How to find third point between two points given coordinates?

The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex] and this can be determined by using the Pythagorean theorem and trigonometric functions.

GIven :

The point (-7, -24) is on the terminal ray of angle θ which is in standard position.

To determine the trigonometric function first determine the value of the hypotenuse and to determine the value of the hypotenuse, the Pythagorean theorem can be used.

[tex]\rm H^2 = P^2 + B^2[/tex]

where H is the hypotenuse, B is the base, and P is the perpendicular.

Now, substitute the value of known terms in the above equation.

[tex]\rm H^2 = 7^2+24^2[/tex]

[tex]\rm H^2=49+576[/tex]

[tex]\rm H^2 = 625[/tex]

H = 25

Now, the values of the trigonometric functions are as follows:

[tex]\rm cos\theta=\dfrac{-7}{25}[/tex]

[tex]\rm sin\theta=\dfrac{-24}{25}[/tex]

[tex]\rm tan\theta=\dfrac{24}{7}[/tex]

[tex]\rm cosec\theta=\dfrac{25}{-24}[/tex]

[tex]\rm sec\theta=\dfrac{25}{-7}[/tex]

[tex]\rm cot\theta=\dfrac{7}{24}[/tex]

The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex].

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To find the six trigonometric values for angle θ (-7, -24) on the terminal ray, we can use sine, cosine, tangent, cosecant, secant, and cotangent ratios.

The given point (-7, -24) lies on the terminal ray of an angle in standard position, denoted by θ. To find the six trigonometric values for angle θ, we can use the values of the coordinates of the point. The coordinate (-7) represents the x-value (adjacent side) and the coordinate (-24) represents the y-value (opposite side).

We can use the trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot), to find the values.

Here, sinθ = y/r = (-24)/7.6, cosθ = x/r = (-7)/7.6, tanθ = y/x = (-24)/(-7), cscθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ. By substituting the respective values, we can find all six trigonometric values.

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Answer: $64000

Step-by-step explanation:

The exponential equation for growth in function with growth factor 'b'in time 't' is given by :-

[tex]y=Ab^x[/tex] , where A is the initial value.

Given : The initial value : [tex]A=\$2000 [/tex]

Growth rate = [tex]b=2\text{ every 9 years} [/tex]

Time periods in 45 years :[tex]t=\dfrac{45}{9}=5[/tex]

Then , the exponential equation for growth for t=5 is given by :-

[tex]y=2000(2)^{5}=64000[/tex]

Hence, the money you would have after 45 years = $64000

Points A, F, and G are three collinear points on line l.

[tex]\boxed{ \ The \ Answer \ is \ B \ }[/tex]

Let us consider the definition of collinear.  

Collinear  

Collinear points represent points that lie on a straight line. Any two points are always collinear because we can constantly connect them with a straight line. A collinear relationship can occur from three points or more, but they don’t have to be.  

Noncollinear  

Noncollinear points represent the points that do not lie in a similar straight line.  

Given that lines k, l, and m with points A, B, C, D, F, and G. The logical conclusions that can be taken correctly based on the attached picture are as follows:  

Hence, the specific answer to this key question is undoubted, i.e., points A, F, and G.  

Note:

All points can, also, be said to be coplanar. This is because the three lines intersect with each other and lie on a planar surface.

Coplanar  

Coplanar points represent a group of points that lie on the same plane, i.e. a planar surface that extends without end in all directions. Any two or three points are always coplanar, but four or more points might or might not be coplanar.  

Keywords: what are, three collinear points A, F, and G, noncollinear, located, similar straight line, definition, represents, relationship, coplanar

Answer: B

Step-by-step explanation:

the correct interpretation of the inequality –2 > –8 is On a number line, −2 is located to the right of –8.

The median salary for the given data set of four salaries ($20,000, $22,000, $24,000, and $26,000) is calculated by averaging the two middle values ($22,000 and $24,000), resulting in a median of $23,000

To calculate the median salary from an ordered data set, you first need to determine if the number of data points is even or odd. In this scenario, there are four data points: $20,000, $22,000, $24,000, and $26,000. As the number of data values is even, the median is the average of the two middle values.

Steps to Calculate Median Salary

Therefore, the median salary for this data set is $23,000

Answer: [tex]w+s=4500[/tex]

[tex] w=1.25s[/tex]

Step-by-step explanation:

Let w be the number of bottles of water and let s be the number of bottles of soda.

Since , the manager needs to buy a total of 4,500 drinks.

Then , we have [tex]w+s=4500[/tex]

Also, the they have 25% more water than soda.

Since 25%=0.25

Then, [tex]w=s+0.25s=s(1.25)[/tex]

[tex]\Rightarrow\ w=1.25s[/tex]

Hence, the  system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to buy.

[tex]w+s=4500[/tex]

[tex] w=1.25s[/tex]

Answer:

120

Step-by-step explanation:

Answer:

The simplified form will be:  [tex]x\sqrt[5]{x^3}[/tex]

Step-by-step explanation:

The given expression is:   [tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}[/tex]

Simplifying the above expression......

[tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}\\ \\ =\sqrt[5]{x^4*x^4}\\ \\ =\sqrt[5]{x^4^+^4}\ [Exponents\ gets\ added\ while\ multiplication]\\ \\ =\sqrt[5]{x^8}\\ \\ =\sqrt[5]{x^5*x^3}\ [As\ 5+3=8] \\ \\ =\sqrt[5]{x^5}*\sqrt[5]{x^3}\\ \\ =x\sqrt[5]{x^3}[/tex]

So, the simplified form will be:  [tex]x\sqrt[5]{x^3}[/tex]

x + y-1 = 0

 if x = 6

 replace x with 6 to get

6 +y-1 =0

subtract 6 from each side

y-1 =-6

add 1 to each side

y = -5

Final answer:

Kevin is 7 years old. The problem is solved by setting up an equation 19 = 2K + 5, subtracting 5 from both sides to get 14 = 2K, and then dividing by 2 to find Kevin's age.

