Use the given triangle to fill in the blank.
tan X= ___

Answer:

Distance = [tex]\sqrt{(1-5)^{2} + (5-2)^{2} }[/tex] units

               = [tex]\sqrt{(-4)^{2} + (3)^{2} }[/tex] units

               =[tex]\sqrt{25}[/tex] units

               = 5 units

Answer:



Step-by-step explanation:

X+

(2x+3)-(x+2)

First you subtract 3 by 2. You wil get 1.

They you subtract 2x by x. You will get 1

So, your answer is x+1

Ramon expression for price on sale d - 0.2d is equal to the calculated expression for the price on sale, hence correct

Raquel expression for the price 0.08d is not equal to calculated expression for price after discount 0.8d , hence incorrect.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Expression by Ramon to show the price of winter clothing with discount

= d - 0.2d

Expression of Price by Raquel = 0.08d

Let the price of the clothing is d,

Discount = 20% = 20% × d = 20d/100 = 0.2d

Price on sale = d - 0.2d

Solving the expression,

Price = d(1 - 0.2)

Price after discount = 0.8d

Hence, by the calculation

Ramon expression for the price on sale d - 0.2d is correct

while Raquel expression is incorrect because the expression for the price is 0.8d.

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The principal amount of $5,000 deposited for 8 years with simple interest gives amount $7,880 at the annual interest of 7.2%.

Total amount 'A' in the Macy account after 8 years = $7,880

Time 't' = 8 years

Principal amount 'P' = $5,000

Let 'r' be the rate of interest given in saving account with annual simple interest.

Simple interest = Amount - Principal

                         = $7,880 - $5,000

                         = $2,880

Simple interest = ( P × r × t ) / 100

Substitute the value we get,

⇒ $2,880 = ( 5,000 × r × 8 ) / 100

⇒ r = ( 2,880 × 100 ) / ( 5,000 × 8 )

⇒ r = 7.2%

Therefore, the annual interest rate for the given amount as per simple interest is equal to 7.2%.

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Answer:

Below

Step-by-step explanation:

Rate of change is   slope  = rise / run =  (0 - -3) / (-3 - -2) = 3/-1 = -3

The value of the domain and the range of the composite function (gof)(x)  as per f(x) = e^x and g(x) = x + 6 is equal to x∈ R⁺  ( real numbers ) and

x > 6 , x∈ R⁺  respectively.

Function f(x) is equal to e^x

Function g(x) = x + 6

Composite function  (gof)(x) is equal to:

(gof)(x)

= g ( f(x))

= g ( e^x )

= e^x + 6

Domain represents all input values and range represents all output values.

Domain of the composite function (gof)(x) is equal to x∈ R⁺  (real numbers)

Range of the composite function (gof)(x)  is equal to  x > 6 , x∈ R⁺

Therefore, the domain and range of the composite function (gof)(x)  is equal to x∈ R⁺  ( real numbers ) and  x > 6 , x∈ R⁺  respectively.

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Step-by-step explanation:

For the first question, let's add the %'s

37% + 13% + 25% + 25% = 100%

So it looks like you have a 100% chance to win a prize.

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

For the second question

It cost $2 to play

Soda - $1

Candy Bar - $1

Toy - $3

Mega Win - $40

It looks like 2 out of 4 (50%) cost more than the price to play.

So we add the % of the Toy and Mega since those are the ones more than $2

25% + 13% = 38% chance to win a prize more than the cost to play

The equation of the parallel lines is y = x + 2.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.

The slope of two parallel lines are equal.

The equation of the given line is:

y = x + 6

here, the slope of the line is 1.

So, the slope of the new line is 1.

The new line has the coordinates (-4, 1).

Using the point-slope form we have:

y - y1 = m (x - x1)

y - 1 = 1 (x + 1)

y - 1 = x + 1

y = x + 2

Hence, the equation of the parallel lines is y = x + 2.

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Step-by-step explanation:

So to start

Perpendicular lines are lines that form 90 degree angles when they meet.

Parallel lines will never touch, no matter how far they go.

So

Top left

A vertical line and a horizontal line

This would be perpendicular

Lines that intersect to form right angles

As mentioned above this would be perpendicular

Two nonvertical lines that have a product of -1 for their slopes.

Parallel lines always have the same slope, so this goes for parallel.

Equations that can be written in slope intercept form

This would be both as all lines can be written in this form

Non vertical lines that have the same slope and different y-intercepts

As they have the same slope this would make it parallel

You can determine the relationship between two lines by comparing their slopes and y-intercepts.

This is both as this is a way to compare all lines

Lines in the same plane never intersect

This would be parallel

Slopes are opposite reciprocals

This is perpendicular as the slopes of perpendicular lines are reciprocals

Vertical lines that have different x-intercepts

This would be parallel

Sorry this is a lot

Hope this helped though :)

A public event or celebration, typically held outdoors and involving stalls, entertainment, and processions.

