Why is there only 180 degrees in a triangle?

In Chapter 3 of "The Strange Case of Dr. Jekyll and Mr. Hyde," we see how Utterson's investigation and how Jekyll's addiction to his dark side starts to unravel.

In this chapter, Dr. Jekyll's friend and lawyer, Mr. Utterson, becomes increasingly concerned about the strange goings-on surrounding his friend and his association with the mysterious Mr. Hyde. Utterson begins to investigate the relationship between the two men, and discovers that Jekyll has made a will leaving all of his property to Mr. Hyde. Utterson also discovers that Jekyll and Hyde have the same handwriting, and becomes convinced that Jekyll is hiding something.

As Utterson continues to dig, he is eventually able to piece together the truth of the situation: Jekyll has been using a potion to transform himself into the violent and evil Mr. Hyde. Jekyll reveals to Utterson that he has been struggling for a long time with his dual nature and that the potion allows him to temporarily indulge his darker impulses without fear of discovery. Utterson urges Jekyll to give up the potion, but Jekyll refuses, saying that he is powerless to stop using it.

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The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.

To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.

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You went to the supermarket to buy 10 bananas. Each banana weighed 50 grams. If the price for bananas was $6.50 per kilogram, how much would you have to pay?

You do 10 x 50 = 500                     /                      Your bananas weigh 500g

$6.50 halved is $3.25                     /                       So $3.25 for 500g

So your answer is $3.25

Hope this helps! :)

The triangle's internal angles add up to 180 degrees. The biggest angle is then 95.22° in size.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes.

The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry.

These functions' inverses are designated by the notations csc(-1)x, cos(-1)x, cot(-1)x, sec(-1)x, sin(-1)x, and tan(-1)x.

Keep in mind that f(-1) here refers to the inverse function, not f to the -1 power.

According to our question-

the biggest angle on a wire that is 30 inches long and bent into a triangle with sides that measure 6 inches, 11 inches, and 13 inches.

cosine rule is given as

cosa= a^2 + b^2 + c^2/2ab

cosa = 36 + 121 - 169/132

a = 95.22°

Hence, The triangle's internal angles add up to 180 degrees. The biggest angle is then 95.22° in size.

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The table representing ratio of peaches in a box should be completed as follows;

Boxes    Peaches

2                 6

3                 9

5                15

6                18

The table representing ratio of strawberries in a box should be completed as follows;

Boxes    Strawberries

2                 6

4                12

5                15

8                24

In order to have a proportional relationship and equivalent ratios that is constant, the variables x for boxes and y for peaches must have the same constant of proportionality. Next, we would determine the constant of proportionality (k) based on the given parameters:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 6/2 = 18/6

Constant of proportionality (k) = 3.

When y = 9 peaches, the value of x is given by;

x = y/k

x = 9/3

x = 3 boxes.

When x = 5 boxes, the value of y is given by;

y = kx

y = 3(5)

y = 15 peaches.

Also, we would determine the constant of proportionality (k) based on the given parameters:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/4 = 15/5

Constant of proportionality (k) = 3.

When x = 2 boxes, the value of y is given by;

y = kx

y = 3(2)

y = 6 strawberries.

When x = 8 boxes, the value of y is given by;

y = kx

y = 3(8)

y = 24 strawberries.

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This expression has no defined meaning. It is not a valid mathematical expression.

− [infinity] [infinity] is not a valid mathematical expression so it has no defined meaning.

The expression − [infinity] [infinity] is not a valid mathematical expression, and thus it has no defined meaning. It is not a valid mathematical expression because it contains two symbols, infinity and negative infinity, which do not interact with each other in any meaningful way. Infinity is a concept that is used to represent an unbounded or infinitely large value, while negative infinity is a concept used to represent a value that is infinitely small. When combined, these two symbols do not represent any meaningful mathematical quantity. Therefore, the expression − [infinity] [infinity] has no defined meaning.

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The equation is y = 1000 - 10x, where y is the number of blankets sold and x is the price in dollars.

This equation represents the relationship between the number of blankets sold (y) and the price of each blanket (x). The equation starts with the total number of blankets Christina has to sell (1000) and then subtracts 10 for every $1 increase in the price of the blanket. This means that as the price of the blanket increases, the number of blankets sold will decrease by 10 for every $1 increase. For example, if Christina charges $50 for a blanket, the number of blankets sold would be 500 (1000 - (10x50)).

