What is meant by linear algebra?

a. Region is below both lines.

b. Region is above both lines

c. No solution

d. Region between both lines

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given inequalities,

a. y < 8+2x and 3 + 2x >y

by the graph

Region is below both lines

b. 5 + x < y and y > 7 + x

by the graph

Region is above both lines

c. y > 12 - 3x and 10 - 3x > y

by the graph,

No solution.

d. 6 - x < y and y < 9 - x

by the graph

Region is between both lines.

Hence,

a. Region for the inequalities is below both lines

b. Region for the inequalities is above both lines

c. Region for the inequalities has no solution

d. Region for the inequalities is between both lines

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The function phi(x) = 2/1-ce³ˣ  is a one-parameter family of solutions to the differential equation dy/dx = 3y² - 6y/2.

A function is a one-parameter family of solutions to a differential equation if it satisfies the equation for all values of the arbitrary constant "c".

In this case, the function phi(x) = 2/1-ce³ˣ is a one-parameter family of solutions to the differential equation because, no matter what the value of "c" is, the function will always satisfy the equation.

So, when we say that

=> phi(x) = 2/1-ce³ˣ

is a one-parameter family of solutions to the differential equation

=> dy/dx = 3y² - 6y/2,

we mean that the function can be used to describe the rate of change of y with respect to x for a range of values of y.

By changing the value of the constant "c", we can get different specific solutions to the differential equation, each corresponding to a different curve in the x-y plane.

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The length, in units, of the rectangle is 7 units

The formula for calculating the area of a rectangle is expressed with the equation

A = lw

Given that the parameters are given as;

Now, we have that;

Length = l

width = 3 - l

Area = 28

Substitute the values, we get;

28 = l(3-l)

expand the bracket

28 = l² - 3l

Solve the quadratic equation

l² - 7l + 4l - 28 = 0

l - 7 = 0

l = 7 or l = -4

Hence, the value is 7 units

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x is a random variable that takes values on all positive integers. Then the events are:

(i) a^c = {0, 1, 5, 6, 7...........}

(ii) b^c = {0, 1, 2, 3}

(iii) ab = {4}

(iv) a ∪ b = {2, 3, 4, 5, 6, 7, 8,..........}

a = {2 ≤ x ≤ 4} and b = {x ≥ 4}.

(i) We have to describe the events a^c

a = {2 ≤ x ≤ 4}

Then a^c = {x : x < 2 or x > 4}

So the elements are

a^c = {0, 1, 5, 6, 7...........}

(ii) We have to describe the events b^c

b = {x ≥ 4}.

Then b^c = {x : x < 4}

Then the elements are

b^c = {0, 1, 2, 3}

(iii) We have to describe the events ab.

The ab = a ∩ b

As we know that a = {2 ≤ x ≤ 4} and b = {x ≥ 4}. So

ab = {x : 2 ≤ x ≤ 4 ∩ x ≥ 4}

ab = {x : x = 4}

So, ab = {4}

(iv) We have to describe the events a ∪ b

As we know that a = {2 ≤ x ≤ 4} and b = {x ≥ 4}. So

a ∪ b = {x : 2 ≤ x ≤ 4 ∪ x ≥ 4}

a ∪ b = {2, 3, 4, 5, 6, 7, 8,..........}

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Therefore , the solution of the given problem of polynomial function comes out to be -3x³ -x² - 2x + 3.

A polynomial is a mathematical statement with coefficients and error that uses only additions, erasures, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to an expression in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that can be added, deducted, multiplied, and increased to negative integer ones of non-variables. A polynomial is an algebraic expression having variables and coefficients.

Here,

Given :

=> - 5 , -4 ,- 3

=> -3 , -1 , -2 ,3

=> 1 , 2, 0

to write a polynomial function in factored form :

=> -5x² - 4x - 3

=> -3x³ -x² - 2x + 3

=> x² + 2x

Therefore , the solution of the given problem of polynomial function comes out to be -3x³ -x² - 2x + 3.

