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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{4}}} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{3 }{ 4 }[/tex]

the following shaded-regions in the plane consists of all points whose polar coordinates satisfy the inequalities 0 ≤ r ≤ 3 and π/6 ≤ θ ≤ π/12.

It is referred to as a polar coordinate system when each point on a plane in a two-dimensional coordinate system is determined by a distance from a reference point and an angle measured from a reference direction. Pole: The object of comparison. The term "polar coordinates" refers to these new coordinates since you interpret the axes' intersection as a pole from which all other points radiate outward. change (degrees are measured in radians) (degrees are measured in radians).

Given that,

0 ≤ r ≤ 3

and π/6 ≤ θ ≤ π/12

In the given condition we can clearly see that the radius is not equal to 3 but it is less than 3. Thus graph number 1, 2, 4 and 6 do not match the given condition.

Now in the given condition 0 ≤ r ≤ 3 the angle is between 30° to 105°

In the graph number 3 radius varies from 0 ≤ r ≤ 3 but angle varies from 75° to 150°, so it is also incorrect.

Thus in the remaining graph number 5, the radius varies from 0  and angle also varies from 30° to 105°.

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The complete question is as follows:

On solving the provided question, we can say that the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.

Mathematicians study numbers and their variations, equations and related structures, shapes and their places, and potential placements for these things. The term "function" refers to the relationship between a set of inputs, of which each has an associated output. An relationship of inputs and outputs known as a function is one in which each input leads to a single, distinct output. Each function is given a domain or a codomain, or scope. The letter f is frequently used to indicate functions (x). Entry is an x. The four major kinds of accessible functions are on functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions.

Function K is given as y = 1/2x + 2, so the slope of K is 1/2 and the y-intercept of K is 2.

To find the slope and y-intercept of function H, we can use the given points (x,y):

When x = -2, y = 0, so we have the point (-2,0)

When x = 1, y = 4.5, so we have the point (1,4.5)

When x = 5, y = 10.5, so we have the point (5,10.5)

When x = 8, y = 15, so we have the point (8,15)

We can use two of these points to find the slope of H:

slope = (change in y) / (change in x) = (10.5 - 4.5) / (5 - 1) = 6/4 = 3/2

To find the y-intercept of H, we can use the point (0,b) where x = 0:

b = y - mx = 4.5 - (3/2)(1) = 3

So the equation for function H is y = (3/2)x + 3, which has a slope of 3/2 and a y-intercept of 3.

Now we can compare the two functions:

A) The slope of function K is greater than the slope of function H. False, since 1/2 < 3/2.

B) The y-intercept of function K is greater than the y-intercept of function H. False, since 2 < 3.

C) The slope of function K is equal to the slope of function H. False, since 1/2 ≠ 3/2.

D) The y-intercept of function K is less than the y-intercept of function H. True, since 2 < 3.

Therefore, the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.

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The first hiker is 2 miles east and 1 mile north of the starting point, so the position can be represented by the coordinate pair (2, 1).

What is the Pythagorean theorem in plain English?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The second hiker is 2 miles west and 3 miles south of the starting point, so the position can be represented by the coordinate pair (-2, -3).

The Pythagorean theorem can be used to calculate the separation between the two points:

d = √((2 - (-2))²  + (1 - (-3))² ) = √((2 + 2)² + (1 + 3)²) = √(4² + 4²) = √(16 + 16) = √32

So, the two hikers are approximately 5.66 miles apart.

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Answer:

975

Step-by-step explanation:

The largest number of pages the book can have is 975 because the maximum number of times the digit 7 can appear in the page numbers is 25. The maximum number of pages is obtained when the page numbers range from 100 to 999, inclusive, which would result in the digit 7 appearing 25 times.

Answer:

Carlos deposited $140 into his savings account, which can be represented by the signed number +140.

Step-by-step explanation:

This indicates an increase in his account balance of $140.

First triangle x = 30

Second triangle N = 55

d. Data is inadequate as it is not possible to determine the direction of D's house relative to A's house.

Directions refer to the relative positions of objects or locations in space. It describes the orientation and location of an object in relation to another object or a reference point.

Based on the information given, . Further information is needed to determine the direction.

Hence, d. Data is inadequate

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Z18 with modulo addition satisfies all four group axioms and is a group.

Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.

what is the binary operation?

In mathematics, a binary operation is a function that takes two elements from a set and returns another element from the same set.

For a set to form a group with a binary operation, the set must satisfy the four group axioms: closure, associativity, identity, and inverse.

1. Z18 with modulo addition:

Hence, Z18 with modulo addition satisfies all four group axioms and is a group.

