Help !!!!!!!!!!!!!!!!!!!!!!!!!!!

Line 1: slope = 1/4

Line 2: slope = -4

Line 3: slope = -1/12

Line 1 and Line 2: perpendicular

Line 1 and Line 3: neither

Line 2 and Line 3: neither

Slope is the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Mathematically, the slope is the change in y divided by the change in x. That is:

Slope = (y₂-y₁) / (x₂-x₁)

Line 1:

(4, -1) and (8, 0)

Slope = (0--(-1)) / (8-4)

          = 1/4

Line 2:

(2, -6) and (0, 2)

Slope = (2-(-6)) / (0-2)

          = 8/(-2)

          = -4

Line 3:

(3, -6) and (6, -7)

Slope = (-7-(-6)) / (6-(-6))

          = -1/12

Remember:

1. When the two lines are parallel, they have the same (equal) slope.

2. When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ * m₂ = -1. Where m₁ and m₂ represent the slope of the lines.

Let's check:

Line 1 and Line 2:

They are not parallel but they are perpendicular (i.e. 1/4 * (-4) = -1).

Line 1 and Line 3:

Neither

Line 2 and Line 3:  

Neither

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the correct answer is B, between 6.5 and 9.5.The solution of given standard deviations Problem isit is unlikely that most of the data points would be located there.

Standard deviation is a statistical measure of the amount of variation or dispersion in a set of data values. It represents the average distance of each data point from the mean of the data set.

The answer to this question can be found using the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

Given that the mean is 8 and the standard deviation is 1.5, one standard deviation above the mean would be 8 + 1.5 = 9.5, and one standard deviation below the mean would be 8 - 1.5 = 6.5. Therefore, approximately 68% of the data would be expected to fall between 6.5 and 9.5.

Based on this information, we can eliminate answer choices A and D. Answer choice C is more than two standard deviations above the mean, so it is unlikely that most of the data points would be located there. Therefore, the correct answer is B, between 6.5 and 9.5.

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In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy  the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).

Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.

From the question, p = number of pounds Juan will buy.

candy=costs $8 per pound

$20/$4 = 5 pounds

p>5

at least 5 pounds

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The surface area of the square pyramid is 416.23 ft²

The surface area of a square pyramid is given by the formula:

A = a² + 2a√(a²/4 + h²)

Where a is the base length of the square pyramid and h is the height of the square pyramid.

From the figure, we have: a = 10 ft and h = 15 ft

A = a² + 2a√(a²/4 + h²)

A = 10² + 2*10√(10²/4 + 15²)

A = 100 + 20√(100/4 + 225)

A= 100 + 20√250

A = 416.23 ft²

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Answer:

There are three steps to find IQR

1. Know how the IQR is used. Essentially, it is a way of understanding the spread or "dispersion" of a set of numbers. The interquartile range is defined as the difference between the upper quartile (the highest 25%) and the lower quartile (the lowest 25%) of a data set.

2. Understand quartiles. To visualize a quartile, chop a list of numbers into four equal parts. Each of these parts is a "quartile."[2] Consider the set: 1, 2, 3, 4, 5, 6, 7, 8.

1 and 2 are the first quartile, or Q1

3 and 4 are the second quartile, or Q2

5 and 6 are the third quartile, or Q3

7 and 8 are the fourth quartile, or Q4

3. Learn the formula. In order to find the difference between the upper and lower quartile, you'll need to subtract the 25th percentile from the 75th percentile.

The formula is written as: Q3 – Q1 = IQR.

Answer:

the answer would be 2.5

Explanation:

The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data).

The surface area of the square pyramid given above would be = 400ft²

The diagram above is a typical example of the square based pyramid which has four triangles connected to a vertex.

To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs

where b = base length= 10ft

s = slant height= 15ft

Surface area = 100+2(10×15)

= 100+300

= 400ft²

Therefore the surface area of the square based pyramid given above would be = 400ft².

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The rowing speed of the crew in still water is:

x = 12 km/h.

What is meant by speed?

Speed is a measure of how fast an object is moving. It is usually expressed in units of distance per unit of time, such as miles per hour or meters per second. Speed can be calculated using the formula speed = distance/time.

According to the given information

We can use the formula:

distance = rate × time

to set up two equations based on the information given.