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The algorithm to find the maximum number of drop points that can be covered by flying over the terrain once is coded below.

To find the maximum number of drop points that can be covered by flying over the terrain once, use the following algorithm:

1. Read the input values:

Read the integer xCoordinate_size, representing the number of x coordinates (N).

Read the N space-separated integers representing the x coordinates.

Read the integer yCoordinate_size, representing the number of y coordinates (M).

Read the M space-separated integers representing the y coordinates.

2. Create two sets to store the unique x and y coordinates.

Let's call them xCoordinatesSet and yCoordinatesSet.

3. Traverse the input x coordinates:

  - For each x coordinate, add it to the xCoordinatesSet.

4. Traverse the input y coordinates:

For each y coordinate, add it to the yCoordinatesSet.

5. Calculate the number of drop points that can be covered:

The maximum number of drop points that can be covered is the minimum between the size of xCoordinatesSet and yCoordinatesSet.

6. Output the result:

Print the calculated maximum number of drop points.

The algorithm in pseudocode:

function findMaxDropPoints():

   Read xCoordinate_size

   Read xCoordinates (N space-separated integers)

   Read yCoordinate_size

   Read yCoordinates (M space-separated integers)

   xCoordinatesSet = new Set()

   yCoordinatesSet = new Set()

   for each x in xCoordinates:

       xCoordinatesSet.add(x)

   for each y in yCoordinates:

       yCoordinatesSet.add(y)

   maxDropPoints = min(xCoordinatesSet.size, yCoordinatesSet.size)

   Print maxDropPoints

By following this algorithm, efficiently find the maximum number of drop points that can be covered by the pilot while flying over the terrain only once.

The solution has a time complexity of O(n), where n is the number of drop points, which is optimal.

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The question attached here seems to be incomplete, the complete question is:

A pilot was asked to drop food packets in a terrain. He must fly over the entire terrain only once but cover a maximum number of drop points. The points are given as inputs in the form of integer co-ordinates in a two- dimensional field. The flight path can be horizontal or vertical, but not a mix of the two or diagonal.

Write an algorithm to find the maximum number of drop points that can be covered by flying over the terrain once.

Input

The first line of input consists of an integer-xCoordinate_size, representing the number of x coordinates (N).

The next line consists of N space- separated integers representing the x coordinates.

The third line consists of an integer- yCoordinate_size, representing the number of y coordinates (M).

The next line consists of M space- separated integers representing the

Coordinator

Jessie and Bob's balloon payment will be $529,229.56.

A balloon mortgage is a type of mortgage in which the borrower makes smaller monthly payments over the term of the loan, with a large balloon payment due at the end.

To calculate the balloon payment, we need to know the amount of the loan, the interest rate, and the term of the loan.

Given that Jessie and Bob are financing $425,500 to purchase a house, the interest rate is 6.55%, and the term of the loan is 30/8 (or 3.75) years, we can use the below formula to calculate the balloon payment:

Balloon payment = Loan amount * (1 + Interest rate * Loan term)

Balloon payment = $425,500 * (1 + 6.55% * 3.75)

Balloon payment = $425,500 * 1.249625

Balloon payment = $529,229.56

Therefore, Jessie and Bob's balloon payment will be $529,229.56.

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The conversion factor to use depends on the type of angle tat is to be converted

From the question, we have the following parameters that can be used in our computation:

Conversion factors = xrad/180 or 180/x rad

The conversion factor to use depends on the type of angle tat is to be converted

Take for instance, we use 180/x rad  from radians to degree and the other from degree to radians

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Multiplying by 0.05 is the same as decreasing by 95%.

Multiplying a number by 0.05 is equivalent to decreasing that number by a certain percentage. To determine this percentage, we can use the formula: 100 - (100 * 0.05) = 100 - 5 = 95. This means that multiplying a number by 0.05 is the same as decreasing it by 95%. For example, if a person has $100 and multiplies it by 0.05, the result will be $5, which is a decrease of 95% from the original amount.