2. Z18 with modulo multiplication:

Hence, Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.

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X+1, R2 is the synthetic division of (x²+3)+(x-1) by In the divisor x + 5, change the constant's sign from 5 to -5 and bring it down.

The number is said to be in variables its simplest form being divided in it's smallest equivalent fraction. When or how to find the most basic form. Look for common factors throughout the denominator and numerators. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two orthogonal axes and even an equal sign in the middle is called an equation in mathematics. The general form of any equation provides the degrees of all the  in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as assumptions or conditional equation.

given

(x²+3)+(x-1)

2x+3 / x = 1

X+1, R2 is the synthetic division of (x²+3)+(x-1) by In the divisor x + 5, change the constant's sign from 5 to -5 and bring it down.

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The volume of the given prism in question is 276.7 cubic yd

The formula for calculating the volume of a square based prism is expressed as:

V = BH/3

where

B is the base area

H is the height of the prism

Determine the height using Pythagoras theorem

b^2 = 13^2 - 10^2

b^2 = 169 - 100

b^2 = 69

b = √69
b = 8.3yd

Determine the required volume

V = (10*10)(8.3)/3

V = 830/3

V = 276.7 cubic yd

Hence the volume of the prism is given as 276.7 cubic yd

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Answer:

House value x Tax rate = Taxes paid

172000 x 0.08 = 13760

The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.

What does the example set?

A set is a logically arranged group of items that can be represented in either set-builder form or roster form in mathematics.

                                 Sets are typically shown using curly brackets; for instance, A = 1, 2, 3, 4 is a set.

The given two sets are

            A = {x, j, a, m} and D = {x, a, b, y}

By definition,

The two sets A and B are equal sets if they contain the same elements.

Here,  j, m and b, y are different in two sets.

Thus, The set A and D does not contain the same elements.

Therefore, The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.

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Answer:frequency

Step-by-step explanation:

-p + 2p^2 is a quadratic function, which is a polynomial function of degree 2.

Quadratic function is a polynomial function of degree 2, written in the standard form as ax^2 + bx + c, where a, b, and c are constants, and x is a variable.

The graph of a quadratic function is a parabola which opens up or down depending on the value of a. The most common application of quadratic functions is in solving problems related to parabolic motion, such as finding the maximum height, time of flight, or range of a projectile.

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The graph of the function h is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Suppose that the function h is defined as follows.

h(x) = -1 if -2.5 < x ≤ -1.5

           0 if -1.5 < x ≤ -0.5

            1 if -0.5 < x ≤ 0.5

            2 if 0.5 ≤ x < 1.5

            3 if 1.5 ≤ x  < 2.5

The above function is a piecewise function

Next, we graph the individual functions in the function h according to their domain

See attachment for the graph of h

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Answer: The value of sin(2x) can be found using the identity:

sin(2x) = 2sin(x)cos(x)

Since sin(x) = -1/2, we can use the Pythagorean identity to find the value of cos(x):

cos^2(x) + sin^2(x) = 1

So

cos^2(x) = 1 - sin^2(x) = 1 - (-1/2)^2 = 1 - 1/4 = 3/4

Taking the square root of both sides:

cos(x) = ± sqrt(3)/2

Since sin(x) is negative and cos(x) must be positive, we get:

cos(x) = sqrt(3)/2

Finally, substituting the values of sin(x) and cos(x) into the formula for sin(2x), we get:

sin(2x) = 2sin(x)cos(x) = 2 * (-1/2) * sqrt(3)/2 = -sqrt(3)

So the exact value of sin(2x) is -√(3).

Step-by-step explanation:

The height of the school is 13.27 m.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have.

From the information given, we can draw the figure given below,

Now,

Triangle ABC and Triangle DCE are similar.

So,

x / 1.25 = 11.15 / 1.05

x = (11.15 x 1.25) / 1.05

x = 13.27 m

Thus,

The height of the school is 13.27 m.

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Answer:this is a rational number

Step-by-step explanation:

The number zero can be written as 0 ÷ any non-zero integer. For example, the rational numbers 0/1 and 0/(-2) are equal to 0. This is in the form of p/q, where p and q are integers and q ≠ 0.

Answer:

hacunamatata

Step-by-step explanation:

it means no worrys

Answer:

80+90

add them together

=170

10% of 170

=17

20-17=3

A function f(x) is said to have a jump discontinuity at x = a if:

3. The left and right limits are not equal.

The function has a jump discontinuity at x = 6 because:

The different lateral limits are the reason given for the jump discontinuity, as shown in the graph presented at the end of the answer.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

If the lateral limits are different, the limit does not exist and the function is not continuous at x = a, being said to have a jump discontinuity.

The function has a jump discontinuity at x = 6 because:

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The consistent state lattice x is equivalent to (0.6, 0.9), and the stochastic matrix P is normal.

To decide if a stochastic grid P is standard, we should initially compute the consistent state matrix x of the Markov chain with a matrix of change probabilities P. To do this, we set up the situation Px = x and address for x.

We can communicate the components of x as far as a boundary t as follows:

x1= 0.5t + 0.1

x2= 0.5t + 0.9

We can then settle for t in view of the amount of x1 and x2. The amount of x1 and x2 ought to be equivalent to 1, so:

0.5t + 0.1 + 0.5t + 0.9 = 1

t = 1

Therefore, The consistent state lattice x is equivalent to (0.6, 0.9).

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The velocity of the two trains are 79m/s and 66m/s

Velocity is the rate of change of displacement with time. It is a vector quantity and it is measured in meter per second.

Using addition of vectors:

The total displacement = d2-d1

displacement = velocity × time

Represent the velocity of faster train by v

therefore the velocity of the slower train = v -13

855 = 5v +5(v-13)

855 = 5v+5v+65

855 = 10v +65

10v = 855-65

10v = 790

v = 790/10

v = 79 m/s

the rate of the second train = 79-13 = 66m/s

therefore the rate of the two trains are 79m/s and 66m/s

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The intervals at which the parabolic equation from the graph is decreasing is (4, ∞).

A parabolic equation is an equation of a curve usually in form of a U-shape when displayed on the graph. In the given diagram, we can use the standard form of a quadratic equation y = ax² + bx + c as the starting point for finding the equation through the three points of the curve.

Using the following points on the curve; (0,-2) (4,6), and (6,4), because these points pass along the x and y-axis of the curve.

Create a system of equations by substituting the x and y values of each point into the standard formula of a quadratic equation to create the three-equation system.

−2 = a(0)² + b(0) + c,

6 = a(4)² + b(4) + c,

4 = a(6)² + b(6) + c

Solve the system of equations to find the values of a, b, and c.

[tex]$$a= - \dfrac{1}{2}$$, b = 4, c = -2[/tex]

Substitute the actual values of a, b, and c into the formula for a quadratic equation to find the resulting equation.

[tex]y = - \dfrac{x^2}{2} + 4x - 2[/tex]

Since we know the resulting equation of the parabola, we can now deduce the intervals at which the parabola is decreasing. As such, the interval at which the parabolic equation is decreasing is (4, ∞)

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In the figure the area of circle is obtained as option C: 144π cm².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of the square is = 144 cm².

The formula for area of square is - (side)²

The equation is -

Area = (side)²

Substitute the value into the equation -

144 = (side)²

side = √144

side = 12 cm

The side of the square is the radius of the circle.

The area of circle is given as -

Area = πr²

Substitute the value into the equation -

Area = π(12)²

Area = 144π cm²

Therefore, the area of circle is 144π cm².

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Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

What is an experiment ?

A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law

In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.

Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

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Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

What is an experiment ?

A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law

In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.

Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

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As per the intersecting point, the length of AC is 4x + 10.

The diagonals of a rectangle are two lines that intersect at the midpoint of the rectangle. In this case, the diagonals of rectangle ABCD intersect at point E.

If AE = 2x + 5 and BD = 5x + 2, then we can calculate the length of AC. We know that AC is the sum of AE and ED, so AC = AE + ED.

Since the diagonals of a rectangle intersect at the midpoint of the rectangle, AE and ED are equal. Therefore, AC = 2x + 5 + (2x + 5) = 4x + 10.

Therefore, the length of AC is 4x + 10. Knowing the lengths of the diagonals can help us find the length of the sides of the rectangle, and can also be useful in finding the area of the rectangle

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The total cost for the rental is calculated by subtracting the first 50 miles from the total miles driven (430 miles) and then multiplying it by the per mile rate ($0.35/mile).

Miles is a unit of distance measurement. It is used for measuring the distance between two places. It is equivalent to 1.609 kilometers. Miles are used for measuring the length of roads, flight distances, distances between cities, and other large distances. Miles can also be used to measure the length of running, swimming, and cycling events. Miles are also used in the United States to measure the speed of vehicles, such as cars and airplanes.

This gives us a total cost of $118.50 for the miles driven. To calculate the total cost for the rental, we add the cost for the miles driven ($118.50) to the daily rate for the 2 days ($46.90 x 2 days = $93.80). This gives us a total cost of $212.30 for the rental.

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