Answer:
4. y = 3x
Step-by-step explanation:
A proportional relationship is one in which the ratio of two variables is always constant. This is also known as direct proportion.
Out of the given options, the equation that shows a proportional relationship is:
4. y = 3x
In this equation, the ratio of y to x (y/x) is always 3, so the relationship between y and x is proportional. As x increases, y also increases at a constant rate, and as x decreases, y decreases at a constant rate. This type of relationship is often represented by the equation y = kx, where k is the constant of proportionality.
The population of town X was 220,000 in 2000, and 252,000 in 2010. Project the population in 2020.
Answer: To project the population in 2020, we can use the linear trend line equation.
First, we need to find the equation of the line. Let's use the two given points, (2000, 220,000) and (2010, 252,000), to find the slope of the line:
slope = (252,000 - 220,000) / (2010 - 2000) = 32,000
Next, we can use the slope-intercept form of the line equation: y = mx + b, where m is the slope and b is the y-intercept.
Plug in the first point: 220,000 = 32,000 * 2000 + b
Solve for b: b = 220,000 - 32,000 * 2000 = -44,000,000
The equation of the line is: y = 32,000x - 44,000,000
Finally, we can use the equation of the line to project the population in 2020:
y = 32,000 * 2020 - 44,000,000 = 264,000
So, the projected population in 2020 is 264,000.
Step-by-step explanation:
2/3y + v = x solve for y
The variable y as the subject formula in the equation (2/3)y + v = x is y = (3/2)(x) - (3/2)(v)
What is y in the given equation?Given the equation in the question;
(2/3)y + v = x
y = ?
Solve for y, we make 'y' the subject of the formula.
(2/3)y + v = x
Subtract v from both sides
(2/3)y + v - v = x - v
(2/3)y = x - v
Multiply both sides by 3/2
(3/2)(2/3)y = (3/2)(x - v)
y = (3/2)(x - v)
Apply distributive property.
y = (3/2)(x) - (3/2)(v)
Therefore, y equals (3/2)(x) - (3/2)(v).
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The length of DE is shown. What other lengths can you determine for this diagram? Choose
all that apply.
The other lengths we can determine for this diagram are;
EF=6 DG=6 About rhombusA rhombus is a flat shape that has four sides that are the same length with the opposite sides parallel to each other and not perpendicular to each other. The four sides of a rhombus are the same length because a rhombus is formed from two congruent isosceles triangles.
The image above includes a rhombus with 90 degree angles between its diagonals.
So that the four outer sides are the same length, namely DE=EF=FG=DG= 6
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What is the discriminant of the quadratic equation 9x^2-2x-9=09x
2
−2x−9=0?
[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-2)^2-4(9)(-9)\implies \text{\LARGE 328}[/tex]
There is a bag filled with 3 blue and 4 red marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 that are different in colour?
Answer: THE ANSWER IS 18/42
Step-by-step explanation:
A report on the income of American households says that the median income of households was about $70,000 in 2021. The mean income of these same households was about $100,000 in 2021. What explains the difference between these two measures of center?
The difference between the median and mean income can be explained by the distribution of the data.
A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When data collection is ranked from least to greatest, the median is the midpoint. The mode is the number that occurs most often in a data set.
The median and mean are both measures of center used to describe a distribution of data. In this case, the median income of American households in 2021 is reported as $70,000, which means that half of the households have an income below $70,000 and a half have an income above $70,000.
On the other hand, the mean income of these same households in 2021 is reported as $100,000. This means that if we were to add up the income of all households and divide by the total number of households, we would get an average of $100,000 per household.
The difference between the median and mean income can be explained by the distribution of the data. If the data is symmetrically distributed around the center (i.e., the median), the mean and median will be similar. However, if the data is skewed, meaning it is not evenly distributed, then the mean and median will be different.
In this case, it is possible that a small number of households have very high incomes, which would pull up the mean income while not affecting the median income as much. This could explain why the mean income is higher than the median income.
It's also worth noting that while the median and mean income are both useful measures, they do not tell the whole story about income distribution.
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Which equation represents the line that passes through points (0, 6) and (2, 0)?
O y=-1/3x+2
O y=-1/3x+6
O y=-3x+2
O y=-3x+6
Answer:
D
Step-by-step explanation:
diff y / diff x = slope
so -6/2 = -3
Y intercept is where x= 0, so it's 6
D
Please help quick
(b) Do the sets A, B, and D form a partition of R? If not, which condition of a partition is not satisfied?