In other words, 0.05 is equivalent to 95% of a number, and multiplying by 0.05 is the same as decreasing the number by 95%. This relationship between multiplication by 0.05 and decreasing by a certain percentage is important in various mathematical and real-world applications.

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The order of steps will be :

Step 1 : p V (q ⇒ r)

Step 2 : p V ¬ q V r

Step 3 : ¬ q V p V r

Step 4 : q ⇒ (p V r)

Given,

¬p → (q → r)  and q → (p ∨ r) are logically equivalent.

Now to prove the equivalence,

¬p → (q → r) to q → (p ∨ r)

The order of steps is given below:

Step 1 : p V (q ⇒ r)

Step 2 : p V ¬ q V r

Step 3 : ¬ q V p V r

Step 4 : q ⇒ (p V r)

Hence the equivalence can be shown.

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There was spent 22.77 dollars on a pass and lunch for each student

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

Total money spend on passes = 664. 58 dollars

Total number of people = 44 + 3 = 47

Money spend on pass for each person = 664.58/47 = 14.14 dollars

Total money spend on lunch =  379.72 dollar

Total number of students = 44

Money spend on lunch for each student = 379.72/44 = 8.63 dollars

Total money spend= 14.14 + 8.63 = 22.77dollars

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Correctly written question:

A school is arranging a field trip to the zoo. The school spend 664. 58 dollar on passes for 44 student and 3 teacher. The school also spend 379. 72 dollar on lunch for jut the student. How much money was spent on a pass and lunch for each student?

The strategy Malcolm and his father could use to find out how much framing material they will need is B. Measure all 4 sides with a ruler to find the perimeter. This will give them the total length of framing material they will need to surround the poster.

Measuring the area in inches with a ruler (option A) or measuring the poster in square inches (option C) will not give them the length of framing material required to surround the poster. Covering the poster with square inches great paper (option D) is also not an effective strategy to find out how much framing material they need. By measuring the perimeter, they can calculate the amount of framing material required and buy the correct length of framing material for their project.

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The outer surface area of the building is 356 m².

The total area of a three-dimensional object's base, top, and any lateral or exterior surfaces is measured as surface area. A cone, cube, cuboid, or cylinder's surface area is the area it covers on the outside. The formula for a cube's total surface area is 6 (side)2. A cuboid's lateral surface area is equal to 2(length + width) height. Similar to this, a cube with side "a" has lateral surface area equal to 4 (side)2.

Given that,

radius of building = 7m

and its saint height = 14m

Outer surface area = πrl + 2πrh

                                  = πr( L + 2h )

                                 = 22/7 × 7 ( 14 + (2×6))

                                  = 22 × (14 + 12)

                                  = 22 × 26

                                  = 356 m².

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The hint about this being a linear function is a critical piece of information.

A linear function has a fixed slope, so you can use the slope formula to find that slope using the two given points, (-3,-5) and (-1,-1).

        [tex]m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{-1-(-5)}{-1-(-3)} = \dfrac{4}{2}=2[/tex]

Now you can use that slope and a point to find the equation of the function.

g(x) = mx + b, but m=2, so g(x) = 2x + b

If we plug in one of the points, we can calculate b:

     -5 = 2(-3) + b

     -5 = -6 + b

       1 = b

Now you have your function: g(x) = 2x + 1

You can use it to calculate the missing values in the table.

Let A be a vector and n be a unit vector in a fixed direction. The scalar projection of A onto n can be represented as:

An = A . n = ||A||cos(θ),

where θ is the angle between vectors A and n.

The projection of A onto a plane perpendicular to n can be represented as:

A - (An) = A - (||A||cos(θ))n = ||A||sin(θ)nₜ,

where nₜ is a unit vector perpendicular to n.

