The net of a triangular prism and its dimensions are shown below. What is the total surface area of the prism? The net of a triangular prism and its dimensions are shown below.



What is the total surface area of the prism?

Answer:

შეგვიძლია ამოვიღოთ რომ CuO და HNO3 რეაგირებენ და ქებისყარის შედეგად Cu(NO3)2 იქნება წარმოდგენისათვის.

სახელში მოცემული მასალების მიხედვით, შეგვიძლია ამოვიღოთ რომ 1 მოლი CuO რეაგირებულია 4 მოლი HNO3-თი, ანუ შესაბამისად, მასალების მიხედვით:

m(CuO) / M(CuO) = n(CuO) = n(HNO3) = m(HNO3) / M(HNO3)

10 გ / 79,55 გ/მოლი = 0,1256 მოლი CuO = 0,1256 მოლი HNO3 = 12,6 გ / 63,01 გ/მოლი

რეაქციის შემდეგ მივიღებთ, რომ 1 მოლი CuO-სთვის გამოვიყენებთ 4 მოლი HNO3-ს, რაც შემდეგ მანამდე გადავაკეთებთ მათ მიერ რეაქციას, ანუ:

n(Cu(NO3)2) = n(CuO) = 0,1256

Step-by-step explanation:

The area of the rhombus is twice the area of one triangle:

A_rhombus = 2 * A

A_rhombus = 2 * (21/4)√10

A_rhombus = 21/2 * √10

A form's area is determined using the surface. To calculate the area of a rectangle or square, multiply its length and width. A is x times y in size.

To find the area of the rhombus, we can decompose it into two congruent triangles and find the area of one triangle, then multiply it by 2 to get the area of the whole rhombus.

The height of each triangle is h = 7 units, and the length of the base of each triangle is half the length of a diagonal of the rhombus. Using the Pythagorean theorem, we can find the length of the diagonal:

d² = x² + y²

d² = 9² + 3²

d² = 90

d = √90 = 3√10

Therefore, the length of the base of each triangle is 1/2 * 3√10 = (3/2)√10 units.

The area of one triangle is:

A = (1/2) * base * height

A = (1/2) * (3/2)√10 * 7

A = (21/4)√10

The area of the rhombus is twice the area of one triangle:

A_rhombus = 2 * A

A_rhombus = 2 * (21/4)√10

A_rhombus = 21/2 * √10

Therefore, the area of the rhombus is 21/2 * √10 square units.

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The expression that represents the area of the given door is (3w+8)w.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.

This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

So, we know that:
width = w

And we also know that:

length = 3w + 8

Now, the area formula is:
l*w

Insert values as follows:

l*w

(3w + 8)w

Therefore, the expression that represents the area of the given door is (3w+8)w.

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It would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

A square meter is a unit of measurement that denotes the surface area of a two-dimensional object or surface that is one metre long and one meter broad. It is frequently used to determine the dimensions of rooms, structures, and other areas as well as the surface area of land or other objects. The imperial method of measurement converts one square metre into 10.764 square feet. Science, engineering, and other fields frequently utilise the square metre, a core unit of the International System of Units (SI).

The area of the room is:

Area = 5m x 5m = 25 square meters

Then, we multiply the area by the cost per square meter:

Cost = 25 square meters x N5.00 per square meter = N125.00

Hence, it would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

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Answer:

To find the percent increase in price, we need to calculate the difference between the original price and the new price, and then express that difference as a percentage of the original price.

The original price of the sweatshirt was $40, and the new price is $65, so the difference is:

$65 - $40 = $25

To express this as a percentage of the original price, we divide the difference by the original price and multiply by 100:

($25 / $40) x 100% = 62.5%

Therefore, the percent increase in the price of the sweatshirt is 62.5%.

Answer:

D

Step-by-step explanation:

2ft×6ft=12ft

12ft÷2=6

6×2=12ft for the two triangles

6×4=24ft for the rectangle

24ft+12ft= 36 square feet

so it's D 36 square feet

Answer:

[tex]\huge\boxed{\sf 36 \ ft.\²}[/tex]

Step-by-step explanation:

Given that,

Base = 2 + 4 = 6 ft.

Height = 6 ft.