(c) Do the sets B, D, and E form a partition of R? If not, which condition of a partition is not satisfied?
a) The sets A, B and D form a partition of the real numbers, as each real number is present in exactly one of of these sets.
b) The sets B, D and E do not form a partition of the real numbers, as the element x = -2 belongs to both sets D and E.
What are the conditions for the partition of a set?The conditions for the partition of a set are given as follows:
No element of the original set is present in more than one of the subsets.Together, the subsets contain all the elements of the original set.More can be learned about partitions of a set at https://brainly.com/question/29495953
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I need help
I don’t understand how to do it
Answer:
tan60 = [tex]\frac{x}{6}[/tex]
x = 6 x tan60
= 10.4 ( cor to 3 significant figures)
cos60 = [tex]\frac{6}{y}[/tex]
y = [tex]\frac{6}{cos60}[/tex]
= 12
si un plano cartesiano se unirán los siguientes puntos Qué figura se formaría
To find points on a Cartesian plane, you need to know the x and y coordinates of the point. The Cartesian plane has two axes, the x-axis and the y-axis, which intersect at the origin (0, 0).
How to explain the informationThe x-coordinate of a point tells you how far the point is from the y-axis, either to the right (if the coordinate is positive) or to the left (if the coordinate is negative).
The y-coordinate of a point tells you how far the point is from the x-axis, either up (if the coordinate is positive) or down (if the coordinate is negative).
So, to find a point on the Cartesian plane, you need to know both its x and y coordinates. For example, the point (3, 4) is located 3 units to the right of the y-axis and 4 units up from the x-axis.
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the formula for the perimeter of a rectangle is p= 2L + 2w
For the perimeter of a rectangle, the formula for w is
⇒ w = (p - 2L) / 2
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The formula for the perimeter of a rectangle is,
⇒ p = 2L + 2w
Hence, The formula for the width (w) is,
⇒ p = 2L + 2w
⇒ p - 2L = 2w
⇒ 2w = p - 2L
⇒ w = (p - 2L) / 2
Thus, For the perimeter of a rectangle, the formula for w is
⇒ w = (p - 2L) / 2
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The complete question is this,
The formula for the perimeter of a rectangle is P=2l+2w. Which is the equivalent equation solves for w?
P-2l/2=w
P+2l/2=w
P+l=w
P-1=w
9. The radius a of a circle inscribed by an isosceles triangle whose sides are A, B and C is given by. a[(S-A)(S-B)(S-C)/S]¹/2 Where S is an abbreviation for (A + B + C)/2. Check this equation for dimensional consistency.
It should be noted that r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.
How to convey the informationThe radius a of a circle inscribed by an isosceles triangle whose sides are A, B and C is given.
r = [(s - a)(s - b) (s - c)/s]1/2, where s = (a + b + c)/2.
a, b , c actual lengths of the sides,
s = average length of the sides
So that we can write
L = [(L - L)(L - L) (L - L)/L]^1/2
= [(L)(L) (L)/L]^1/2
= [L^2]^1/2
= L
Therefore r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.
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Consider the function below.
f(x)=8x−6
What would be the output if the input is 8?
Responses 2
in pavlov's experiments he paired the presentation of food with a buzzer and measured salivation to each. in this experiment the buzzer was the
In Pavlov's experiments, he paired the presentation of food with a buzzer and measured salivation to each. In this (b) conditioned stimulus (CS)
Like many great scientific advances, Pavlovian conditioning (aka classical conditioning) was discovered accidentally. Ivan Petrovich Pavlov (1849–1936) was a physiologist, not a psychologist.
During the 1890s, Russian physiologist, Ivan Pavlov was researching salivation in dogs in response to being fed. He inserted a small test tube into the cheek of each dog to measure saliva when the dogs were fed (with a powder made from meat).
Pavlov predicted the dogs would salivate in response to the food placed in front of them, but he noticed that his dogs would begin to salivate whenever they heard the footsteps of his assistant who was bringing them the food.
The complete question is-
In Pavlov's experiments, he paired the presentation of food with a buzzer and measured salivation to each. In this
experiment the buzzer was the ___.
A. unconditioned stimulus (US)
B. conditioned stimulus (CS)
C. unconditioned response (UR)
D. conditioned response (CR)
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Adding improper fractions 5/12 + 1/4
By adding improper fractions 5/12 + 1/4, we get 8/12 or 2/3.
What is the least common multiple?