Combining these two results, we have:

A = (An) + (A - (An)) = (||A||cos(θ))n + ||A||sin(θ)nₜ

By doing so, it is demonstrated that a vector A may be written as the product of its scalar projection along a unit vector n and its projection onto a plane perpendicular to n. This breakdown of a vector is helpful for looking at its parts from various angles.

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We're dealing with linear functions. f(x) = mx + b, We have here the first function. g(x) = 3x That is a linear function with a slope and no linear coefficient because, However, because all of the functions below have the same slope value, they all describe parallel lines.  

Their non-zero linear coefficients are -6,-18,6,18, despite the fact that they all have the same slope value. The first one, though, was

[tex]$\begin{aligned} & h(x)=3(9 x-2) \rightarrow h(x)=27 x-6 \\ & i(x)=9(3 x-2) \rightarrow i(x)=27 x-18 \\ & j(x)=3(9 x+2) \rightarrow j(x)=27 x+6 \\ & k(x)=9(3 x+2) \rightarrow k(x)=27 x+18\end{aligned}$[/tex]

A possible solution would be adjusting any of these, whose operation would result in g(x)=3x, but

Like

[tex]$y=9\left(\frac{3 x}{9}-2\right)+18=3 x$[/tex]

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Ethan is in the process of constructing an equilateral triangle. So, option(A) is the correct answer.

Circle:

Polygon:

Triangle:

Therefore, Ethan is in the process of constructing an equilateral triangle.

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The complete question is:

Ethan is using his compass and straightedge to complete the construction of a polygon inscribed in a circle. Which polygon is he in the process of constructing?

1. An equilateral triangle

2. A square

3. A regular pentagon

4. A regular hexagon

Answer:

6

Step-by-step explanation:

cause 18 is a multiple of 6 and 24

The area of the composite figure is equal to 58 square inches. (Correct choice: C)

In this problem we find the case of composite figure formed by an irregular pentagon and an triangle, the resulting can be found as a combination of triangles and rectangles, whose area formulas are:

Triangle

A = 0.5 · w · l

Rectangle

A = w · l

Where:

Now we proceed to determine the area of the composite figure:

A = 0.5 · (8 in) · (6 in) + (8 in) · (6 in) - 2 · 0.5 · (1 in) · (5 in) - 2 · 0.5 · (3 in) · (3 in)

A = 24 in² + 48 in² - 5 in² - 9 in²

A = 72 in² - 14 in²

A = 58 in²

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The solution to the equation f(x) - g(x)=0 is the x-intercept of the two lines, which is the point at which the two lines intersect.

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Answer:

Step-by-step explanation:

PLACEHOLDER

The results of the mathematical multiplications contained in the annex to the question are:

It corresponds to the steps used to solve a mathematical problem, it is usually a method taught in elementary school, and is useful for solving problems with the mathematical operations of addition, subtraction, multiplication and division.

Therefore, to solve multiplication problems through the standard algorithm, the student must solve the problem by multiplying the problem in parts, that is, by multiplying one digit at a time from right to left, to arrive at the final solution.

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A and B are vertical angles. If angle A=(4x13) ∘and B=(7x4) ∘ then the value of x is 3.

Since A and B are vertical angles, they must and should have equal measures. Therefore, we can set the two expressions equal to each other and solve for x:

4x + 13 = 7x + 4

Subtracting 4 from both sides:

4x + 9 = 7x

Subtracting 4x from both sides:

9 = 3x

Dividing both sides by 3:

x = 3

So the value of x is 3.

After solving the x value, we should subtract 4 from both sides of the equation, which results in 4x + 9 = 7x. Then, we subtract 4x from both sides, then we get 9 = 3x.

Finally, we divide both sides of the equation by 3 to find that x = 3.

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The probability of getting an odd number or number less than three is 5 / 6.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

The samples are given below:-

S = { 1, 2 , 3 , 4 , 5 , 6 }

Favourable outcome = Odd numbers = { 1 , 3 , 5 } = 3

Less than three = { 1 , 2 } = 2

The probability will be calculated as:-

Probability = ( 3 / 6 )  + ( 2 / 6 )

Probability = ( 1 / 2 )  + ( 1 / 3 )

Probability = ( 3 + 2 ) / 6

Probability = 5 / 6

Therefore, the probability will be 5 / 6.

