angle to be 90 degrees, a circle must be divided into 360 equal degrees.
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Help with geometry similar triangles. Solve for x if ABC ~ JKL.
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $725 per week. How much did she earn last week if she sold $4,300 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Danielle earned a total of $1,058.25 last week.
What is Commission?A commission is a percentage of total sales as determined by the rate of commission. A commission is a profit paid due to making a sale.
commission=rate of commission⋅total sales.
To find the commission on a sale, multiply the rate of commission by the total sales.
commission = rate of commission⋅total sales.
commission = 7.75% x $4,300
commission = 0.0775 x $4,300
commission = $333.25
Danielle's earnings will be the addition of both her commission and base salary
Total = commission + base salary
Total = $333.25 + $725
Total = $1,058.25
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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function h(t)=1250(0.865)^t. Evaluate the function when t=3 . Round your answer to the nearest tenth.
When t = 3, the exponential function has a value of 809.0.
What is exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.
Here,
Given the exponential function h (t) = 1250(0.865)^t
When t = 3
h(3) = 1250(0.865)^3
h(3) = 1250 (0.6472)
h(3) = 809.0
The exponential function when the value of t is 3 is 809.0.
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Kathy has a job on the farm she earns $3.20 every 15 minutes she picks green peppers.
she earns $3.00 every 20 minutes she picks carrots.she picked green peppers for 45 minutes and then spent an hour picking carrots. how much money did Kathy earn?
The total money earned after working the given number of hours is $18.60.
What is cross-multiplication?When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.
Given that to pick green peppers:
15 minutes = $3.20
45 minutes = x
Using cross multiplication solve the above equation:
[tex]x = \frac{(3.20)(45)}{15} \\\\x = 9.60\\[/tex]
For picking carrots:
20 minutes = $3. 00
1 hour = 60 minutes = x
Using cross multiplication solve the above equation:
[tex]x = \frac{(3)(60)}{20}\\ \\x=9[/tex]
The total amount made after all the work is:
A = 9.60 + 9
A = 18.60.
Hence, the total amount of money she earned after all the work is $18.60.
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need help with this can you help me
When two lines are parallel, they do not intersect, so there will be no angle formed between them. Therefore, the number of 90° angles formed by the intersection of EF and the two parallel lines AB and CD is zero.
gunnar's car get 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. how many miles can gunnar travel if he uses all of his gas tank
In the given word problem the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.
What is word problem?A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Gunnar's car travel using per gallon of gas = 22.4 miles.
According to the given question,
Gunnar's car can hold 17.82 gallons of gas. Then number of miles does Gunnar's car can travel is ,
=> 22.4 × Car's total tank has hold
=> 22.4 × 17.82
=> 399.17 miles
Hence the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.
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What is the scale factor of the dilation in the similarity transformation?
The scale factor of a similarity transformation is the ratio of the lengths of the corresponding sides of the two similar figures.
What is scale factor?The scale factor is a ratio between two corresponding lengths, areas, or volumes of two similar figures. It is used to compare the size of one figure to another, as well as to enlarge or reduce the size of a figure. The scale factor is expressed as a ratio, such as 1:2, where the first number is the original size and the second is the new size.
It is usually represented as a decimal or fraction, and can be calculated by dividing the length of one of the sides of one figure by the length of the corresponding side of the other figure. For example, if we have two triangles with corresponding sides that measure 3 units and 6 units, then the scale factor of the dilation is 0.5 (3/6). This means that the second triangle is half the size of the first.
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A fruit shop bought 500 kg of apples for R900 and sold them for R2,80 per kg. a) What is the profit per kilogram?
Profit per kilogram = R1.90
The profit per kilogram is the difference between the selling price and the cost price per kilogram.
a) To find the profit per kilogram, we can use the following formula:
Profit per kilogram = Selling price per kilogram - Cost price per kilogram
Therefore,
Profit per kilogram = R2.80 - R0.90
Profit per kilogram = R1.90
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V/-15=20 what does V equal?
Answer:
-300
just do inverse operation, and multiply both sides of the equation by -15 to cancel out the -15 from the denominator and you get V=20(-15)
solve for 20(-15) and you get -300
Find an expression to present the area of the trapezoid below
Area of a trapezoid is found with the formula, A=(a+b)/2 x h. so the answer is 9(w-3) / (w + 7) (w + 2).
What is meant by trapezoid ?
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.The trapezoid belongs to the category of shapes that only has one set of parallel sides. The isosceles trapezoid, which has two non-parallel sides of the same length, falls under a specific category. Although they are both quadrilaterals, a rhombus and a trapezoid are not the same thing.An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the place where the diagonals intersect.To learn more about trapezoid refer to
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I need help asap! Please and thank you
What is the law of exponential change?
The law of exponential change states that when a quantity grows or decays at a rate proportional to its size, then the quantity changes exponentially over time. In other words, it follows an exponential function as opposed to a linear function.
The law of exponential changeThe law of exponential change describes the phenomenon of a quantity changing exponentially over time. This means that the rate of change is proportional to the quantity itself. For example, if a quantity increases by 10% each minute, then the quantity will double every 7.2 minutes. This is because each time the quantity increases by 10%, it is multiplying by 1.1. This process is ongoing and the rate of growth or decay will continue to increase exponentially.
The law of exponential change is used in many areas of science and mathematics, such as population growth and radioactive decay. It is also an important concept in economics, as it can be used to measure the growth of money over time.
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Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 50% end up investing in bonds, and 44% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?
Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks. The probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both) is 66%.
How to find the probability?60% invest in stocks
50% invest in bonds
44% invest in both bonds and stocks
Percent (only stock) = 60% -44%
Percent (only stock) = 16%
Percent (only bond) = 50% - 44%
Percent (only bond) = 6%
Percent (both) = 44%
Total = 16% + 6% + 44%
Total = 66%
Therefore the probability is 66%.
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help is needed please
Answer:
A = 72 units²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
note that the middle section of the lower base = upper base = 6
here h = 8 , b₁ = 3 + 6 + 3 = 12 , b₂ = 6 , then
A = [tex]\frac{1}{2}[/tex] × 8 × (12 + 6) = 4 × 18 = 72 units²
Assume the two triangles shown are similar then the missing length
On solving the provided question, we can say that - Since the two triangle are similar and each sides are 3 times the others, so x= 3 X 4 = 12 cm
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Since the two triangle are similar
\and each sides are 3 times the other,
so x= 3 X 4 = 12 cm
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