The LCM is multiple which is useful if fractions need to be expressed in the same name, and the further discussion can be defined as follows: When the other number is multiple, LCM will have the larger number: Example: So, the 2 and 4 LCM.
1/4 and 5/12 do not have a common denominator, so we first take LCM of the denominators.
LCM = 12
Therefore, we make 1/4 with denominator 12,
i.e, 1x3/4x3 = 3/12
Now, we can add the two fractions which have a common denominator.
3+5/12 = 8/12 which can be simplified to 2/3 (after cutting the numerator and denominator with 4.)
Hence, by adding improper fractions 5/12 + 1/4, we get 8/12 or 2/3.
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The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins.When the two crews start working together, what part of all the garbage bins will the first garbage truck empty?
The first truck did 62% of all the job.
When the two crews start working together?First, from the problem we know that the first truck does its job at a rate per hour:
And, the second truck has a rate per hour of:
So, the rate per hour with both trucks working together will be the sum:
Now, we have to find the time it will take to do the whole job with both trucks, the whole job done will be represented by 100% or 1:
Where t is the unknown time that it takes to do all the job. Solving this we have:
This means that the whole job will be done after 3.08 hours using both trucks. However, the problem is asking just about the first truck. To find that answer we just have to multiply its rate with the time:
This decimal number represents the portion that the first truck finished to have the job done. 0.62 means that it did 62% of all the job.
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correct question:
The city just assigned a second garbage truck to empty the bins in Kat’s neighborhood on trash day. The crew from the first garbage truck used to empty all the bins by themselves in 5 hours. In their training, it took the crew from the second garbage truck 8 hours to empty all the bins. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? To the nearest tenth, the first garbage truck will empty about of all the bins.
Answer:
Step-by-step explanation:
When the two crews start working together, the part of all the garbage bins that the first garbage truck will empty is; A: 0.6
We are told that the first truck empties all bins in 5 hours. Thus;
Rate of first truck per hour = ¹/₅
Second truck empties all bins in 8 hours. Thus;
Rate of second truck per hour = ¹/₈
If both trucks work together, their rate per hour is;
Combined rate per hour = ¹/₅ + ¹/₈
Combined rate per hour = ¹³/₄₀
Thus, number of hours it will take for both of them to do the whole job, we will solve as;
¹³/₄₀t = 1
where t is the time it will take both of them combined to finish the whole job.
Thus;
t = ⁴⁰/₁₃
The part that the first garbage truck will empty when they both work together = ¹/₅t = ¹/₅ * ⁴⁰/₁₃
⇒ Approximately 0.6
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Prove that
cos 75° = √2 (√3-1)÷4
Answer:
The Pythagorean Theorem states that, for a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Therefore, if we have a right triangle with angles A, B, and C, then:
$$A^2 + B^2 = C^2$$
Now, let's consider a triangle with angles of 75°, 45°, and 30°. We know that the sum of the angles must equal 180°, so these three angles add up to 180°.
We can now plug in the angles into the formula above and solve for the hypotenuse C:
$$(45^2) + (30^2) = C^2$$
$$2025 = C^2$$
$$\sqrt{2025} = C$$
Therefore, the length of the hypotenuse C is 45 units.
Now, let's look at the cosine of angle A, which is 75°. By definition, the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Therefore, for this triangle:
$$\cos 75° = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{\text{Adjacent side}}{45}$$
We can now find the length of the adjacent side by subtracting the length of the opposite side from the hypotenuse:
$$\text{Adjacent side} = 45 - \text{Opposite side}$$
The length of the opposite side is equal to the length of the other leg, which is 30 units in this case. Therefore, the length of the adjacent side is 15 units.
Putting this all together, we can now solve for the cosine of 75°:
$$\cos 75° = \frac{15}{45} = \frac{\sqrt{2} (\sqrt{3}-1)}{4}$$
Therefore, cos 75° = √2 (√3-1)÷4.
This graph shows the equations y= - 1/2x + 3 and y=2x-2.
A coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
a) Given that, the graph shows the equations y= - 1/2x+3 ------(i) and y=2x-2 ------(ii).
From the graph, the solution is (2, 2)
b) Put x=1 in equation (i), we get
y= -1/2(1)+3
y= 2.5
Put x=2 in equation (i), we get
y= -1/2(2)+3
y= 2
Put x=3 in equation (i), we get
y= -1/2(2)+3
y= -1/2 (3)+3
y= -1.5+3
y= 1.5
So, a coordinate that is a solution to the first equation is (3, 1.5)
Therefore, a coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
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Five more than five times a number is 30, What is the number?
Answer:
5
Step-by-step explanation:
We can set up an equation.
Let x be the number.
So 5x+5 would be equal to 30.
5x+5 = 30
Subtract 5 on both sides:
5x = 25
Divide by 5 on both sides:
x = 5
92÷3= solving the equation
32.66 repeated :>))))))))))))))
Answer:
30.6666666667
Step-by-step explanation:
92÷3 = 30.6666666667
What is the equation of a vertical line passing through the point (−5, −1)?
Answer:
x=-5
I think this is right
Step-by-step explanation:
Check the picture below.
A car has x litres of petrol in its tank. One half is used on Monday. A further 2 litres on Tuesday. How much petrol is left
The amount of petrol left remaining in the car after Tuesday journey is (x/2) - 2
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
A car has x litres of petrol in its tank. One half is used on Monday. Therefore:
Amount of petrol remaining = x - (1/2) of x = x - x/2 = x/2
A further 2 litres on Tuesday, hence:
Amount of petrol left = (x/2) - 2
The amount of petrol left is (x/2) - 2
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If $a$ and $b$ are integers with $a > b$, what is the smallest possible positive value of $\frac{a+b}{a-b} + \frac{a-b}{a+b}$?
The smallest positive value for (a+b)/(a-b)+(a-b)/(a+b) where a and b are integers is 2.
What exactly are integers?In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
Now
For given expression (a+b)/(a-b)+(a-b)/(a+b)
where a>b and both are integers.
solving the expression
((a+b)(a+b)+(a-b)(a-b))/((a+b)(a-b))
=2(a²+b²)/a²-b²
As (a+b)²=a²b²+2ab and a²-b²=(a+b)(a-b)
So for given expression negative and positive values for a,b gives same result then smallest values will be a=1, b=0
Then
=2*1/1
=2
Hence, The smallest positive value for (a+b)/(a-b)+(a-b)/(a+b) where a and b are integers is 2.
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Order of Operations Consider the numerical expression: 3 + 6 × (5 + 4) ÷ 3 − 7.
Question 1
To evaluate the numerical expression, what is the first step in the order of operations?
A Perform any calculations inside parentheses.
B Perform all additions, working from left to right.
C Perform all multiplications, working from left to right.
D Perform all divisions, working from left to right.
Question 2
Evaluate the given numerical expression.
Responses
A 21
B 14
C 9
D 12
Answer:
Add 5 +4 × 6 ÷ 3 - 7 + 3and you will get 14 and that is your answer
How many people have to be in a room to have a 50% probability of at least two people having the same birthday?
Answer:
183
365/2
you get 182.5 but you round up because you don't have half a person in the room.
Step-by-step explanation:
what statistical test would you do ? explain why you chose this test
The statistical test to be chosen depends on the nature of the data and the research question being answered. There are several statistical tests available, each with different assumptions and purposes.
Describe Statistical test?A statistical test is a method used to evaluate data and make inferences about a population based on a sample of the population. The purpose of a statistical test is to determine if the results of an experiment or survey are statistically significant, which means that they are unlikely to have occurred by chance. Statistical tests use mathematical models to determine the likelihood of an event occurring and provide a level of confidence in the results.
Here are some common statistical tests and when they might be used:
T-test: A t-test is used to compare the means of two groups to determine if there is a significant difference between them. This test is often used in experiments where one group is treated differently from another.
ANOVA: ANOVA (Analysis of Variance) is used to compare the means of three or more groups to determine if there is a significant difference between them.
Chi-square test: A chi-square test is used to determine if there is a significant relationship between two categorical variables.
Linear Regression: Linear regression is used to study the relationship between a dependent variable and one or more independent variables.
Logistic Regression: Logistic regression is used to predict a binary outcome based on one or more independent variables.
It is important to choose the right statistical test to ensure that the results are meaningful and accurate. The choice of the test depends on the research question, the nature of the data, and the assumptions of the test. It is advisable to consult with a statistician to determine the appropriate test for a given situation.
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This geometry and my teacher did not teach me this please help
Answer:
[tex](x, y ) \rightarrow (\boxed{\dfrac{x}{3}}, \boxed{-\dfrac{y}{3}})[/tex]
Step-by-step explanation:
The image(the smaller inverted triangle) obtained from the pre-image(the larger triangle) by compressing it by a factor of -1/3(called a dilation) and then reflected across the y-axis
If you examine the two triangles you will see that
Point A(-3, -3) ==> Point X(-1, 1)
Point B(-3, 3) ==> Point Z(-1, -1)
Point C(3, -3) ==> Point Y(1, 1)
So the x coordinates and y coordinates of the image are transformed as follows:
x' = x/3
y' = - y/3
A plumber uses an average of 20 meters of copper
pipe each week. Copper pipe costs $5 per meter. If
the plumber wants to reduce her weekly expenditure
on copper pipe by $4, what length of copper pipe
should she buy each week, in meters?
Answer:
$80
Step-by-step explanation:
Can someone help me with these questions pls
The given fractions are sorted in ascending order following the rules of sorting fractions.
What are fractions?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. The number of components of a specific size is expressed as a fraction.
Some of the rules for arranging fractions are as follows:
If the fractions have the same denominators, the fraction with the smallest numerator has the least value and the fraction with highest numerator have the highest value.If the fractions have same denominator, the fraction with highest denominator has least value and the fraction with lowest denominator has the highest value.If the fractions have different numerators and denominators, make either numerator or denominator the same and follow the above rules to arrange them.Now following the above rules, we can solve each question.
[tex]\frac{21}{40} , \frac{29}{40} ,\frac{17}{20},\frac{3}{4},\frac{4}{5}[/tex]We will make the denominators the same.
The LCM of 40, 40, 20,4,5 = 40
So the fractions become,
[tex]\frac{21}{40} , \frac{29}{40} ,\frac{34}{40},\frac{30}{40},\frac{32}{40}[/tex]
Now sort them.
[tex]\frac{21}{40} , \frac{29}{40} ,\frac{30}{40},\frac{32}{40},\frac{34}{40}[/tex]
2. [tex]\frac{7}{9} , \frac{2}{9} ,\frac{5}{6},\frac{13}{18},\frac{3}{18}[/tex]
LCM of 9,6,18 = 18
So the fractions become,
[tex]\frac{14}{18} , \frac{4}{18} ,\frac{15}{18},\frac{13}{18},\frac{3}{18}[/tex]
Now sort them.
[tex]\frac{3}{18} , \frac{4}{18} ,\frac{13}{18},\frac{14}{18},\frac{15}{18}[/tex]
3. [tex]\frac{9}{4} , \frac{4}{3} ,\frac{5}{3},\frac{7}{4},\frac{7}{5}[/tex]
LCM of 4,3,5 = 60
[tex]\frac{135}{60} , \frac{80}{60} ,\frac{100}{60},\frac{105}{60},\frac{84}{60}[/tex]
Now sort them.
[tex]\frac{80}{60} , \frac{84}{60} ,\frac{100}{60},\frac{105}{60},\frac{135}{60}[/tex]
4. [tex]\frac{17}{7} , \frac{23}{7} ,\frac{24}{5},\frac{17}{5},\frac{11}{35}[/tex]
LCM of 7,5,35 = 35
[tex]\frac{85}{35} , \frac{115}{35} ,\frac{168}{35},\frac{119}{35},\frac{11}{35}[/tex]
Now sort them.
[tex]\frac{11}{35} , \frac{85}{35} ,\frac{115}{35},\frac{119}{35},\frac{168}{35}[/tex]
Therefore the above fractions are sorted in ascending order.
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A board is 71 cm in length and must be cut so that one piece is 15 cm longer than the other piece. Find the length of each piece. Round your answers to the
nearest centimeter, if necessary.
The short piece is 28 cm and the other piece is 43 cm longer or (28+15 = 43 cm).
About mathematical modelBased on the question, One piece will be length x and the other piece will be 15 cm longer, so it will be x + 15 cm long.
Added together the length of these two boards will equal 71 cm. So the equation will be:
x + (x + 15) = 71
2x+15=71
2x=71-15
2x=56
x=28 cm
The short piece is 28 cm and the other piece is 43 cm longer or 28+15 = 43 cm.
Mathematical modeling can be done by taking the following steps, namely:
Read the problem carefully and then determine what is known about the problem and what is not known. Completely write down all the complete information from reading the problem. Use variables for anything that is not known or searched for. Construction of diagrams or charts to facilitate or determine the relationships that exist between known elements and variables. State the mathematical model you are looking for in the form of an equation or inequality or a system of equations.Learn more about mathematical model at https://brainly.com/question/29641814
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