= Base × Height

= 6 × 6

[tex]\rule[225]{225}{2}[/tex]

Answer: As a fraction: 1/2

              As a decimal: 0.005

Step-by-step explanation:

FRACTION:

To figure out how to write 0.5% as a fraction, all you need to know is that 0.5 = to a half, or 1/2 because 0.5 is half of 1.

DECIMAL:

0.5% as a decimal form is 0.005 because it is 1000 times less than 1, so you move the 0 3 times right.

The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is given as follows:

5/6.

The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is obtained applying the proportions in the context of the problem.

We have that both the x-coordinate and the y-coordinate of A and B have a difference of 6 units.

We also have that both the x-coordinate and the y-coordinate of point P(3,1) have a difference of five units from the coordinates of the starting point of the segment A.

Then the ratio is given as follows:

5/6.

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Answer:

55 cards

Step-by-step explanation:

Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.

A mathematical assertion that two expressions are equivalent is known as an equation. The equal symbol (=) separates the two sides, which are labeled as the left-hand side (LHS) and the right-hand side (RHS). The equation must have identical values on both sides, and it is frequently used to determine an unknown variable's value.

Numerous mathematical processes, such as addition, subtraction, multiplication, division, exponents, logarithms, and more, can be used in equations.

given

a. The formula for the stamp's worth V after t years is as follows:

[tex]V = 14.50(1 + 0.02)^t[/tex]

where t is the period of time since Leroy got the stamp, and 0.02 denotes a 2% annual increase in value.

b. We enter t = 18 into the equation to estimate the stamp's value after 18 years:

[tex]V = 14.50(1 + 0.02)^{18[/tex]

[tex]V = 14.50(1.02) (1.02)^{18[/tex]

V = 14.50(1.485) (1.485)

V = 21.54

Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.

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Answer:

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro c

Step-by-step explanation:

Answer: A quarter and 4 pennies

Step-by-step explanation:

25+4=29

geometric series:

[tex]\dfrac{4}{-8} = - \dfrac{1}{2}[/tex]

[tex]\dfrac{-2}{4} = - \dfrac{1}{2}[/tex]

[tex]\implies r = - \dfrac{1}{2} \ \ and \ \ a_{1} = -8[/tex]

[tex]\boxed{S_{n} = \dfrac{a_{1}\cdot (1 - {r}^{n}) }{1 - r}}[/tex]

a. n = 3

[tex]S_{3} = - 8 + 4 - 2 = 4 - 10 = \bf -6\\[/tex]

b. n = 6

[tex]S_{6} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{6}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 - \dfrac{1}{2^{6}}\Big)}{1 + \dfrac{1}{2}} = \dfrac{-8 + \dfrac{1}{2^{3}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= \dfrac{-64+1}{2^{3}} \cdot \dfrac{2}{3} = -\dfrac{63}{2^{2}(3)} = \bf -\dfrac{21}{4}[/tex]

c, n = 25

[tex]S_{25} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{25}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 + \dfrac{1}{2^{25}}\Big)}{1 + \dfrac{1}{2}} = - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} = - \dfrac{1 + 2^{25}}{2^{22}} \cdot \dfrac{2}{3} = \bf - \dfrac{1 + 2^{25}}{(3)2^{21}}\\[/tex]

Answer:

To solve this problem, we need to use vector addition. We can start by breaking down each force into its x and y components.

For muscle A:

Force = 100 lbs

Angle = 15 degrees

X-component = 100 * cos(15) = 96.93 lbs

Y-component = 100 * sin(15) = 25.04 lbs

For muscle B:

Force = 150 lbs

Angle = 30 degrees

X-component = 150 * cos(30) = 129.90 lbs

Y-component = 150 * sin(30) = 75.00 lbs

For muscle C:

Force = 75 lbs

Angle = 10 degrees

X-component = 75 * cos(10) = 73.83 lbs

Y-component = 75 * sin(10) = 13.03 lbs

Next, we can add up the x and y components separately:

X-component = 96.93 + 129.90 + 73.83 = 300.66 lbs

Y-component = 25.04 + 75.00 + 13.03 = 113.07 lbs

We can use these components to find the magnitude and direction of the resultant force:

Magnitude = sqrt(X^2 + Y^2) = sqrt((300.66)^2 + (113.07)^2) = 321.23 lbs

Direction = tan^-1(Y/X) = tan^-1(113.07/300.66) = 21.65 degrees (measured counterclockwise from the positive x-axis)