When the crew rows upstream for 5 km, the time it takes is:

time = distance/rate

time = 5 / (x - 8)

When the crew rows downstream for 5 km, the time it takes is:

time = distance/rate

time = 5 / (x + 8)

The total time for the round trip is 1 hour 30 minutes, or 1.5 hours:

total time = time upstream + time downstream

1.5 = 5/(x-8) + 5/(x+8)

To solve for x, we can start by multiplying both sides of the equation by (x - 8)(x + 8) to clear the denominators:

1.5(x - 8)(x + 8) = 5(x + 8) + 5(x - 8)

Expanding and simplifying, we get:

1.5x^2 - 72 = 10x

Bringing all the terms to one side of the equation, we get:

1.5x^2 - 10x - 72 = 0

We can factor this quadratic equation by first dividing both sides by 1.5:

x^2 - (10/1.5)x - 48 = 0

We can then factor this expression as:

(x - 12)(x + 4) = 0

This gives us two possible values of x: x = 12 and x = -4.

Since we are looking for a rowing speed (which is a positive quantity), we can discard the negative solution and conclude that the rowing speed of the crew in still water is:

x = 12 km/h.

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The coordinates of the figure after translation & dilation are A''(1,3) ,R''(-1/2,1) , G''(-1,-3/2), Y''(5/2,5/2).

A quadrilateral is a polygon with four sides and four vertices. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Scale factor refers to the ratio of the length or size of an object in one dimension to the length or size of a corresponding object in another dimension. It is commonly used in mathematics and geometry to describe the relationship between two similar figures. For example, if one square has a side length of 4 cm and another square is similar to it with a side length of 8 cm, the scale factor between the two squares is 2:1.

A(2,8) R(3,4) G(2,-1) Y(9,7)

Translate it to 4 units left gives the result:

A'(-2,6) ,R'(-1,2) ,G'(-2,-3), Y'(5,5)

Now dilate it:

A''=(-1,3), R''(-1/2,1), G''(-1,-3/2), Y''(5/2,5/2)

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The given function h(x) is h(-5) = -2, h(-2) = -1 and h(5) = -2.

The set of all possible inputs is the domain of a function. For instance, all real integers other than x=0 are in the domain of f(x)=x2 and g(x)=1/x, respectively. Additionally, custom functions with more restricted domains can be defined.

The definition of the function h(x) is as follows:

h(x) =

-2 if x < 2

-1 if x = -2

Using this definition, we can find the values of h(-5), h(-2), and h(5) as follows:

h(-5): Since -5 < 2, we use the first part of the definition and set h(-5) = -2.

h(-2): Since -2 = -2, we use the second part of the definition and set h(-2) = -1.

h(5): Since 5 > 2, we use the first part of the definition and set h(5) = -2.

Therefore, we have:

h(-5) = -2

h(-2) = -1

h(5) = -2

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Answer:

To determine the possible values of h, we need to first understand what is meant by the range.

The range is the difference between the highest value and the lowest value in a set of numbers. In this case, we don't know what the full set of numbers is, but we know that the range is 3.

The highest number in the set is 4 (since there are no higher numbers in the set than 4), and the lowest number in the set is either 1 or 2. This is because the range is 3, and there are only two possible sequences of three consecutive integers that include the number 4: 2, 3, 4 and 1, 2, 3.

So to find the possible values of h, we need to add 3 to each of the possible lowest numbers in the sequence.

If the lowest number is 1, then the possible highest numbers are 4 and 5 (4 + 3 = 7 but the sequence only goes up to 4 so the highest should be 5). Therefore, the possible values of h are either 10 or 11.

Therefore, the correct answer is B. 11.

The ones that are symmetric with respect to the x-axis is:

A function is symmetric with respect to the x-axis if replacing y with -y in the equation does not change the equation. In other words, if the graph of the function is the same when reflected across the x-axis.

Therefore, only the equation y = -7x^2 is symmetric with respect to the x-axis.

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Step-by-step explanation:

x^2 -6x - 72   =  ( x-12)(x+6)

If you can't do this 'in your head'  you can always use Quadratic Formula

  with  a = 1      b= - 6    and   c= -72

      to find roots   x = 12 and  -6      then write the equation as above

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

The correct statements describing the area and perimeter of the patio are:

The area of a rectangle is given by the product of its length and width. So, the area of the patio is:

Area = length x width

Area = (1 + 2x)(2 - 3x)

Therefore, the area of the patio is (1 + 2x)(2 - 3x) square yards.

The perimeter of a rectangle is given by the sum of the lengths of all four sides.

So, the perimeter of the patio is:

Perimeter = 2(length + width)

Perimeter = 2(1 + 2x + 2 - 3x)

Perimeter = 2(3 - x)

Therefore, the perimeter of the patio is 2(3 - x) yards.

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Applying the Two-Tangent Theorem, the length of segment LM in the circle is: A. 18.

What is the Two-Tangent Theorem?

If two tangent segments are drawn to one circle from the same external point, the Two-Tangent Theorem states that both segments are congruent together.