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Carbon is released back into the atmosphere when organisms die, volcanoes erupt, fires blaze, fossil fuels are burned, and through a variety of other mechanisms.

The atmosphere is the layer of gas that surrounds a planet, including Earth. Atmosphere is taken from the Greek words "atmos" and "sphaira". Atmos means water vapor or gas and sphaira means blanket.

As mentioned above, the atmosphere also surrounds the planets other than Earth. Generally the thickness of the atmosphere is approximately 1,000 kilometers. On Earth alone, the atmosphere is 560 kilometers thick from the ground to space.

The mass of Earth's atmosphere is known to be 59 x 1014 tonnes. The gas content of each planet's atmosphere is usually different, depending on the most abundant gas elements or compounds on that planet.

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By adding and subtracting 9, we will be able to complete squares and rewrite the expression as:

x^2 + 6x = (x + 3)^2 - 9

Remembert that the perfect square trinomial is:

(a + b)^2 = a^2 + 2ab + b^2

Here we have the quadratic expression:

x^2 + 6x

We can rewrite the second term as:

x^2 + 2*3*x

Then, comparing with the variables on the first equation, we can use:

x = a

3 = b

Then what we need to add to complete squares is 3^2 = 9

To not change the expression, we will add and subtract that number (which is equivalent to adding 0).

x^2 + 2*3*x + 9 - 9

(x^2 + 3*3x + 9) - 9

(x + 3)^2 - 9

That is the expression after we complete squares.

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Analia can define the quantity by either the % of students in sports clubs divided by SAT average or the Number of sports medals won. Hence, options A and C are the correct options.

Analia wants to know which school has the higher SAT average relative to the resources invested per student. In order to do so, she has to think of ways using which she would easily be able to do so.

From the given options we can deduce that she can either use the % of students in sports clubs divided by SAT average or the Number of sports medals won.  Since Percentage of students in sports clubs divided by SAT average and the Number of sports medals won defines the quantitative characteristic of SAT. These are the two ways in which Analia defined the given quantity

The complete question that you might be looking for is given below.

Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.

A) % of students in sports clubs divided by SAT average

B) Graduation rate divided by SAT average

C) Number of sports medals won

D) Number of sports medals divided by SAT average

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A tree diagram for the scenario is:

      Start

      /    \

    Blue    Red

    /    \

 Blue    Red

 /    \

Blue    Red

A probability space can be represented by a tree diagram in probability theory. A series of independent events or conditional probabilities may be represented using a tree diagram. The diagram's nodes each represent an occurrence and their respective probabilities.

To calculate the probability of picking a blue sweet twice in a row, we need to multiply the probability of picking a blue sweet on the first try (7/10) by the probability of picking a blue sweet on the second try (7/10), resulting in (7/10) * (7/10) = 49/100.

Similarly, to calculate the probability of picking a red sweet on the first try and a blue sweet on the second try, we need to multiply the probability of picking a red sweet on the first try (3/10) by the probability of picking a blue sweet on the second try (7/10), resulting in (3/10) * (7/10) = 21/100.

So the probability of picking a red sweet twice in a row is (3/10) * (3/10) = 9/100.

Thus, the probability of picking blue twice in a row is 49/100, and the probability of picking red-blue or blue-red is 21/100.

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a.) M(t) = 2500 + 40t is a representation of the savings account amount after t years. The $2500 starting sum is added to a $40 annual increase using this function.

b.) The total balance of the two accounts at the end of t years may be written as B(t) = m(t) + 500. In this function, the constant $500 checking account amount is added to the savings account balance, m(t).

Investment is the act of allocating funds or capital to buy securities or other assets with the hope of making a profit or seeing their value rise.