Therefore, the resultant force of the muscles is 321.23 lbs at an angle of 21.65 degrees. Here is a diagram to illustrate the vectors:

Step-by-step explanation:

      25.04 lbs    73.83 lbs    129.90 lbs

         /\           /\           /\

        /   \        /   \        /   \

       /      \     /      \     /      \

 100 lbs     15°  75 lbs    10°  150 lbs  30°

      \         /  \         /  \         /

       \      /     \      /     \      /

        \   /        \   /        \   /

      96.93 lbs   13.03 lbs   75.00 lbs

Answer:

One solution at (2, -1)

Step-by-step explanation:

You will want to write the equations for both pairs of points:

(-2,-3) and (0,-2)

The slope is the change in y over the change in x.  The first number of the ordered pairs is the x value and the second number in the ordered pair is the y values.  Find the change by subtraction

[tex]\frac{-2 - -3}{0 - -2}[/tex] = [tex]\frac{-2+ 3}{0 + 2}[/tex] = [tex]\frac{1}{2}[/tex]

The slope (m) is 1/2.

The y intercept is when x = 0.  In the point (0,-2) x is 0, so the y-intercept is -2.

The y-intercept (b) is -2.

y = mx + b  Substitute 1/2 for m and -2 for b

y = [tex]\frac{1}{2}[/tex]x - 2

(0,3) and (1,1)

The slope is

[tex]\frac{1-3}{1-0}[/tex] = [tex]\frac{-2}{1}[/tex] = -2

The slope is --2.

The y intercept is 3.

y = mx + b  Substitutes -2 for m and 3 for b.

y = -2x + 3

Set the 2 equation equal to each other and solve for x.

-2x + 3 = 1/2 x -2   Multiply all the way through by 2 to clear the fraction.

-4x + 6 = x - 4   Add 4x to both sides

-4x + 4x + 6 = x + 4x -4

6 = 5x -4  Add 4 to both sides

6 + 4 = 5x - 4 + 4

10 = 5x  Divide both sides by 5

2 = x

Take either of the two original equations and substitute 2 for x and solve for y

y = -2x + 3

y = -2(2) + 3

y = -4 + 3

y = -1

The solution is (2,-1)

Helping in the name of Jesus.

Therefore , the solution of the given problem of equation comes out to be  y = 6x + 11.

Mathematical formulas frequently use the same letter to try to impose uniformity between two claims. Many variable academic numbers are shown to be equal using mathematical equations, also known as assertions. The normalise divides 12 and b + 6 into two parts using the result y + 6 = 12 as an illustration. It is possible to determine the connection between each sign component and the number of lines. The significance of a symbol usually contradicts itself.

Here,

In slope-intercept form, the provided equation y = -1/6x - 2 has a slope of -1/6. Consequently, this line's perpendicular inclination is as follows:

=> m2 = -(1/-1/6) = 6

Now that we know the desired line's slope and the spot through which it passes (-2, -1). To determine the solution of a linear equation, we can use its point-slope form:

=> y - y1 = m(x - x1) (x - x1)

where m is the slope 6 and (x1, y1) is the position (-2, -1). By replacing these numbers, we obtain:

=> y + 1 = 6(x + 2) y + 1

=> 6x + 12 y + 1

=> 6x + 11 y - (-1)

=> 6(x - (-2))

As a result, the equation for the line passing through the position (-2, -1) and perpendicular to y = -1/6x - 2 is y = 6x + 11.

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The proportionality constant (mm to cm) is 10 and the complete table is -

9 cm                 90 mm

12.5 cm             125 mm

50 cm               500 mm

88.49 cm          884.9 mm

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given is a proportional relationship between two scales.

{ 1 } -

We can write the proportionality constant (mm to cm) as -

{k} = (20 - 10)/(2 - 1)

{k} = 10

{ 2 } -

We can write the complete table as -

9 cm                  9 x 10 = 90 mm

12.5 cm             12.5 x 10 = 125 mm

50 cm               50 x 10 = 500 mm

88.49 cm          88.49 x 10 = 884.9 mm

Therefore, the proportionality constant (mm to cm) is 10 and the complete table is -

9 cm                 90 mm

12.5 cm             125 mm

50 cm               500 mm

88.49 cm          884.9 mm

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Part A: the drone would need to fly up 1.3 miles  Part B:  the drone would need to fly up 1.8 miles. Part C:  the value of zero represents the top of the waterfall . Part D: the absolute value of -1.8 is the same as the absolute value of 1.8, we have shown that you hiked the same distance in both directions.

It can be measured in various units such as meters, kilometers, feet, miles, etc. In mathematics, the distance between two points in a coordinate plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √[(x2 - x1)² + (y2 - y1)²]

Where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them

Part A: The distance from the top of the waterfall to the place where you eat lunch is 1.3 miles, so the drone would need to fly up 1.3 miles

Part B: The distance from the top of the waterfall to the place where you go swimming is 1.8 miles, so the drone would need to fly up 1.8 miles

Part C: In this problem, the value of zero represents the top of the waterfall where you and your friend are currently located.

Part D: Let x be the distance you hiked to go swimming, and let y be the distance you hiked to go back to the top to meet your friend. Then, the total distance you hiked is the sum of the absolute values of x and y, which can be written as |x| + |y|. Since you hiked down 1.8 miles to go swimming and then hiked back up 1.8 miles to the top, x = -1.8 and y = 1.8. Substituting these values, we get |(-1.8)| + |1.8| = 1.8 + 1.8 = 3.6. Since the absolute value of -1.8 is the same as the absolute value of 1.8, we have shown that you hiked the same distance in both directions.

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The complete question is :

The table makes it abundantly evident that buying costs less than renting does. Buying a house is therefore better over the course of 15 years. By buying a home instead of renting one, you can save $5,222.4.

Every object's length can be determined using measuring tools like a ruler, measuring tape, etc. For example, a ruler may be utilized to measure the length in inches of a pencil. A foot scale can be used in a classroom to gauge the heights of the students.

Step 1

Buying a home is more advantageous if someone is looking for somewhere to live for an extended period of time. Second, if a person buys the home, it can be sold at a higher price in the future since rental prices after a specified term and after a few years, say 10 or 15, cumulative rental charges become greater than the initial purchase price.

However, according to the above table, renting a property is preferable if the need for the home is for a shorter duration, like fewer then 5 or 10 years, in order to save money.

Step 2

1 year

The cost for Purchasing a house = 30,000 + 1 × 12 × 809.32 = $39,711.84

The cost of renting a house = 1 × 12× 900 = $10,800

So, it is evident that there's a difference between buying and renting a home of $28,911.84. So, renting a home is preferable.

Step 3

5 year

The cost of purchasing the home for five years is listed as $78559.20, whereas the cost of renting the home for five years was $54,900.

Again, renting is more affordable than buying. By renting a home, one could save $23,659.2 (78559.20-54900).

10 years

The cost of purchasing the home over 10 years is shown as $127,118.40, while the cost of renting the home for 10 years was $115,200.

Renting is less expensive than buying. Yet, buying a house is advantageous if it can be bought or rented out; otherwise, leasing one is advantageous.

Step 4

15 years

The table clearly shows that purchasing is less expensive than renting. Over the period of fifteen years, purchasing a home is therefore preferable. You can save $5,222.4 by buying a house instead of renting one.

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The required from Frack's city rate of miles, Seattle and Orlando are less expensive while Miami and Honolulu are more expensive.

Rate of change is defined as the change in value with rest to another value is called rate of change.

Here,
In Frank's city,
y = 0.3x + 2

The rate per mile is represented by the slope of the linear equation.
So,
m = $0.3 per mile

For Seattle

The rate per mile is given by the slope of the relation shown in the graph. So,
m = 3.2 - 2.4 / 6 - 2
m = $0.2 per mile

Similarly,
For Orlando, m = $0.25 per miles
For Miami, m = $0.4 per mile
For Honolulu m = $0.75 per mile

Thus, the required from Frack's city rate of miles, Seattle and Orlando are less expensive while Miami and Honolulu are more expensive.

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Answer:

Let's assume Pena's favorite number as "p".

According to the problem, Tonya's number is 9 more than Pena's favorite number, so Tonya's favorite number would be p + 9.

But Tonya says her favorite number is 44, so we can write:

p + 9 = 44

This equation represents the relationship between Pena's and Tonya's favorite numbers.

Therefore , the solution of the given problem of  expressions comes out to be option C. 69x is the right response.