Applying the theorem, we have:

4x - 2 = 3x + 3

Find the value of x:

4x - 3x = 2 + 3

x = 5

Find the length of LM:

LM = 3x + 3

Plug in the value of x:

LM = 3(5) + 3

LM = 18

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For the given right angled triangle cosine of angle B is 5√89/89.(option A).

What is right angled triangle?

It is a particular type of triangle having one angle is 90° or right angle. The adjacent sides of the right angle are called base and the perpendicular and the opposite side of 90° is called hypotenuse.

The given triangle is the right angled triangle. The three sides of a right angled triangle are called base, perpendicular and hypotenuse.

In the given figure base=  5 inches and perpendicular = 8 inches

By Pythagoras theorem at first we will find out the hypotenuse. Let the hypotenuse= c inches

For any right angled triangle,

(perpendicular)² +(base)²= (hypotenuse)²

⇒ (8)² + (5)² = (c)²

⇒ 64+ 25 = c²

⇒ c² =89

⇒ c= ±√89

As hypotenuse cannot be negative

So hypotenuse = √89 inches.

Now to find cosine of angle B that is cos B we will use the trigonometric function.

cos B= Adjacent side/ hypotenuse

         = 5/√89

        = 5√89/89 [ Multiplying the numerator and the denominator by √89 ]

Hence, cosine of angle B is 5√89/89.

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The x-coordinates of the points on the curve where the tangent line is horizontal will be option A.

(x² + y²)² = 4(x² – y²)

x⁴ + 2x²y² + y⁴ = 4x² - 4y²

y⁴ + 2x^2y² + 4y² - 4x² = 0

Now we can use implicit differentiation to find the derivative of y with respect to x:

4y³(dy/dx) + 4xy² + 4y(dy/dx)x² + 8y(dy/dx) - 8x = 0

Simplifying this expression, we get:

4y³(dy/dx) + 4xy² + 4xy²(dy/dx) + 8y(dy/dx) - 8x = 0

(dy/dx)(4y³ + 4x²y²) + 8y(dy/dx) = 8x - 4xy²

(dy/dx)(4y³ + 4x^2y² + 8y) = 4x(2-y²)

(dy/dx) = 4x(2-y²)/(4y³ + 4x²y² + 8y)

Based on the information, x-coordinates of the points on the curve where the tangent line is horizontal will be option A.

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The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.

Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.

The Situation column should have two entries: "finding part of a total" and "difference".

The Operation column should have only one entry: "minus".

The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.

To solve for s, we can add 2.3 to both sides of the equation:

s - 2.3 + 2.3 = 6.8 + 2.3

s = 9.1

Therefore, Sam ran 9.1 kilometers.

So, the Situation entries are: "difference" and "finding part of a total".

The Operation entry is: "minus".

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The number of fewer students to get to school by skateboard than by car and bus combined would be 60 fewer students.

To find how many fewer students get to school by skateboard than by car and bus combined, we need to add the number of students who use car and bus and then subtract the number of students who use skateboard.

Car: 30 students

Bus: 40 students

Car + Bus = 30 + 40 = 70 students

Skateboard: 10 students

Difference = (Car + Bus) - Skateboard

Difference = 70 - 10 = 60 students

So, 60 fewer students get to school by skateboard than by car and bus combined.

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The solutions are explained in the solution below.

1) t³ = 216

t = ∛216

t = ∛6×6×6

t = 6

2) a² = 15

a = √15

a = 3.87

3) m³ = 8

m = ∛8

m = ∛2×2×2

m = 2

4) c³ = 343

c = ∛343

c = ∛7×7×7

c = 7

e) f³ = 181

f = ∛181

f = 5.65

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We need to first determine how many totally odd counting numbers there are between 1 and 9. The answer is 250.

It is an integer that is not divisible by two and therefore has a remainder of 1 when divided by two. It is also referred to as an odd number, an odd integer, or an uneven number.

For this, let us consider all the digits from 1 to 9, and their respective sums.

Digit: 1 Sum: 1 (odd)

Digit: 3 Sum: 3 (odd)

Digit: 5 Sum: 5 (odd)

Digit: 7 Sum: 7 (odd)

Digit: 9 Sum: 9 (odd)

Since all the digits between 1 and 9 and their respective sums are all odd, it means that any counting number less than 10 that is composed of only these digits would be totally odd. This means that there are 5 totally odd counting numbers less than 10, i.e., 1, 3, 5, 7 and 9.

Now, since any counting number less than 1000 can be composed of any combination of these 5 digits, the total number of totally odd counting numbers less than 1000 can be calculated by multiplying the number of digits (5) by the number of combinations of those digits (999). The result of this calculation is 250, which is the answer to the question.

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The indefinite integral, given the integral can be found to be √14x + C.