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The graph C. represents the polynomial with zeros of -3, 0 and 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information about the graph's x-intercepts for the polynomial.

Alternately, we might state that the zeros of the polynomial are the x-intercept of its graph. Thus, the needed function is represented by the graph with the coordinates -3, 0, and 2.

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The complete question is as follows:

Select the correct answer.

Which graph best represents a function with zeros of -3, 0, and 2?

The stem represents the tens place and the leaves represent the unit place of each data point, allowing for easy visualization of the distribution of the data.

A stem-and-leaf plot is a type of graph used to display the distribution of a set of data. It is a way to show the frequency of different values in a dataset. In this case, it is showing the number of days of snowfall at a winter sports resort for each of the past 171717 years.

Continuous and discrete data distributions are the two main forms found in statistics. Continuous data is information having a wide range of possible values. When measuring this kind of information, such weight or temperature, a scale is frequently used. A histogram is another tool for representing continuous data.

The complete question will be :

The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past years. represents a year with days of snowfall. Here is the five-number summary for these data Five-number summary According to the - IQR rule for outliers, how many high outliers are there in the data set?

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Answer:

0

Step-by-step explanation:

The blend contains 16% of type A and 8% of type B.

When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.

Let p be the percentage of type b used for the mix

2p be the percentage of type a used for the mix

2p × 300 + p × 500 = 0.11 × 800

simplifying the above equation, we get

p = 0.08 or 8%

Substitute the values in the above equation

2p = 2 × 0.08 = 0.16 or 16%

16 % of type a and 8 % of type b exists utilized for the mix.

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The required percentage of raisins are each type of raisin bran are 16% and 8%.

When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.

Let p be the percentage of type b used for the mix

2p be the percentage of type a used for the mix

2p × 300 + p × 500 = 0.11 × 800

simplifying the above equation, we get

p = 0.08 or 8%

Substitute the values in the above equation

2p = 2 × 0.08 = 0.16 or 16%

16 % of type a and 8 % of type b exists utilized for the mix.

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The percent increase is 50%.

The percentage increase in a quantity is the rate of difference in the old and new value to the old value, express in percentage.

i.e percentage increase = (old value - new value)/ old value

If the new quantity were be have decreased, then the percentage decrease can also be determined.

Considering the given question, the percentage increase can be determined by;

old quantity = 8

new quantity = 4

So that,

percentage increase = (old value - new value)/ old value

                                   = (8 - 4)/ 8 *100%

                                   = 4/ 8 * 100%

percentage increase = 50%

The percent increase is 50%.

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After making the subject of [tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be [tex]$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$[/tex]

An expression is a combination of symbols, such as numbers and operators, that represent a computation or a value. Expressions can be used to perform calculations, assign values to variables, and control the flow of a program. They are a fundamental concept in computer programming.

Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.

For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as 2x^2 + 4x = 2x(x+2)).

Glven expression,

[tex]$$\begin{aligned}& n^2=4 \mathrm{~d}+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+1 \\& n^2-1=4 \mathrm{~d} / t^3 \\& t^3=4 \mathrm{~d} / n^2-1 \\& \mathbf{t}=\sqrt[3]{4 d / n 2-1}\end{aligned}$$[/tex]

Hence after making [tex]$\mathbf{t}$[/tex] the subject of[tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be

[tex]$$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$$[/tex]

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Personal assets are the list of things which are owned by any person for the present or the future use such as house , saving accounts, Cash etc.

Therefore, the personal assets represent the valuable  items owned by any individual for present or the future use.

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The value of m ∠ Q is 23°.

What are complementary angles?

Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary. We say two angles "Complement" one other when their sums equal 90 degrees.

Here, we have

Given: m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles.

The sum of the measures of two complementary angles is 90°.

So, m∠P + m∠Q = 90°

Substitute 12x+7 for m∠P and 6x−7 for m∠Q.

12x+7 + 6x−7 = 90°

18x = 90°

x = 5°

To find m∠Q, substitute 5 for x in 6x−7.

