How do you prove irrational rational and irrational?

On solving the provided question, we can say that - the slope of the following will be slope, m = [tex]4-6/4-2 = -2/2 = -1[/tex]

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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On solving the provided question, we can say that - the slope of the following will be slope, m = -1

what is slope?

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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The unit rate of constant means that for every 1 pound, the output is 1.96 dollar.

Proportionality is a relationship between two variables in which their ratio is always equal to a constant value. In mathematical terms, it can be expressed as y = kx, where y and x are the two variables, and k is the constant of proportionality.

A rate is a measure of how one quantity changes in relation to another quantity. It is usually expressed as a ratio and has units of measurement, such as miles per hour, dollars per pound, etc. A unit rate is a rate in which the second quantity is one unit of measurement.

The unit rate of the constant of proportionality is found by dividing the change in y (output) by the change in x (input).

In this case:

$9.8/5$ = $1.96$, so the unit rate of the constant of proportionality is 1.96 pounds/dollar.

It means that for every 1 pound, the output is 1.96 dollar.

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Answer:

ANGLE 5 IS CONGURENT TO ANGLE 4

PLEASE MARK BRAINLIEST

The equation y = 5x - 8 and y = 9x - 8 have one solution at

(0, -8)

The equation is solved simultaneously by elimination method as follows

y = 5x - 8

y = 9x - 8

subtraction the equations

0 = -4x - 0

-4x = 0

x = 0

substituting x = 0 into y = 5x - 8

y = 5x - 8

y = 5 * 0 - 8

y =0 - 8

y = -8

The solution of the equation is at the point (0, -8)

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Answer:

The line pairs that are pendicular are shown in option c.

c.    y = − 3x + 7, y = x / 3 + 11

Step-by-step explanation:

Perpendicular lines have slopes that are the negative inverse of each other.  For example, a line with slope of 5 would have a line perpendicular to it if the second line has a slope of -(1/5)  [the negative inverse of +5].

Cmpare the slopes of each pair of linear equations:

a.  -3 and 3  The negative inverse of -3 would be (1/3), not 3.  These lines are not perpendicular.

b.  3 and (1/3).  The negative inverse of 3 would be -(1/3), not (1/3).  These lines are not perpendicular.

c.  -3 and (1/3).  The negative inverse of -3 would be (1/3).  These lines are perpendicular.

d.  -3 and (-1/3).  The negative inverse of - 3 would be (1/3).   These lines are not perpendicular.

3x-y=-9

Step-by-step explanation:

Answer: 3x - y = - 9

Step-by-step explanation:

Re-write the equation in the following form:

3x + 9 = y

Take the y to LHS:

3x + 9 - y = 0

Now, take the 9 to the RHS:

3x - y = -9. This is your answer.

The equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].

What is slope intercept form of the line?

Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.

Given:

The line passes through the points (7, 6) and (- 1, 2).

We have to find the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.

First to find the slope of the line using the formula,

Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1, y_1)= (7, 6), (x_2,y_2)=(-1, 2)[/tex]

Plug the values in the above formula.

[tex]m = \frac{2-6}{-1-7} = \frac{-4}{-8}=\frac{1}{2}[/tex]

Now consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)\\y-6=\frac{1}{2}(x-7) \\y-6=\frac{1}{2}x-\frac{7}{2}\\ y=\frac{1}{2}x -\frac{7}{2}+6 \\y=\frac{1}{2}x+\frac{5}{2}[/tex]

Hence, the equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].

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Answer:

1.5 kilograms

Step-by-step explanation:

You need to convert grams to kilograms, this means you must divide the mass value by 1000 to find your answer.

1,500/1,000 = 1.5

Answer:

For 1500 grams in kilogram we get 1.5 kg

Step-by-step explanation:

to convert a gram into a kilogram we have to divide the gram term by 1000

Answer:

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

According the the table the slope is:

Use slope-intercept form:

And substitute one of the ordered pairs, to find the value of b:

The y-intercept is (0, 8).

If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.

Let d represent the distance that is needed to travel 1 hour

1 hour late decreased to 0.5 hours early = 1.5

Hence,

d/50 + 1.5 = d/35

Simplify

7d + 525 =10d

Collect like terms

525 = 10d - 7d

525 = 3d

Divide both side by 3d

d = 525/3

d = 175

Total number of miles :

Total number of miles = 175 + 35

Total number of miles = 210

Therefore we can conclude that the correct option is C.