Explanation:

The question asks us to find Kevin's age given that James's age is five more than two times Kevin's age and that James is 19 years old. To solve this, we'll set up an equation based on the information provided.

Let K represent Kevin's age. According to the problem, we have:
James's age = 2 × Kevin's age + 5
Since James's age is 19, we can write:
19 = 2K + 5

To solve for K, we first subtract 5 from both sides of the equation:
14 = 2K
Then, we divide both sides by 2 to isolate K:
K = 7

Therefore, Kevin is 7 years old.

The value the given expression x + 20 – 1 is, the solution is A. 28.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

w = 13, x = 9, y = 1.9, z = 0.5

x + 20 – 1

Since X Is 9 ,

You're Problem Would Now Be

= 9 + 20 - 1

Then You Subtract 20

And 1 Which Will Give You 19

Then , You're Left With 9 + 19

Which Is 28.

Hence, the solution is A. 28.

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Final answer:

The volta in Sonnet 73 is a shift that occurs between lines eight and nine, serving to transition from metaphors of aging to considering their impact on love. This turn is common in sonnets, marking a change in argument or tone.

Explanation:

Finding the Volta in Sonnet 73

The volta, or the turn, in a sonnet marks a shift in thought or argument and is crucial to understanding the poem's structure and meaning. In Sonnet 73, the volta can be identified between lines eight and nine, where the poet moves from reflecting on the images that convey the passage of time and coming to terms with mortality, to directly addressing the beloved and discussing the importance of this realization for their relationship. The logical relationship between the octet (the first eight lines) and the following sestet (the last six lines) in Sonnet 73 is that the octet sets up a series of metaphors about aging and the passage of time, which the sestet then responds to by contemplating the impact of these realizations on love and connection.

The Petrarchan sonnet typically follows a structure with an octave that presents a problem that is resolved or responded to in the following sestet. Although the rhyme scheme might vary, the purpose of the volta remains the same across different sonnets: it signifies a pivot or shift in the argument or mood of the poem.

The reference to Shakespearian and Petrarchan sonnet styles in the question helps us understand that the student likely confuses the structure. Sonnet 73 is a Shakespearian sonnet that consists of three quatrains and a concluding couplet, with the volta being a conceptual rather than structural shift in Shakespeare's sonnets, typically occurring at the start of the third quatrain or the couplet.

Answer:  The given number is NOT rational.

Step-by-step explanation:  We are given to check whether the number 0.12112111211112 . . . a rational number or not.

We know that

if the digits after the decimal in a number are either repeating or terminating, then the number is rational.

The given number is

[tex]x=0.12112111211112 . . .[/tex]

We can see that the digits after the decimal are neither repeating nor terminating.

Therefore, the given number is NOT rational.

Using algebraic equation, the negative number that is squared is: -9.

An algebraic equation can be used to find an unknown value, by making the unknown value the variable.

Let the negative number that would be squared be represented by the variable, x. Thus, we have -x². Therefore:

2x² - 5 = 157

2x² = 157 + 5

2x² = 162

x² = 162/2

x² = 81

x = √81

x = -9

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Answer:

cos(Z) = 12/13

Step-by-step explanation:

Given that the triangles ABC and XYZ are similar (their corresponding angles are congruent and the corresponding sides are in proportion), then cos(Z) is equal to cos(C).

From the picture attached:

cos(C) = adjacent/hypotenuse

cos(C) = 12/13

Final answer:

Without additional information about triangle XYZ or its similarity ratio to triangle ABC, it is impossible to provide the exact value of cos(Z).

Explanation:

The question involves finding the value of cos(Z) in a triangle similar to triangle ABC. When triangles are similar, their corresponding angles are equal. However, without additional information such as side lengths or other angle values, it's not possible to calculate the exact value of cos(Z). But in general for any triangle, the value of cosine for any angle can be found using the cosine formula or by using the ratio of the adjacent side to the hypotenuse in a right triangle. For non-right triangles, one could utilize the Law of Cosines to determine the cosine of the included angle.

Answer: [tex]40^{\circ}[/tex]

Step-by-step explanation:

Given: A regular nonagon with 9 sides.

For a regular nonagon, it maps onto itself 9 times during a rotation of 360°.

Mow, the angle at Lusia can rotate the regular nonagon through to map it onto itself=[tex]\frac{360}{\text{number of sides of regular polygon}}=\frac{360}{9}=40^{\circ}[/tex]

A shape that maps onto itself after rotation, has a rotation symmetry

The angles of rotation that would map the nonagon onto itself are:

[tex]\mathbf{40, 80, 120\ and\ 160}[/tex]

A regular nonagon has nine equal sides i.e.

[tex]\mathbf{n = 9}[/tex]

The angle at the center of the nonagon is:

[tex]\mathbf{\theta = 360}[/tex]

So, the angle of rotation symmetry is:

[tex]\mathbf{\alpha = \frac{\theta}{n}}[/tex]

This gives:

[tex]\mathbf{\alpha = \frac{360}{9}}[/tex]

[tex]\mathbf{\alpha = 40}[/tex]

This means that, the nonagon would map onto itself, when rotated at 40 degrees.

Other angles of rotation symmetry must be a multiple of 40

i.e.

[tex]\mathbf{\alpha = 40, 80, 120, 160, 200, 240, 280......}[/tex]

Using the above list of angles, the angles of rotation that would map the nonagon onto itself are:

[tex]\mathbf{40, 80, 120\ and\ 160}[/tex]

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