6×5 - 7 = 23°

m ∠ Q = 23°

Hence, the value of m ∠ Q is 23°.

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The least possible unit of the perimeter of the triangle will be 85 units.

In order for the three sides of a triangle to fit together, any two sides' differences must be bigger than the length of the third side.

Draw some triangles on a piece of paper and try to accept that this is the case.

So, by properties of triangle = 42 - 33 = 9

The third side must be greater than 9 units.

Given that it is an integer, 10 must be the minimum possible value.

The perimeter is the sum of all sides.

So our least possible perimeter will be 42 + 33 + 10 = 85 units.

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B typically stands for "Be" in texting. Depending on the context, it could mean different things. For example, it could mean "Be mine" or "Be mine forever" when expressing affection for a girl. It could also mean "Be safe" when wishing someone well.

1. B is a commonly used acronym in texting.

2. It typically stands for the word "Be".

3. Depending on the context, it could mean different things such as expressing affection for a girl or wishing someone well.

B is an acronym commonly used in texting that typically stands for the word "Be" and can have different meanings depending on the context.

B typically stands for "Be" in texting. Depending on the context, it could mean different things. For example, it could mean "Be mine" or "Be mine forever" when expressing affection for a girl. It could also mean "Be safe" when wishing someone well.

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Note that It is not a good idea to guess what a value on a graph might be if it is beyond the points that are already plotted. The reason for this is that the guess might not be accurate. Generally, it is better to stay within the defined data limits.

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

Because they display information quickly and readily, graphs and charts are powerful visual aids. It's no surprise that graphs are widely utilized in print and electronic media. Data can often be easier understood when displayed as a graph rather than a table since the graph might illustrate a pattern or comparison.

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Answer:

The slope of line r is -3/4

Step-by-step explanation:

First, let's find the slope of line q. We can find the slope by finding the change in y over change in x.

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Therefore, substitute in:

[tex]\displaystyle{m=\dfrac{8-4}{6-3}}\\\\\displaystyle{m=\dfrac{4}{3}}[/tex]

Therefore, the slope of line q is 4/3. Since we want to find the slope of line r and we know by the given that line r is perpendicular to line q. By the definition of perpendicular line is [tex]\displaystyle{m_1m_2=-1}[/tex].

Let [tex]m_1[/tex] be slope of the line q which is 4/3. Therefore, substitute in and solve for [tex]m_2[/tex] (slope of line r)

[tex]\displaystyle{\dfrac{4}{3}m_2=-1}\\\\\displaystyle{4m_2=-3}\\\\\displaystyle{m_2=-\dfrac{3}{4}}[/tex]

Therefore, the slope of line r is -3/4

Answer:  First, let's consider the rotation of 180 degrees clockwise. This can be thought of as a reflection over the x-axis, followed by a reflection over the y-axis.

The reflection over the x-axis will negate the y-coordinate, while the reflection over the y-axis will negate the x-coordinate. So after the rotation, the coordinates of point C will become (-5,-5)

Next, we'll consider the translation 5 units up. Translating a point up means that we'll add 5 to its y-coordinate. So the coordinates of point C'' will become (-5,-5) + (0, 5) = (-5, 0)

So the coordinates of C'' are (-5,0)

Therefore the answer is B.

Step-by-step explanation:

Answer:

  23.5 cm

Step-by-step explanation:

You want the height of the model of a 94 m tall roller coaster when the model scale is 1 cm = 4 m.

The model dimensions are assumed to be proportional to the real-world dimensions, so the model height h will satisfy the proportion ...

  h/(94 m) = (1 cm)/(4 m)

Multiplying by 94 m gives ...

  h = (1 cm)(94/4) = 23.5 cm

The height of the model is 23.5 cm.

The value of x from the given triangle is 7√2 units.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, one of the angle in right angle triangle is 45°, opposite side is 7 units and hypotenuse is x units.

We know that, sinθ =Opposite/Hypotenuse

sin45°=7/x

1/√2=7/x

x=7√2 units

Therefore, the value of x is 7√2 units.

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Coordinate (0,1) of y-intercept implies that a line or curve cross the Y axis

at 1.

The location of a point on the cartesian coordinate plane where a straight line or curve line as well as a plane crosses the Y axis is called Y-intercept. The coordinate of y-intercept is expressed as (0, y). This y value is y-intercept. The X coordinate of y intercept is zero.

In case of an equation of line while writing in slope-intercept form it is denoted by b such as y = mx+ b

in the above equation, b is y-intercept and m is the slope.

The y -intercept given by coordinate (0, 1) defines that a straight-line or curve line cross the Y axis at 1. The x coordinate of y -intercept is always zero because over the Y axis there is no value of X.

The y-intercept can have negative or positive value.

Suppose we have an equation of line 4x + 8y + 10 = 0

                                we will write it in a slope-intercept form

                                     8y = -4x - 10

                                     y = - 4x/8 - 10/8

                                    y = -1/2x - 5/4

In the above equation - 5/4 or -1.25 is the y-intercept that means the line crosses the Y-axis at -1.25

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Answer:

-1 - 3/(5 - 2x)

Step-by-step explanation:

f/g (x) =

f(x) / g(x) =

(2x − 3) / (5 - 2x) =  ==> plugin 5 - 2x for g(x) and 2x − 3 for f(x)

              -1 - 3/(-2x + 5)

-2x + 5 | 2x - 3

        + (-2x)

               0 - 3

Answer: -1 - 3/(5 - 2x)

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

The capacity of an object is expressed in terms of volume. The quantity of space a three-dimensional item takes up can also be referred to as volume.  It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.

Given

The bounds for z are 0 ≤ z ≤ x.

The bounds in the xy-plane are x ≤ y ≤ 5 - x and x in [0, 5/2]

So, V = ∫∫ (x - 0) dA

= ∫(x = 0 to 5/2) ∫(y = x to 5 - x) x dy dx

= ∫(x = 0 to 5/2) x (5 - 2x) dx

= ∫(x = 0 to 5/2) (5x - 2x^2) dx

= (5x^2/2 - 2x^3/3) {for x = 0 to 5/2}

=  125/24.

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

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Using PEDMAS to solve the mathematical expression given, the value is 2

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is an acronym used to remember the order of operations in math problems. It is also sometimes referred to as Order of Operations.

In this problem, we will need to use and apply the rules of PEMDAS.

We will need to break this into different components and then bring them together afterwards.

[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3(1/3)] + [6(3/4) + 5(1/2)] / [(26 ÷ 3(5/7)] - 0.05

This becomes ;

[10.2 / 34] + [12.25 / 7] - 0.005

We can further resolve this into

2.05 - 0.005

And then we just subtract the values from one another

2.05 - 0.005 = 2

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Answer:

x = 8

Step-by-step explanation:

x + 4 = 12

Subtract 4 from both sides

x = 8

Let's check

8 + 4 = 12

12 = 12

So, x = 8 is correct!

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F ∘ G is a mathematical operation that is used to find the composite of two functions, f and G. This operation is also known as function composition or composition of functions.

Function composition (also known as function composition of functions) is a mathematical operation that allows one to combine two or more functions into a single, larger function. This operation is symbolized by F ∘ G. The composite of two functions, f and G, is defined as the composite of two functions f and G, which is a new function h, such that h(x) = f(G(x)) for all x in the domain of the function. This means that the output of G is the input of f and the output of f is the output of h. Function composition is a useful tool for combining functions in order to create more complex functions. It can also be used to simplify and shorten existing functions, as well as to simplify an equation by reducing the number of operations that need to be performed.

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A negatively skewed distribution, sometimes referred to as a left-skewed distribution, is a kind of distribution where more values are clustered on the right side (tail) of the scatterplot but the left tail of the distribution graph is longer.

The mean of positively skewed data will be lower than median in a distribution that has a negative skewness, which is the exact reverse of what would be expected. The distribution exhibits zero skewness if the data is graphed symmetrically, regardless of how long or thick the tails are.

More values are plotted on the graph's right side, the distribution's tail is longer on the left, and the distribution is said to be negatively skewed.

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The value of the sequence is (c) 13, 25, 37, 49

The definition of the sequence is given as

a(1) = 13

a(n) = a(n - 1) + 12

The above definitions imply that we simply add 12 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a(2) = 13 + 12 = 25

a(3) = 25 + 12 = 37

So, the sequence is 13, 25, 37

Hence, the value is (c)

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