An indefinite integral is an antiderivative of a function. More specifically, if f(x) is a function, then an antiderivative of f(x) is a function F(x) such that F'(x) = f(x), where F'(x) represents the derivative of F(x) with respect to x.

To find the indefinite integral of a constant (in this case, √14) with respect to x, simply multiply the constant by x and add a constant of integration (C):

∫√14 dx = √14 × ∫dx = √14 × x + C

So, the indefinite integral of √14 with respect to x is:

√14x + C

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Answer:

The answer for Surface area is 332m²

Step-by-step explanation:

S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle

S.A=2×1/2×4×3 + 2(20×5) + 20×6

S.A=12+2(100)+120

S.A=12+200+120

S.A=212+120

S.A=332m²

The volume of the rectangular prism in cubic centimeters is 3,600,000

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

Dimension = 120 centimeters by 2 meters by 1.5 meters

The volume of the rectangular prism is the product of the dimensions

i.e.

Volume = Length * width * height

Substitute the known values in the above equation, so, we have the following representation

Volume = 120 * 2 * 1.5

Convert to cm

Volume = 120 * 200 * 150

Evaluate

Volume = 3600000

Hence, the volume in cubic centimeters is 3,600,000

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The requried  [tex]\int_a^{oo} g(x) dx[/tex] must be convergent. Option C is correct.

Since f(x) is greater than or equal to g(x) for all x, we know that:

[tex]\int_a^{oo} f(x) dx\geq\int_a^{oo} g(x) dx[/tex]

If [tex]\int_a^{oo} f(x)[/tex]dx is convergent, then by comparison test, [tex]\int_a^{oo} g(x) dx[/tex] must also be convergent. Therefore, the correct answer is (C) g(x)dx is convergent.

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The rate at which the college student is earning credits, given the semesters taken, would be E. 14 credits per Semester.

The formula to find the number of credits the student takes per semester, would be :

( total credits after 3 semesters - total credits at the start ) / number of semesters = credits per semester

total credits after 3 semesters = 54 credits

total credits at the start = 12 credits

The credits per semester is therefore;

= ( 54 - 12 ) / 3

= 42 / 3

= 14 credits per semester

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The complete question is:

Which of these expresses the rate at which she is earning credits? Select the correct answer below:

3 credits per semester

42 credits per semester

14 semesters per credit

12 credits per semester

14 credits per Semester

7 semesters per credit

Answer:

x=5

Step-by-step explanation:

2^x= 32

2^x=2^5

(comparing, common denominator)

therefore x=5.

The only function that represents a range as less than zero only is: Option C: 1/(x - 2)²

The range of a function is defined as all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.

Now, we want to find the function for which the range is a set of all real numbers less than zero. This means that the range is made up of only negative numbers.

The only option that denotes the range to be less than zero is option C because no matter the domain value, the range will remain a negative number.

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Answer: 20.64 miles.

Step-by-step explanation: The assignment of nomenclature to the location of the boat's initiation as point A, the termination of the first course of the excursion as point B, and the termination of the second course of the journey as point C is proposed. The present study reveals that the spatial positioning of point A and point B is separated by a distance of precisely 15 miles in an eastward direction. Similarly, point B and point C are separated by a distance of 15 miles, but oriented along the vector of N 20° E.

The application of trigonometry provides a means to determine the spatial separation between point B and point C. Based on computations, the distance from point B to point C has been estimated to be approximately 7.83 miles along the northward direction and approximately 14.16 miles along the eastward direction.

Henceforth, the computation of the distance between point A and point C (i.e., the prevailing separation of the boat from the pier) can be determined by the ensuing method:

The mathematical expression denoting the distance between points A and C, designated as AC, is given by the square root of the sum of the squares of the distances between points A and B, designated as AB, and between points B and C, designated as BC. In formulaic notation, this can be expressed as AC = √((AB)² + (BC)²).

The magnitude of the distance denoted by AC, between two points A and C, can be calculated using the Euclidean distance formula, which involves the square root of the sum of the squares of the differences between the corresponding coordinates of the two points. In this particular case, the calculation results in the expression √(15² + 14.16²).

The distance between points A and C, denoted as AC, can be expressed mathematically as the square root of the sum of the squares of the horizontal and vertical distances between them. Thus, AC = √(225 + 200.89), where 225 and 200.89 represent the square of the horizontal and vertical distance, respectively. This equation can be simplified to yield the measurement of the physical distance between points A and C in the applicable units of length.

The distance between points A and C is determined to be the square root of 425.89 in units of length.

The measurement of the distance between point A and point C is approximately equivalent to 20.64 miles.

Answer: Graph A.

Step-by-step explanation: