Assignment: Waves Math Exploration


What is the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m?

Please answer immediately if able to!

Applying the property of the diagonals of a kite, the measure of angle F is calculated as: 71°.

The property of the diagonals of a kite is that they intersect at a right angle, while the shorter diagonal divides it into two isosceles triangles.

Thus, FH is a diagonal that divides the kite into two isosceles triangles, therefore:

m<EFH = 1/2(180 - 142)

m<EFH = 19°

m<GFH = 1/2(180 - 76)

m<GFH = 52°

m<F = m<EFH + m<GFH

m<F = 19 + 52

m<F = 71°

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Answer:

--------------------------

Property of kites:

In the given kite we can see a pair of different angles, ∠G and ∠E.

It means the other two angles are congruent:

We know the sum of interior angles of a quadrilateral is 360°.

Find the missing angle measure:

Thus, the value of the quadratic function obtained using the zeros is found as: f(x) = [tex]x^{2}[/tex] + 5x - 14.

f(x) = a[tex]x^{2}[/tex] + bx + c, for which a, b, and c are numbers and an is not equal to zero, is a quadratic function.

A parabola is the shape of a quadratic function's graph. Even though "width" or "steepness" of a parabola can vary as well as its path of opening, they all share the same fundamental "U" structure.

Given zeroes of the quadratic function is:

x1 = -7 and x2 = 2

Zeros in terms of factors are written as:

(x + 7) and (x - 2)

Let f(x) be the quadratic function:

f(x) = (x + 7)(x - 2)

On simplifying:

f(x) = [tex]x^{2}[/tex] + (7 -2)x - 7*2

f(x) = [tex]x^{2}[/tex] + 5x - 14

Thus, the value of the quadratic function obtained using the zeros is found as: f(x) = [tex]x^{2}[/tex] + 5x - 14.

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The expression for the total amount of money collected in Keiko's class is 0.25 x 27 + 0.10 x 92 + 0.05 x 140 + 0.01 x 255

To find out how much money Keiko’s class collected, the teacher needs to add up the value of each coin.

The value of a quarter is 25 cents, a dime is 10 cents, a nickel is 5 cents, and a penny is 1 cent.

In dollars, the expression to find the total amount of money collected  can be written as follows:

0.25 x 27 + 0.10 x 92 + 0.05 x 140 + 0.01 x 255 = $25.50

Therefore, the total amount of money collected by Keiko’s class was $25.50

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If Liam buys a laptop for Rs 840 (including 15% VAT) then the price of the laptop without VAT could be Rs 730.

Let the price of the laptop be 100 rupees.

After including 15% VAT, the price of the laptop would be 115 rupees.

The original price = (100 × 840)/115 = 730.

Hence the price of the laptop could be Rs 730.

This problem is the concept of discount and tax. In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax. In this lesson, we will study the tax computation when the selling price or price before tax is given. We calculate tax on a product by multiplying the tax rate with the product's net selling price.

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In this case, the graph crosses the x-axis that is x intercept at x = -3 and x = 3,thus the answer is B. (x-3)(x+3).

Intercept is the point where a graph intersects with either the x-axis or y-axis. It is the value at which a line crosses the axis.

To determine the factored form of the related polynomial, we must first identify the zeroes of the function.

A zero is a point on the graph where the value of the function is equal to zero.

In the graph given, there are two zeroes, one at x=-3 and one at x=3.

The factored form of the polynomial can be expressed as (x-3)(x+3).

This is because the two zeroes of the function correspond to the two linear factors,

x-3 and x+3.

This matches the equation of the polynomial given in the graph, confirming that the correct factored form is (x-3)(x+3).

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Thus, the total number of clients that got haircuts have blond hair is 9.

A prospective outcome of an experimentation or trial is described to as an outcome in probability theory. Only one result will materialise on each trial of an experiment since each possible outcome is distinct and numerous results are mutually exclusive.

Given number of hair colours:

Total colours = 12

Probability = favourable event / total outcome

Probability(blond hair) = 3/12 = 1/4

Total customers = 36

Number of clients have blond hair = 1/4 *36 = 9

Thus, the total number of clients that got haircuts have blond hair is 9.

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Answer:

Marcus has to multiply the height times the length times the width.

Step-by-step explanation:

The formula for the volume of a rectangular prism is the following:

Volume of rectangular prism = length x width x height

Step-by-step explanation:

given -

2

x

−

3

y

=

18

The slope of the equation of the form

a

x

+

b

y

=

c

is -

m

=

−

a

b

=

−

2

−

3

=

2

3

To find the y-intercept put

x

=

0

2(0)−

3

y=

18

−

3

y

=

18

y

=

18

−

3

=

−

6

Slope

m

=

2

3

Y intercept

(

0

,

−

6

)

graph{2x-3y=18 [-6.58, 13.42, -7.28, 2.72]}

2x+3y = -18

First, I'm going to find the x-intercept.

2x+3(0)= -18

2x+0= -18

2x=-18

x=-9

Next, the y-intercept.

2(0)+3y= -18

3y= -18

y= -6

Hope this helps!

a. The product of the expressions is 15[tex]x^{3}[/tex] - 26[tex]x^{2}[/tex] + 26x - 24.

b. No, the product of [3x - 4 and 5[tex]x^{2}[/tex] - 2x + 6] and [4 - 3x and 5[tex]x^{2}[/tex] - 2x + 6] is not same.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be sufficiently explained by the four basic operations, also referred to as "arithmetic operations." In mathematics, quotient, product, sum, and difference are the operations that come after division, multiplication, addition, and subtraction.

a. We are given two expressions as 3x - 4 and 5[tex]x^{2}[/tex] - 2x + 6.

Using the multiplication operation, we get the product as

⇒ (3x - 4) * (5[tex]x^{2}[/tex] - 2x + 6)

⇒ 15[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] + 18x - 20[tex]x^{2}[/tex] + 8x - 24

⇒ 15[tex]x^{3}[/tex] - 26[tex]x^{2}[/tex] + 26x - 24

b. The product of 4 - 3x and 5[tex]x^{2}[/tex] - 2x + 6 is as follows,

⇒ (4 - 3x) * (5[tex]x^{2}[/tex] - 2x + 6)

⇒ 20[tex]x^{2}[/tex] - 8x + 24 - 15[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex] - 18x

⇒ 26[tex]x^{2}[/tex] - 15[tex]x^{3}[/tex] - 26x + 24

This is not same as the product of previous expressions.

Hence, the required solutions have been obtained.

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[tex]A= \pi r^{2}[/tex]

Answer:

it’s A=pi R squared

lolll it’s fine

Answer: -1

Step-by-step explanation

The triangle formed by a complex number and its complex conjugate with the origin is an isosceles right triangle.

When a complex number and its complex conjugate are plotted in the complex plane, the two points are reflected about the real axis. Thus, the triangle formed by these points and the origin is an isosceles triangle with the real axis as its axis of symmetry.

Since the complex conjugate has the same magnitude as the original complex number, the two sides of the isosceles triangle have equal length. Therefore, the angle opposite the base (i.e., the origin) is a right angle, since it is the angle between the real axis and the imaginary axis.

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The period of the function represented by the sinusoidal graph has a value of 0.7

Given that we have the graph of the sinusoidal function

By definition, the period of the function is the distance between cycles

i.e. the length of a cycle

From the given graph, we have

Initial = 0

Final = 0.7

So, we have

Period = 0.7 - 0

Period = 0.7

This can also be calculated from the equation as

Period = 2π/B

From the function, we have

B = 3π

This means that

Period = 2π/3π

Evaluate

Period = 0.67

When approximated, we have

Period = 0.7

So, the period is 0.7 (approximately)

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Therefore, the surface area of the prism is 139 square feet.

Area is the measure of the size of a two-dimensional region or surface, typically measured in square units such as square inches or square meters. It is calculated by multiplying the length of a shape by its width or height, or by using specific formulas depending on the shape. The concept of area is important in various fields such as mathematics, geometry, physics, engineering, and more.

Here,

To calculate the surface area of the prism, we need to find the area of each face and add them up.

The prism has two congruent triangular faces and three rectangular faces. The area of each triangular face is 1/2(base x height), where the base is 6 feet and the height is 7 feet, so the area of each triangular face is:

1/2(6)(7) = 21 square feet

The rectangular faces have dimensions of 6 feet by 5 feet, 7 feet by 5 feet, and 7 feet by 6 feet. The areas of these faces are:

6 x 5 = 30 square feet

7 x 5 = 35 square feet

7 x 6 = 42 square feet

Adding up the areas of all five faces, we get:

2(21) + 30 + 35 + 42 = 139 square feet

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Complete question:

A prism 5 feet tall whose base is a right triangle with legs length 6 feet and 7 feet. Find the area of the combined figure.

140 ml of Ensure
To prepare a tube feeding of Ensure 280 ml (50% solution), the nurse should use 140 ml of Ensure. Here's the explanation: Given: Ensure is available in a 240 ml can.

The required amount of Ensure is 280 ml (50% solution). Formula: To calculate the number of milliliters of Ensure to be used, we will use the formula: percent strength (as a decimal) × volume required ÷ percent strength in stock = volume to be administered Solution: Since Ensure is available in a 240 ml can, we will use that as our percentage strength in stock. Now we'll plug in the values:0.5 × 280 ÷ 1 = 140 ml Therefore, the nurse should use 140 ml of Ensure to prepare the feeding.

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The expression that will make the given equation true when simplified is: B. (4 x 3) ÷ 2

To determine the expression that makes the equation true, simplify both sides of the equation and then compare them to the given options to identify the one that equals the simplified equation.

Let's simplify the left-hand side of the equation first:

1/2 * (3 * 5 + 1) - 2 = 1/2 * (15 + 1) - 2 = 1/2 * 16 - 2 = 8 - 2 = 6

Now we can check which expression equals 6:

4 * (2+3) = 4x5 = 20

(4x3) ÷ 2 = 12÷2 = 6

6 ÷ 3 + 2 = 2+2 = 4

6+8 ÷ 4 = 6 + 2 = 8

Therefore, the expression that makes the equation true is (4x3)÷2, which equals 6.

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Using Order of operations, the expression that makes the equation true is: (4 × 3) ÷ 2

The order of operations has an acronym which is PEMDAS. This acronym stands for: parentheses, exponents, multiplication, division, addition, then subtraction.

We are given the equation as:

¹/₂ × (3 × 5 + 1) - 2

Using order of operations, we use multiplication inside the bracket first to get:

¹/₂ × (15 + 1) - 2

We solve the bracket to get:

¹/₂ × 16 - 2

We use multiplication to get:

8 - 2 = 6

Looking at the given options, the only that gives same answer as the above is option B as seen below:

(4 × 3) ÷ 2

= 12 ÷ 2

= 6

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Answer:

4.275 L

Step-by-step explanation:

Pitcher starts with 6.2 L.

7 glasses

each glass has 0.275 L

total water in 7 glasses: 7 × 0.275 L = 1.925 L

water remaining in pitcher: 6.2 L - 1.925 L = 4.275 L

Answer: 4.275 L is left in the pitcher.

Answer:

128

Step-by-step explanation:

Sue's average for 9 games of bowling is 108. Therefore, the total scores for the 9 games is:

[tex]= 108 \times 9[/tex]

[tex]= 972[/tex]

To have an average of 110 in 10 games, her total score will be:

[tex]= 110 \times 10[/tex]

[tex]= 1100[/tex]

Therefore, the lowest score that she can get will be the difference between the values calculated above and this will be:

[tex]= 1100 - 972[/tex]

[tex]\bold{= 128}[/tex]

Given that sin B = -5/13 and angle B is in quadrant III, we can use the Pythagorean identity to find the value of cos B:cos² B + sin² B = 1

cos² B + (-5/13)² = 1

cos² B = 1 - 25/169

cos² B = 144/169

cos B = -12/13 (since cos B is negative in quadrant III)a) To find csc B, we can use the reciprocal identity:

csc B = 1/sin B

csc B = 1/(-5/13)

csc B = -13/5b) To find cot B, we can use the quotient identity:

cot B = cos B/sin B

cot B = (-12/13)/(-5/13)

cot B = 12/5c) To find cos B, we have already calculated it above:

cos B = -12/13d) To find sec B, we can use the reciprocal identity:

sec B = 1/cos B

sec B = 1/(-12/13)

sec B = -13/12e) To find tan B, we can use the ratio identity:

tan B = sin B/cos B

tan B = (-5/13)/(-12/13)

tan B = 5/12Therefore, the values of the trigonometric functions for angle B in standard position with terminal side in quadrant III and sin B = -5/13 are:

a) csc B = -13/5

b) cot B = 12/5

c) cos B = -12/13

d) sec B = -13/12

e) tan B = 5/12

Step-by-step explanation:

The value of f^−1(4)f is the result of applying the inverse of the function f to 4.

To calculate f^−1(4)f, the inverse of the function f must be applied to 4.

Firstly, the inverse function of f, denoted as f^−1, is obtained by exchanging the x and y coordinates of all points on the graph of f. This means that the equation of f^−1 is obtained by solving the equation of f for y.

Next, 4 is substituted into the equation of f^−1 and the resulting equation is solved for x. This gives the value of f^−1(4).

Finally, the value of f^−1(4) is then substituted into the equation of f and the resulting equation is solved for y. This gives the value of f^−1(4)f.

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Answer:

12.25pi

Step-by-step explanation:

area of ciricle: pi* r^2

the radius can be found by divding the diameter in half so, 3.5

now square 3.5 and multiply with pi

so, 12.25pi

~lmk if you got Qs

The minimum perimeter of a rectangle with an area of 80 ft2 is 56 ft. The dimensions of this rectangle would be 8 ft x 10 ft.

explanation: Let length be L and breadth be B of the rectangular room. A = L × B, given A = 80 ft² (Area of the room)The perimeter of the rectangle, P = 2(L + B) = 2L + 2BTo minimize P, we need to express one variable in terms of the other.

Let's consider L as the variable, and write B in terms of L from the given equation.=> B = (A/L)Therefore, P = 2L + 2B= 2L + 2(A/L) => P = 2(L² + 40/L)Differentiate P w.r.t L to find the critical point.= 2[(d/dL)(L²) + (d/dL)(40/L)]= 2(2L – 40/L²)For the critical point, dP/dL = 0=> 2L – 40/L² = 0=> L = ±2√10

Therefore, L = 2√10 (since L cannot be negative)Thus, B = (A/L) = 80/(2√10) = 4√10The dimensions of the room are 2√10 × 4√10 = 8.94ft × 35.76ft (rounded to the nearest hundredth).

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Rate of change is not a method that can be used to solve a system of equations.

When solving a system of equations, it is important to use a valid method to find the solution. A system of equations is a set of two or more equations with multiple variables that must be solved simultaneously. There are different methods to solve a system of equations, but some methods are more effective than others.

Elimination (Linear Equations) is a method of solving a system of equations by adding or subtracting the equations to eliminate one of the variables. This allows the remaining variable to be solved easily. Substitution is another method where one variable is solved for in one equation and then substituted into another equation to solve for the other variable. Graphing involves plotting the equations on a graph and finding the intersection point(s) of the two lines. This is the solution(s) to the system of equations.

Rate of change, on the other hand, is not a method of solving a system of equations. It refers to the ratio of the change in one variable to the change in another variable. It is a concept used in calculus and differential equations, but it is not a valid method to find solutions to systems of equations. Therefore, when solving a system of equations, it is important to use a valid method to ensure accurate results.

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8. The value of x is 3.5

9; The solution from the proportion is x = 3

Note that from the diagram given, we have that;

ΔRST ≅ ΔUVW

Also, we can see that a side of the larger triangle ΔRST measures 4 and the smaller triangle  ΔUVW measures 2.

We have a scale factor of 2

For the value of x, we have;

x = 7/2

Divide the values

x  = 3.5

For the proportion

Given the equation as;

12/x = 4/2x - 5

cross multiply

12(2x - 5) = 4x

expand the bracket

24x - 60 = 4x

collect like terms

24x - 4x = 60

subtract the values

20x = 60

x = 3

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Answer:

rotation to the right in the coordinate plane

The BEST definition for clockwise rotation on the coordinate plane is "rotation to the right in the coordinate plane." option B is correct.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

"Rotation to the right in the coordinate plane" is the BEST definition for clockwise rotation on the coordinate plane. In the coordinate plane, a rotation that turns a point or object to the right of the origin is referred to as being clockwise.

It follows that if a straight line were to stretch from the origin to the point or item, it would spin as it traveled in a clockwise direction. In comparison, a rotation in the other direction would cause the line to spin to the left.

Although notation can be used to depict the magnitude and direction of rotation in the coordinate plane, this does not always mean that the rotation is clockwise.

Therefore, Rotation to the right in the coordinate plane is the BEST definition for clockwise rotation on the coordinate plane.

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The dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 cantered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

A scale factοr is defined as the ratiο between the scale οf a given οriginal οbject and a new οbject, which is its representatiοn but οf a different size (bigger οr smaller).

5).Tο find the cοοrdinates οf the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K, we need tο perfοrm the fοllοwing steps:

Find the cοοrdinates οf pοint K after dilatiοn.

Since the center οf dilatiοn is K, the image οf K will be itself.

Therefοre, the cοοrdinates οf the image οf pοint K will be (8, 12).

Find the cοοrdinates οf the images οf pοints J, L, and M after dilatiοn.

Tο find the image οf pοint J, we can use the fοrmula fοr dilatiοn:

(image οf J) = (center οf dilatiοn) + (scale factοr) x (vectοr frοm center tο J)

(image οf J) = (8, 12) + (1/4)(vectοr JO)(image οf J) = (8, 12) + (1/4)(-4, 0)

(image οf J) = (7, 12)Similarly, we can find the images οf pοints L and M:

(image οf L) = (8, 12) + (1/4)(vectοr ZK)(image οf L) = (8, 12) + (1/4)(-4, -12)

(image οf L) = (7, 9)(image οf M) = (8, 12) + (1/4)(vectοr KM)(image οf M) =

(8, 12) + (1/4)(-16, -8)(image οf M) = (4, 10)

Therefοre, the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).

6). Tο find the image οf triangle XYZ after a dilatiοn centered at the οrigin with a scale factοr οf k = -3/2, we need tο apply the dilatiοn fοrmula tο each vertex.

Fοr vertex X(0, 2):

x-cοοrdinate οf image = k * x-cοοrdinate οf X = -3/2 * 0 = 0y-cοοrdinate οf image = k * y-cοοrdinate οf X = -3/2 * 2 = -3

Sο the image οf vertex X is X'(0, -3).

Fοr vertex Y(4, 6):x-cοοrdinate οf image = k * x-cοοrdinate οf Y = -3/2 * 4 = -6y-cοοrdinate οf image = k * y-cοοrdinate οf Y = -3/2 * 6 = -9

Sο the image οf vertex Y is Y'(-6, -9).

Fοr vertex Z(8, 0):x-cοοrdinate οf image = k * x-cοοrdinate οf Z = -3/2 * 8 = -12y-cοοrdinate οf image = k * y-cοοrdinate οf Z = -3/2 * 0 = 0

Sο the image οf vertex Z is Z'(-12, 0).

Therefοre, the image οf triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

Hence, the dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

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To find the lengths of the sides of the triangle with vertices at a(0, -4), b(0, -9), and c(-2, -5), we can use the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's label the sides of the triangle as AB, BC, and CA, where A = (0, -4), B = (0, -9), and C = (-2, -5).

Length of AB:

AB = √((y2 - y1)² + (x2 - x1)²) (Note: We switched the order of x and y for this calculation to match the order of the points given)

= √((-9 - (-4))² + (0 - 0)²)

= √(5²)

= 5

Length of BC:

BC = √((y2 - y1)² + (x2 - x1)²)

= √((-5 - (-9))² + (-2 - 0)²)

= √(4² + 4²)

= √32

= 4√2

= 5.66

Length of CA:

CA = √((y2 - y1)² + (x2 - x1)²)

= √((-4 - (-5))² + (0 - (-2))²)

= √(1² + 2²)

= √5

= 2.24

Therefore, the lengths of the sides of the triangle areAB = 5

BC = 4√2 ≈ 5.66

CA = √5 ≈ 2.24

Since they are unequal, the triangle is a scalene triangle.

2)
To determine if AABC is a right-angled triangle, we need to check if any of its angles measure 90 degrees. We can use the slopes of the sides to determine this.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slopes of the three sides of AABC:

Slope of AB:

AB passes through the points A(0, -4) and B(0, -9).

slope_AB = (-9 - (-4)) / (0 - 0) = -5/0 (undefined)

Note that the slope of AB is undefined, since the line is vertical and has no defined slope.

Slope of BC:

BC passes through the points B(0, -9) and C(-2, -5).

slope_BC = (-5 - (-9)) / (-2 - 0) = 2

Slope of CA:

CA passes through the points C(-2, -5) and A(0, -4).

slope_CA = (-4 - (-5)) / (0 - (-2)) = 1/2

Since AB is vertical and has undefined slope, we cannot use its slope to determine the angle at A. However, we can use the slopes of BC and CA to check the other angles.

The angle at B is opposite the side BC, so we need to check if the slope of BC is the negative reciprocal of the slope of AB. Since AB has undefined slope, we cannot determine its reciprocal or negative reciprocal. Therefore, we cannot use this method to check if the angle at B is 90 degrees.

The angle at C is opposite the side CA, so we need to check if the slope of CA is the negative reciprocal of the slope of BC. If it is, then the angle at C is 90 degrees. Let's check:

slope_BC * slope_CA = 2 * 1/2 = 1

The negative reciprocal of slope_BC is -1/2.

Since slope_CA is not equal to the negative reciprocal of slope_BC, we can conclude that the angle at C is not 90 degrees.

Therefore, we CANNOT conclude that AABC is a right-angled triangle based on the slopes of its sides.

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