What is number 3 on the plot diagram?

a. The trigonometric ratio tanθ = -√(sec²θ - 1)

b. The trigonometric ratio secθ = -1/√(1 - sin²θ)

Trigonometric ratios are the following mathematical expressions sinθ, cosθ, tanθ,secθ,cosecθ and cotθ.

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

tan²θ + 1 = sec²θ

Making tanθ subject of the formula, we have that

tan²θ = sec²θ - 1

tanθ = ±√(sec²θ - 1)

Since in Quadrant II, tanθ is negative, we choose the negative answer.

So, tanθ = -√(sec²θ - 1)

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

secθ = 1/cosθ and

sin²θ + cos²θ = 1

Making cosθ subject of the formula, we have that

cos²θ = 1 - sin²θ

cosθ = ±√(1 - sin²θ)

So, secθ = 1/cosθ

= ±1/√(1 - sin²θ)

Since in Quadrant III, secθ is positive, we choose the positive answer.

So, secθ = -1/√(1 - sin²θ)

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On observing the provided question we can say that - the function f(x) = a^x is Range : (−∞,∞) or all real numbers

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the number and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The answer to the question is that all real numbers or (−∞,∞)

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Multiplying the  second equation by -4 eliminates the x terms when adding the first equation.The second equation is 4x + 5y = -8

In order to eliminate the x terms when adding the first equation, you need to multiply the second equation by -4. The formula and calculation steps are as follows:

Formula:

Equation 1 + (-4 x Equation 2)

4x + 5y = -8

-4(4x + 5y) = -4(-8)

-16x -20y = 32

Adding the two equations together gives:

0x + 25y = 24

Therefore, multiplying the second equation by -4 eliminates the x terms when adding the first equation.

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this is a question of arithmetic and the solution is as follows,

The expression 8x + 12y represents the sum of harry and mike’s total monthly wages.

Generally the equation for the  The Distributive property is mathematically given as,

a x (b +c) = a x b+ b x c.

Where

8x+12y

Therefore,

= 4 x 2x + 4 x 3x

= 4 x( 2x + 3x)

= 4( 2x + 3x)

Arithmetic

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division.

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Using basic concept of proportion value and percentage from the total, The answer is there are 15 students in the club.

A percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, 50% means 50/100 or 0.50. It is commonly used to express rates and proportions. Percentages can be used to express a variety of information, such as discounts, increases, and proportions. For example, if a product is on sale for 20% off, that means the price has been reduced by 20/100 or 0.20 times the original price. If a company's profits have increased by 10%, that means they have gone up by 10/100 or 0.10 times the original amount.

A proportion is a mathematical relationship between two values that indicates that they are in a specific ratio to each other. Proportions can be expressed in a variety of ways, but one common way is to use the symbol ":" to separate the two values. In statistics, it is common to use proportions to express the relationship between different groups or categories in a population. In physics, proportions can be used to calculate different quantities in systems.

total = x

40% of x =6

40/100 * x =6

x=6*100/40

=15

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Answer:

4/8
3/8 + 1/8 = 4/8

The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:

23x + 5 = 13x + 15

23x - 13x = 15 - 5 {collect like terms}

10x = 10 {divide through by 10}

x = 1

angle J = 23(1) + 5 = 28°

Angle K and angle J are supplementary so:

K = 180 - 28

K = 152°

Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°

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Less than 2 units separate the median from the lower quartile for customers making purchases.

The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q1. The median or second quartile is also referred to as Q2. Third quartile: Also referred to as the higher quartile or Q3.

Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q3) and lower quartile (Q1) can be used to depict quartile deviation as the letters QD. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.

The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.

Therefore, the correct answer is option E. The difference between the median and the lower quartile for the customers making a purchase is less than 2.

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Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

y = x+5

2.When x = 10,y = x+5 = 10+5 = 15

3.When x =15,y = x+5 = 15+5 = 20

4.When x = 20,y = x+5 = 20+5 = 25

Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.

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A total of 3 five ounces glass are needed so have the same alcohol as that of a 12 ounce glass.

In order to find the number of glass of capacity five ounces that will have the same capacity as that of the twelve ounce glass can be calculated as followed,

Let us say that n number of five ounces glasses are required to equate 12 ounce glass.

Now, we can write the relation,

using simple algebra,

n(Five ounces glasses) = 1 Ounce alcohol content

n = 12/5

n = 2.4

But, we have to answer an integral value, so, we will say that the required number of the glasses is 3.

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Based on the table, an equation of the linear relationship in slope-intercept form include the following: A. y = 2x − 8

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope of the data points in this table as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-6 - (-8))/(1 - 0)

Slope, m = 2/1

Slope, m = 2.

At point (0, -8), an equation of this line can be calculated in slope-intercept form as follows:

Note: The y-intercept is equal to -8.

y = mx + c

y = 2x + (-8)

y = 2x - 8.

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Answer:

A. y = 2x − 8

Step-by-step explanation:

The property of congruence illustrated in the statement is the transitive property.

The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.

here,

In the statement "If AB ≅ DE, EF ≅ DE then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.

The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.

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The graph of y is a straight line parallel to the x−axis through the point (0,-2)

Now, According to the question:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The given equation is Y = -2

y = -2 is a line in which all points have the y-value -2. The line has a slope of 0 (horizontal line) since the y-value does not change for any value of x.

The point-intercept form for the equation of a line is:

y = mx + b

We can write y = -2

As y = 0x - 2;

slope = 0, y-intercept = -2

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Answer:

4x - 5y = 10

Step-by-step explanation:

We can use the point-slope form to find the line equation:

[tex] \displaystyle{y - y_1 = m(x - x_1)}[/tex]

Where (x1,y1) is the point that the line intersects and m is slope. We know the line passes through (-5,-6) and the slope is parallel to the line 4x - 5y = 35. Meaning the slope of that line is equal to slope of 4x - 5y = 35.

In this equation form Ax + By = C, we can find slope by m = - A/B. Therefore, m = -4/-5 which equals to 4/5. Hence, the slope is 4/5

[tex] \displaystyle{y - y_1 = \dfrac{4}{5}(x - x_1)}[/tex]

And also it intersects the point (-5,-6). Therefore:

[tex] \displaystyle{y - ( - 6) = \dfrac{4}{5}(x - ( - 5))} \\ \\ \displaystyle{y + 6 = \dfrac{4}{5}(x + 5)}[/tex]

Then convert to Ax + By = C to match with the given equation in problem:

[tex] \displaystyle{5(y + 6 )= 5 \left(\dfrac{4}{5}(x + 5) \right)} \\ \\ \displaystyle{5y + 30 = 4(x + 5)} \\ \\ \displaystyle{5y + 30 = 4x + 20} \\ \\ \displaystyle{ \therefore 4x - 5y = 10}[/tex]

On solving the provided question, we can say that - by fraction we karime walks = 3/4 so, 3/4  X 5 = 15/4

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

karime walks = 3/4

for = 5 days

so, 3/4  X 5 = 15/4

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Answer: 8-4+5

Step-by-step explanation: Best I could do

Answer: Shift right 20 units

Answer:

PF = 9

Step-by-step explanation:

the incentre of a triangle is equally distant from the triangle's 3 sides, that is

PD = PE = PF

using PD = PE to solve for x

5x - 6 = 3x ( subtract 3x from both sides )

2x - 6 = 0 ( add 6 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

then

PE = 3x = 3 × 3 = 9

PF = PE = 9

The percentage markup the store made before selling those speakers

are 136.33%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A store bought a set of speakers for $82.86 and sold them for

$195.82.

So, The amount of profit is $(195.82 - 82.86).

= $112.96.

Now, The markup percentage can be obtained by the concept of the percentage change.

Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,

= (112.96/82.86)×100%.

= 136.33%.

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Answer: The relationship between the x-coordinates of the first and second bus stop is that the x-coordinate of the second bus stop is 4 units greater than the x-coordinate of the first bus stop.

The relationship between the y-coordinates of the first and second bus stop is that the y-coordinate of the second bus stop is 2 units greater than the y-coordinate of the first bus stop.

Step-by-step explanation:

Answer:

  36.9°

Step-by-step explanation:

You want to know the pitch angle of a staircase with a riser height of 6 inches and a tread depth of 8 inches.

The tangent of an angle is the ratio of the side opposite to the side adjacent:

  Tan = Opposite/Adjacent

The tangent of the staircase angle to the floor will be the ratio of the riser height to the tread depth:

  tan(α) = (6 in)/(8 in) = 3/4

The angle is found using the inverse tangent function.

  α = arctan(3/4) ≈ 36.9°

__

Additional comment

You need to be a little bit careful here. Different authors define "tread depth" differently. For the purpose of this question, it must be defined as the horizontal distance between corresponding points on adjacent treads, as shown in the attached illustration.

Some authors define tread depth as the distance from the nosing to the riser. If that definition is used, the "run" of the step will be the tread depth less the nosing depth. The pitch angle will be the arctangent of the ratio of riser height to "run".

The tread depth of 8 inches is a little too narrow to be in compliance with some building codes. A more usual minimum is about 10 inches with a riser height of 7 1/2 inches.

Answer:

0.75 tangent 0.75

Step-by-step explanation:

Answer: Solve one equation for one of the variables.

Step-by-step explanation:

The number of concrete masonry units needed to construct a foundation wall is 102.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given, a foundation wall 104" high with a 120" perimeter.

Since, perimeter of square =  4 * side

120 = 4 * side

side  = 30"

Hence area of the foundation wall = side²

area of the foundation wall = 30² = 900

volume of the foundation wall  = area * height

the volume of the foundation wall  = 104 * 900 = 93,600"

The volume of the concrete masonry whose length, width, and depth are 16, 8, and 8 respectively is

Volume of masonry = 8 * 8 * 16

The volume of masonry = 1024

since 10 % of masonry goes to waste.

Thus the effective volume of the masonry  = 1024*0.9 = 921.6

total masonry required = 93600/ 921.6 = 101.56

therefore, To build a foundation wall, 102 concrete masonry units are required.

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Answer:

46

Step-by-step explanation:

You multiply 23×2 and that is how I got my answer.

The value of c will be 0.

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

m = y2 - y1 / x2 - x1

where m = 0

y2 = c

y1 = 0

x1 = -2

x2 = -8

0 = c - 0 / -8 - -(2)

0 = c - 0 / -8 + 2

0 = c - 0 / -6

c - 0 = -6(0)

c - 0 = 0

c = 0

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No, the sides of a right triangle do not include 8, 15, and 17. The sides of a right triangle must follow the Pythagorean theorem, so the sum of the squares of the two shorter sides must equal the square of the longest side. 8² + 15² does not equal 1

8² + 15² = 64 + 225 = 289

17² = 289

Therefore, 8, 15, and 17 are not the sides of a right triangle.

The Pythagorean theorem is an important mathematical concept used to determine if three numbers form the sides of a right triangle. This theorem states that the sum of the squares of the two shorter sides must equal the square of the longest side. In the case of 8, 15, and 17, 8² + 15² does not equal 17², so it is not a right triangle. To test this, we can calculate 8² + 15² = 289, and then 17² = 289. Since the two values are not equal, we can conclude that 8, 15, and 17 are not the sides of a right triangle.

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We determined that the probability of lunch cost is between the above-mentioned value is P (0.2011 < Z < 0.2748)

Probability is the possibility of happening an event. It is expressed as the ratio of the number of favorable outcomes to the total possible outcome.

We can find probability from a statistical data based on the mean value and standard deviation.

given, average cost for lunch per person = mean value = $5.97

standard deviation of cost = $2.25

number of samples = 46

assume distribution of money spent is normal.

the probability of a single lunch patron that has a cost between $6.4225 and $6.5884 can be calculated by the following way.

Z-score = (actual price - mean price) / standard deviation

Z-score when actual price is $6.4225.

                    Z = ($6.4225 - $5.97) / $2.25

    Z = 0.2011

Now, Z-score when actual value is $ 6.5884.

 Z = ($6.5884 - $5.97) / $2.25

Z = 0.2748

If actual value is denoted by X than the probability is shown as

P (6.4225< X< 6.5884) and P (0.2011< Z< 0.2748)

For the group of 46 patrons the above probability is also the same.

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Answer: 26

Step-by-step explanation:

In the picture, we are given a right triangle. Based on that, we can use the Pythagorean Theorem, which helps us find the missing side length with the formula [tex]a^2+b^2=c^2[/tex].

a and b represent the legs, and c is the hypotenuse. The hypotenuse is the longest side of the right triangle. It is also the side that is diagonal from the right angle.

In the picture, we are presented with the legs. So, we can plug in the legs into a and b to solve for c.

[tex]a^2+b^2=c^2[/tex]               [plug in a and b]

[tex]10^2+24^2=c^2[/tex]            [exponent]

[tex]100+576=c^2[/tex]            [add]

[tex]676=c^2[/tex]                      [square root both sides]

[tex]c=26[/tex]

This tells us that the length of the third side is 26.

Answer:

It's B, -2, v/5 4, and 3².