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Answer:

[tex]5 \sqrt{3} [/tex]

Step-by-step explanation:

Frist find which perfect square goes into 75. In this case its 25 * 3. You then find out what is the square root of 25. Which is 5. you put that number outside the radical and the other number inside the radical. resulting in 5 square roots of 3.

Answer: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

5√3

Decimal Form:

8.66025403…

Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the centre of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

There is just one peak in a unimodal distribution, two peaks in a bimodal distribution, and three or more peaks in a multimodal distribution. If the data is skewed or symmetric, such information can also be used to characterise the histogram's structure.

Therefore, the correct answer is option b) Unimodal.

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The required correct option for the given question is uni-modal.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the center of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bi-modality or any multi-modality, box-plots are best reserved for distributions with a single mode.

There is just one peak in a uni-modal distribution, two peaks in a bimodal distribution, and three or more peaks in a multi-modal distribution. If the data is skewed or symmetric, such information can also be used to characterize the histogram's structure.

Therefore, the correct answer is option b) Uni-modal.

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The coordinate of 3 4 indicates a point on a cartesian plane.

In mathematics, the coordinate system refers to the method in which a location of a point is identified in the plane or space.

There are two coordinate system, one is cartesian coordinate system and the other is polar coordinate system.

Each coordinate system has some reference lines called reference axis or reference direction or point called reference direction and point.

As per the definition of a cartesian coordinate system, a location of a point is identified by a pair of numerical terms. The first one indicates the X coordinate and the second one indicates the Y coordinate.

So, the above coordinate 3 4 refers to a point on the XY coordinate system where 3 is the X coordinate and the distance from Y axis and 4 is the Y coordinate and distance from the X axis.

ordinate refers to y point in (x, y)

in (3,4)

ordinate = 4

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The value of {a} in the given modelled statement equation is 5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is that the ages of three cats are (a) , (a + 4) and (2a - 3). Their total age is 21.

We can model the given equation is -

(a) + (a + 4) + (2a - 3) = 21

a + a + 4 + 2a - 3 = 21

4a + 1 = 21

4a = 20

a = 5

Therefore, the value of {a} in the given modelled statement equation is 5.

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{

Complete question is given below -

The ages of three cats are a, a+4 and 2a-3. Their total age is 21. Determine a.

}

The range of the accidents reported from the grouped frequency table is 22.

The range is the difference between the highest value and the lowest value of a given set of data.

We have,

The number of accidents reported from the grouped frequency table.

The largest number of accidents = (19 - 25)

The smallest number of accident = (3 - 7)

Now,

Range.

= 25 - 3

= 22

Thus,

The range of the reported accidents is 22.

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To find the area of a triangle, you can use the formula:

area = (base * height) / 2

In this case, the base of the triangle is 24 inches and the height is 20 inches, so plugging these values into the formula gives:

area = (24 * 20) / 2

area = 240 / 2

area = 120 square inches

So the area of the top of the cheese board is 120 square inches.

The equation of the line parallel to y = 5x + 9 which intersects the point (-2, -3).

Parallel lines are coplanar, infinite straight lines in geometry that don't cross at any point. Planes in the same three-dimensional space that never cross each other are said to be parallel.

Curves that are parallel to one another and maintain a set minimum distance do not touch or intersect. A line and a plane that do not share a point are also referred to as being parallel in three-dimensional Euclidean space. But skew lines are used to describe two noncoplanar lines.

We know that slope of parallel line are same. Thus, slope is 5 in y = 5x + 9

Now we need to put the values in y intercept form to find out the equation

y - y1 = m(x - x1)

y - (-3) = m(x - (-2))

y + 3 = 5(x + 2)

y = 5x + 10 - 3

y = 5x + 7

Thus, The equation of the line parallel to y = 5x + 9 which intersects the point (-2, -3).

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No, It is not possible to have a complex number in the form of a + bi when b = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Complex number.

It is in the form of a + ib.

Where a and b are real numbers.

Now,

If b = 0 then we can not have a complex number.

Example:

a + bi

a = 1 and b = 0

1 + 0i = 1 which is not a complex number.

In order to have a complex number a can be any real number and 0 but b  can not be a zero.

Thus,

It is not possible to have a complex number in the form of a + bi when

b = 0.

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Answer: 3

Step-by-step explanation:

Factor of 15: ±1, ±3, ±5, ±15
Factor of 18: ±1, ±2, ±3, ±6, ±9, ±18
Factor of -45: ±1, ±3, ±5, ±9, ±45
=> GCF of 15, 18, -45 is 3

The dot plot in option E is correct.