Calculations like multiplying, dividing, joining, and presently removing are required. If they were put together, it would say: An equation, some statistics, and a mathematical formula A statement of truth is composed of values, components, and mathematical processes like additions, subtractions, errors, subdivisions, and arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

The formula 21x + 19(2x) + 2(5x) can be made simpler as follows:

=> 21x + 38x + 10x = 69x

Maliq's total scores can therefore be written as 69x.

To determine which decision is equivalent to 69x, we can also look through the answer options.

A.

=> (21+19)2x + 10x = 40(2x) + 10x = 80x + 10x = 90x,

which is not equivalent to 69x..

B. 42x and 69x are not equal.

C. 69x is the same as 69x.

D. The sum of

=> (21+19+2)(x+2x+5x) = 42(8x) = 336x does not equal 69x.

Therefore, C. 69x is the right response.

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Answer: 2%

Step-by-step explanation:

annual interest rate is based off a year
monthly is based off month
there are 12 months in a year, so to find the monthly interest you just divide the annual interest by 12.

Answer:

3(x + 12)(x + 2)

Step-by-step explanation:

Given

3x² + 42x + 72 ← factor out 3 from each term

= 3(x² + 14x + 24) ← factor the quadratic

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term.

The factors are + 12 and + 2, since

12 × 2 = 24 and 12 + 2 = 14, thus

x² + 14x + 24 = (x + 12)(x + 2) and

3x² + 42x + 72

= 3(x + 12)(x + 2) ← in factored form

The domain and the range of the function f(x) = log₂(x) are (6, ∞) and [0, ∞)

The equation of the function is given as

f(x) = log₂(x)

In this case, the argument of the logarithm is x - 6 must be greater than 0 for the function to be defined.

So, we have

x - 6 > 0

Adding 6 to both sides of the inequality, we get:

x > 6

This means that

Domain: (6, ∞)

The range of a logarithmic function is the set of all possible output values of the function.

In this case, the base of the logarithm is 2, which means that the function will not take negative values

Therefore, the range of the function is:

Range: [0, ∞)

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Answer:

c

Step-by-step explanation:

2 x 2=4

2 x 2 =4
2 x 2 = 4

4 ^3 = 64

48 x 3 =192
Or:
192/2 = 96
96/2=48
48/2 = 24

24/2= 12
12/3=4

4/2=2
2 x 2 x 2 x 2 x 2 x 2 x 3

The next number in the sequence is 47, 1, and 27.

A series of numbers is called a number series. We must identify the rules that lead to the formation of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.

One possible pattern in this sequence is that each number is the reverse of the sum of the digits of the previous number, followed by the next odd number. Applying this pattern to the given sequence, we have:

The reverse of 63 is 36. The sum of the digits of 63 is 6 + 3 = 9. Therefore, the next number is 36 + 9 = 45, followed by the next odd number, which is 47. So the next number is 47.

The reverse of 00 is 00. The sum of the digits of 00 is 0 + 0 = 0. Therefore, the next number is 00 + 0 = 0, followed by the next odd number, which is 1. So the next number is 1.

The reverse of 22 is 22. The sum of the digits of 22 is 2 + 2 = 4. Therefore, the next number is 22 + 4 = 26, followed by the next odd number, which is 27. So the next number is 27.

Therefore, the next number in the sequence is 47, 1, 27.

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The requried (a) median for the chocolate candy and nonchocolate candy sales are $3040 and $1566.5 respectively. (b) The range for the chocolate candy sales, the range is ($1941, $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).

A histogram is a graphical representation of the distribution of a set of numerical data. It consists of a set of rectangles, where the area of each rectangle is proportional to the frequency (or count) of the observations falling within a particular interval, called a bin.

Here,
A. The interval for the median for each data set can be found by arranging the data in ascending order and finding the middle value. For the chocolate candy sales, the median falls in the interval of 2800-3,099 dollars. While for the Nonchocolate candy, it falls under 1300 -1599

The median for the chocolate candy sales  = $3040
The median for the Nonchocolate candy sales  = $1566.5

B. The range for each data set can be found by subtracting the minimum value from the maximum value. For the chocolate candy sales, the range is ($1941, to $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).

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Answer: Without a perpendicular cut, we cannot determine the height of the triangle directly. However, we can use the Pythagorean Theorem to find it indirectly.

Let's assume that Francine has cut the paper into a right triangle ABC, where AB and BC are the legs of the triangle, and AC is the hypotenuse. Let x be the length of AB and y be the length of BC. We can then use the Pythagorean Theorem to find the length of AC:

AC^2 = AB^2 + BC^2

We don't know the exact values of AB and BC, but we do know that the area of the triangle is given by:

Area = (1/2) * AB * BC

We can use this formula to find the area in terms of x and y:

Area = (1/2) * x * y

Now we need to eliminate one of the variables (either x or y) so that we can express the area in terms of the other variable and AC. We can do this by rearranging the Pythagorean Theorem to solve for one of the variables:

x^2 = AC^2 - y^2

y^2 = AC^2 - x^2

Let's solve for y:

y^2 = AC^2 - x^2

y = sqrt(AC^2 - x^2)

Now we can substitute this expression for y into the formula for the area:

Area = (1/2) * x * sqrt(AC^2 - x^2)

To find the maximum possible area, we need to maximize this expression. We can do this using calculus, by taking the derivative of the expression with respect to x, setting it equal to zero, and solving for x. However, since we only need an approximate answer to the nearest tenth of a square centimeter, we can use trial and error to find the value of x that gives the maximum area. We can start by trying different values of x, and using a calculator to evaluate the expression and find the corresponding area.

Let's try a few values of x:

If x = 0, then the area is 0.

If x = AC/2 (i.e., if the triangle is isosceles), then the area is (1/8) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.

If x = AC/sqrt(3) (i.e., if the triangle is equilateral), then the area is (1/4) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.

Since the area is maximized when the triangle is equilateral, we can assume that the piece of paper is an equilateral triangle, and use the formula for the area of an equilateral triangle:

Area = (sqrt(3)/4) * side^2

where side is the length of one of the sides of the triangle. To find the side length, we need to know the length of AC. We don't know the exact value of AC, but we can estimate it by measuring the length of the longest side of the piece of paper (assuming that it is the hypotenuse of the triangle). Let's say that the longest side is 30 cm. Then, by the Pythagorean Theorem, we can find the length of the other two sides:

x^2 + y^2 = 30^2

x^2 + (sqrt(AC^2 - x^2))^2 = 30^2

2x^2 + AC^2 - x^2 = 900

x^2 = (900 - AC^2)/

Step-by-step explanation:

The total area of the composite figure is 107/216 square yards.

What is Area?

Area is a measure of the size of a two-dimensional shape or surface. It is the amount of space inside the boundaries of a flat object, measured in square units such as square meters, square feet, or square inches.

To find the total area of the composite figure, we need to first convert the dimensions from inches to yards, since the given scale is in inches per yards.

Since 1 yard is equal to 3 feet, which is equal to 36 inches, we have:

The height of the triangle is 6/36 = 1/6 yards.

The base of the triangle is 9 times the height, which is 9/6 = 3/2 yards.

The length of the rectangle is 7/9 yards.

The width of the rectangle is 6/9 = 2/3 yards.

The area of the triangle is:

(1/2) x (1/6) x (3/2) = 1/8 square yards.

The area of the rectangle is:

(7/9) x (2/3) = 14/27 square yards.

Therefore, the total area of the composite figure is:

1/8 + 14/27 = 107/216 square yards.

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(I) Break even sales: S = 40,000

(ii) Sales needed to earn a profit  Rs 6000 per period: S = Rs. 45,000.

The formula for the Break even sales is:

(S‐v) /S= F + P  

s x P/V Ratio = Contribution

First calculate P/V Ratio:

P/V Ratio = Contribution/sales x 100

P/V Ratio = (40‐24)/40 x 100

P/V Ratio= 16/40 x 100

P/V Ratio = 40%

(I) Break even sales  

S x P/V Ratio = Fixed Cost

For break even sales, deposition equals fixed cost.

Thus,

Put the values:

S x 40/100 = 16,000

S = 16,000 x 100 / 40

S = 40,000

S = 1000 units

(II) Sales to gain a profit of Rs. 6,000

S x P/V Ratio = F + P

Put the values:

S x 40/100 = 16000 + 2000

S = 18,000 x 100/40  

S = Rs. 45,000

S =  1125 units

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