The required value of x, if the side length of Terrarium A is four times the side length of Terrarium B is 3.63.

A terrarium is a glass container with soil and plants inside of it that can be opened for maintenance purposes. Terraria, however, can be exposed to the atmosphere rather than being sealed. Terraria are usually kept as decorative or ornamental items.

The volume of Terrarium B is 2 m³, so its side length is the cube root of 2, which is approximately 1.26.

The side length of Terrarium A is 4 times that, or approximately 5.04. The volume of Terrarium A is [tex]2^x[/tex] cubic meters, so we can set up the equation:

(5.04)³ = [tex]2^x[/tex]

Taking the cube of both sides, we get:

125.7376 = [tex]8^x[/tex]

Taking the log base 8 of both sides:

x = log(125.7376) / log(8)

x is approximately 3.63.

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Answer:

I could but can you please put down the problem.

Step-by-step explanation:

The plane is travelling at a speed of 424.26 mph.

Velocity of an object is the speed of the object with a given direction. Therefore velocity is a vector quantity and speed is a scalar quantity.

Given that,

A plane is traveling Northeast.

If the plane is travelling northeast, then the angle that the plane makes with the horizontal component will be 45°.

The eastern component of it's velocity is 300 mph.

Vector v can be represented as v cos (θ) i + v sin(θ) j.

Here v cos (θ) is the eastern component and v sin(θ) is the northern component.

v cos (θ) = 300

v cos(45°) = 300

v = 300 / cos(45°)

  = 300 / (1/√2)

  = 424.26 mph

Hence the speed of the plane is 424.26 mph.

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The chart fits the functional equation for all values of x, according to the claim made.

The Geometric Mean (GM) in mathematics is the average or mean that, by calculating the product of the values of the collection of numbers, denotes the central trend of the numbers. In essence, we combine the numbers collectively and calculate their nth root, in which n is the entire amount of data values.

We can use the given functional equation f(x+1) = 4(f(x)) to find the values of f(x) for each value of x, given that we know f(1) = 4. We start by computing:

f(2) = 4(f(1)) = 4(4) = 16

f(3) = 4(f(2)) = 4(16) = 64

f(4) = 4(f(3)) = 4(64) = 256

f(5) = 4(f(4)) = 4(256) = 1024

Now, we have determined all the values of f(x) for x=1 to 5. Since the table has 5 rows, we can write:

x f(x)

1 4

2 16

3 64

4 256

5 1024

We can check that the table satisfies the given functional equation f(x+1) = 4(f(x)). For example, when x = 3, we have:

f(x+1) = f(4) = 256

4(f(x)) = 4(f(3)) = 4(64) = 256

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The solution of the expression (9t³n³)(−2t n²) will be -18t⁴n⁵.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is (9t³n³)(−2t n²). The given expression will be solved as:-

E =  (9t³n³)(−2t n²)

E = 9 x -2 x t³ x t x n³ x n²

E = -18 x t³⁺¹ x n³⁺²

E = -18t⁴n⁵

Therefore, the solution of the expression is E = -18t⁴n⁵.

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The line perpendicular to the line with an equation y = 6x have a slope of -1/6

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Two lines are perpendicular if the product of their slopes is -1.

Line M goes through the points (0, 0) and (1, 6). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-0=\frac{6-0}{1-0} (x-0)\\\\y=6x[/tex]

The slope of the line y = 6x is 6.

The line perpendicular to y = 6x have a slope of -1/6

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Simultaneous equation is a finite set of equations for which common solutions are soughtThe equivalent expression is 5x + 7y = 37

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the simultaneous equation below:

-2x - y = -4

7x + 8y = 41

In order to compress the equation into 1, we need to add the equation or subtract the equation

On adding, we will have:

(-2x + 7x) + (-y + 8y) = -4 + 41

5x + 7y = 37

Hence the equivalent expression is 5x + 7y = 37

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The term that best describes the analysis conducted by the researcher is "descriptive statistics".

What is Descriptive statistics?

A descriptive statistic is a summary statistic that quantitatively describes or summarizes features from a set of data, whereas descriptive statistics is the process of employing and analyzing those statistics.

The term that best describes the analysis conducted by the researcher is "descriptive statistics".

Descriptive statistics is the branch of statistics that deals with the summarization, presentation, and interpretation of data. In this case, the researcher recorded the height of all 217 adult members of a tribe and calculated the average height, which is a measure of central tendency. The purpose of this analysis was to describe the distribution of height among the tribe members, rather than to make inferences about the population or test hypotheses about the population parameters.

In summary, the researcher used descriptive statistics to describe the distribution of height among the tribe members by summarizing the data using measures such as the average height.

Therefore, The term that best describes the analysis conducted by the researcher is "descriptive statistics".

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The value of m for which the equation will have two equal solutions is given as follows:

m = -2.5.

A quadratic equation is modeled by the rule presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:

For this problem, the discriminant is given as follows:

Δ = 2m + 5 (it is the term that goes inside the root during the solution).

Hence, to have two equal solutions, the condition is:

Δ = 0.

Hence:

2m + 5 = 0

2m = -5

m = -5/2

m = -2.5.

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No, it is not possible to have a connected graph with six vertices of degrees 1, 1, 2, 2, 2, and 3.

As we know that the sum of the degrees of the vertices in a connected graph must be equal to twice the number of edges.

So, in this case, the sum of the degrees must be equal to 2 * K, where K is the number of edges in the graph.

Since the degrees of the vertices are 1, 1, 2, 2, 2, and 3,

the sum of the degrees is 1 + 1 + 2 + 2 + 2 + 3 = 11.

The number of edges must be K = 11 / 2 = 5.5,

which is not possible as the number of edges must be a positive integer.

Therefore, it is not possible to have a connected graph with six vertices of degrees 1, 1, 2, 2, 2, and 3.

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Therefore, the new triangle XYZ with vertices X'(-8,3), Y'(-1,2) and Z'(-2,-7) is obtained after the transformation.

Triangles are called polygons if they have four quadrants or more. Its form is a simple geometric figure. When put together, the characters ABC create a right-angled triangle. When the boundaries are incompatible, Euclidean geometry generates a new rectangle with square corners. Triangles are regarded as polygons because they have three edges and three corners. Where a triangle's three edges intersect determines where its corners are. A triangle's interior sides add up to 180 degrees.

Here,

After the transformation, the new vertices of the triangle will be:

X(1-9, 8-5) = (-8,3)

Y(8-9, 7-5) = (-1,2)

Z(7-9, -2-5) = (-2,-7)

Therefore, the new triangle XYZ with vertices X'(-8,3), Y'(-1,2) and Z'(-2,-7) is obtained after the transformation.

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Answer: -13

Step-by-step explanation:

Implications of an empty row in the roof portion of the house of quality Customer requirements are potentially not being met by the product.

The house of quality serves as a form of conceptual road map for interfunctional communication and planning. In order to discuss design goals, people with various issues and responsibilities can refer to evidence patterns on the grid of the home.

Quality function deployment is a set of planning and communication procedures that concentrates and organises capabilities inside an organisation in order to first create, then manufacture, and finally sell products that consumers want to buy and will continue to buy. The idea that items should be high-quality is the cornerstone of the house of quality.

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Answer:

b=95; c=85

Step-by-step explanation:

B is equivalent to 85 degrees because of the vertical angle theorem. B is equivalent to 95 degrees because b and c lie along a straight line; a straight line is 180 degrees, so 180-85=95.

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Answer:

b equals 95 c equals 85 that's what I think and I have straight A's so I think I'm right

The similarity statement for the triangle is ΔPQR ~ ΔSTM

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words similar triangles have the same angles and the sides of the triangles are ratio of each other.

Hence, let find the statement of proportionality of the triangles as follows:

Therefore,

∠P ≅ ∠S

∠Q ≅ ∠T

∠R ≅ ∠M

And finally,

ΔPQR ~ ΔSTM

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Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15), the scale factor used is: A. 5.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = -15/-3

Scale factor = 5.

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Answer: its 5

Step-by-step explanation: I did it in a test and got it right

Answer:

Option A (You chose it right)

Step-by-step explanation:

Base of triangle = [tex](\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2})[/tex] units

Since the two fractions have the same denominator, the resulting simplified fraction will have the same denominator and everything written in the numerator level will be copied down as it is:

                           = [tex]\frac{\sqrt{2} + \sqrt{2}}{2}[/tex]

                           =[tex]\frac{2\sqrt{2}}{2}[/tex]

                           = [tex]\sqrt{2}[/tex] units

Area:

Area of a triangle = [tex]\frac{1}{2}[/tex] × base of triangle × perpendicular height

                             = [tex]\frac{1}{2}[/tex] × ([tex]\sqrt{2}[/tex] units) × ([tex]\frac{\sqrt{3}}{2}[/tex] units)

                             = ([tex]\frac{\sqrt{2}}{2}[/tex] ×[tex]\frac{\sqrt{3}}{2}[/tex]) square units

     ∴ Area            [tex]= \frac{\sqrt{6}}{4}[/tex] square units

Perimeter:

It is the sum of all the outer sides (or outer boundaries) of the triangle:

Perimeter = Base of triangle + first slanted height + second slanted height

                = [tex](\sqrt{2} + \sqrt{2} + \sqrt{2})[/tex] units

                [tex]= 3\sqrt{2}[/tex] units

∴ Option A