Investments come in a variety of shapes and sizes, including stocks, bonds, mutual funds, and other types of real estate and commodities. Choosing the appropriate mix of investments is a crucial component of a smart investing plan since each form of investment has unique risks and possible returns.

Investments are mostly made with the intention of increasing wealth over time. By investing, people can build wealth for long-term financial stability or save for future costs like retirement. Due to the fact that investment returns frequently outperform inflation rates, investing can also act as a hedge against inflation. The type of assets a person chooses and the amount of risk they are ready to take depend on their investment objectives and time horizon.

According to the question

A linear function, m(t) = 2500 + 40t, may be used to describe the savings account balance, where t is the number of years that have elapsed. The $2500 starting sum is taken into consideration, and for each year that has gone, an additional $40 is added. This gain might be compared to an annual interest rate or investment growth.

Then, B(t) = m(t) + 500 may be used to represent the combined balance of both accounts. This function transfers the fixed balance of $500 in the checking account to the savings account balance, m(t). We may simply fill in the value of t to get the total financial condition at any given year by merging both accounts.

Making decisions about spending, saving, and investing may be done using this kind of depiction, which is helpful for tracking financial development over time. It may also be used to define financial objectives and monitor progress toward them. One may change their spending patterns and investing strategies to get to the desired financial position by keeping an eye on the trend in the growth of the overall balance.

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a.) M(t) = 2500 + 40t is a representation of the savings account amount after t years. The $2500 starting sum is added to a $40 annual increase using this function.

b.) The total balance of the two accounts at the end of t years may be written as B(t) = m(t) + 500. In this function, the constant $500 checking account amount is added to the savings account balance, m(t).

Investment

Allocating money or capital to purchase securities or other assets in the hopes of turning a profit or seeing their value increase is known as investing.

Stocks, bonds, mutual funds, and other forms of real estate and commodities are just a few examples of the many shapes and sizes that investments can take. As each type of investment carries specific risks and potential rewards, selecting the right balance of investments is essential to a sensible investing strategy.

Most investments are made with the hope of accumulating money over time. By investing, people can increase their wealth and secure their long-term financial well-being or save for future expenses like retirement. Investing can also serve as an inflation hedge because it frequently outperforms inflation rates in terms of returns. The kind of assets a person selects and the level of risk they are willing to accept are determined by their investment goals and time horizon.

According to the question,

A linear function, m(t) = 2500 + 40t, may be used to describe the savings account balance, where t is the number of years that have elapsed. The $2500 starting sum is taken into consideration, and for each year that has gone, an additional $40 is added. This gain might be compared to an annual interest rate or investment growth.

Then, B(t) = m(t) + 500 may be used to represent the combined balance of both accounts. This function moves the fixed $500 check account balance to the savings account balance m(t). To obtain the complete financial situation for any given year by merging both accounts, we can simply enter in the value of t.

This form of depiction can be used to make decisions regarding spending, saving, and investing and is useful for following the evolution of your finances over time. Setting financial goals and tracking progress toward them are other uses for it. By keeping an eye on the trend in the growth of the overall balance, one can adjust their spending habits and investment methods to reach the desired financial position.

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Answer:

square root of (l^2 + b^2)

The formula for the diagonal of a rectangle is given by the d = √(l² + w²).

What is the length of the diagonal of the rectangle?

We can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

The diagonal of a rectangle is a line segment connecting two opposite corners of the rectangle and passes through the interior of the rectangle.

The formula for the diagonal of a rectangle is given by the Pythagorean theorem:

d = √(l^2 + w^2)

Where,

d is the length of the diagonal,

l is the length of the rectangle,

and w is the width of the rectangle.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

In the case of a rectangle, the two shorter sides are the length and the width of the rectangle, and the longest side is the diagonal.

Therefore, the diagonal of a rectangle can be considered as the hypotenuse of a right triangle with sides equal to the length and width of the rectangle.

Hence, The formula for the diagonal of a rectangle is given by the d = √(l² + w²).

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