What is sample size?

Choosing the number of observations or replicates to include in a statistical sample is the process of determining sample size. Any empirical study whose objective is to draw conclusions about a population from a sample must take the sample size into consideration.

Finding your sample size in five steps

Clarify the term "population size" or "people"

Specify your error margin.

Decide how confident you are.

Calculate the expected variance.

Decide on the sample size.

As long as it doesn't go over 1,000, 10% of the population serves as a good maximum sample size.

The dot plot in option E is correct.

Because we conduct 50 trials, dot plot should have 50 points, one point per each trial.

On X axis, we take no. of successes out of 10.

Hence it having 0 to 10 numbering.  

Hence, the dot plot in option E is correct.

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It is false that the cost of two pounds of apple cast is more than $ 3.50.

Here to find the cost of the given quantity we need to find the cost of 1 unit i.e 1 pound in the given problem so that we can find the cost of given quantities. It is called a unitary method.

Given that  

Andrew buy 8 pounds of apples for $ 12.00  

Let 'x' be the cost of 1 pound of apples

By the given data,

=> 8x = $ 12

=> x = 12/8

=> x = 1.5  

The cost of 1 pound of apples = $ 1.5

Cost of 2 pounds apples = 2 × 1.5 = 3

Therefore,

It is false that the cost of two pounds of apple cast is more than $ 3.50.

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The given series is convergent and the sum S∞ is 5.555

Think about 10 - 8 - 6.4 - 5.12

If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.

the average ratio,

r = -8/10

⇒ r = -0.8

This equals 1 - 0.8 - 1.

The presented series is hence convergent.

Sum of series = S∞ = a/(1 - r)

Here, first term(a) = 10,

common ratio(r) = -0.8,

S∞ = a/(1 - r)

⇒ S∞ = 10/(1 - (-0.8))

⇒ S∞ = 10/(1 + 0.8)

⇒ S∞ = 10/1.8

⇒ S∞ = 5.555

Therefore, the given series is convergent and the sum S∞ is 5.555

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Answer:

around 18%

Step-by-step explanation:

14.30/80=0.17875

0.17875*100=17.875

18%

Answer:

Step-by-step explanation:

the answer is [tex]\frac{14.30}{80}[/tex]=17.875%

Answer:

  9 cm

Step-by-step explanation:

You want the radius of the sphere that has a surface area of 324π cm².

The area of a sphere is given by the formula ...

  A = 4πr²

Filling in the given values, we can solve for r:

  324π = 4πr²

  81 = r² . . . . . . . . . divide by 4π

  9 = r . . . . . . . . . . . take the square root

The radius of the sphere is 9 cm.

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The residual values are -0.1, 3.8, 0.32, and 0 respectively for the given coordinate pairs.

A residual is a difference between the observed value (y) and the predicted value (y-hat) for a given x value. To find the residual for each coordinate pair (x,y), we need to substitute the x value into the equation for the line of best fit and calculate the difference between that value and the observed y value.

The equation for the line of best fit is y = 1.1x + 3.4

The residual for each coordinate pair (x,y) is given by -

Residual = Yactual - y

A. (5, 8.8) ; Yactual = 8.8

Residual = 8.8 - (1.1(5) + 3.4) = - 0.1

B. (2.5, 9.95) Yactual = 9.95

Residual = 9.95 - (1.1(2.5) + 3.4) = 3.8

C. (0, 3.72) Yactual = 3.72

Residual = 3.72 - (1.1(0) + 3.4) = 0.32

D. (1.5,5.05)​ Yactual =

Residual = 5.05 - (1.1(1.5) + 3.4) = 0

It's worth noting that residuals are used to measure how well the line of best fit represents the data set. The residuals should be as close to zero as possible, indicating that the line of best fit is a good representation of the data set.

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The complete question is -

The line of best fit for a data set is y=1.1x+3.4. Find the residual for each of the coordinate pairs, (x,y).

A. (5, 8.8)

B. (2.5, 9.95)

C. (0, 3.72)

D. (1.5,5.05)​

The number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let the number of calories per cup of popcorn be x and the number of calories per ounce of soda be y.

Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories.

3x+6y=162 ------(I)

Carmel has 1 cup of popcorn and 11 oz of soda for a total of 162 calories.

x+11y=182

x=182-11y------(II)

Substitute equation (II) in equation (I), we have

3(182-11y)+6y=162

546-33y+6y=162

546-162-27y=0

384-27y=0

384=27y

y=384/27

y=14

Substitute y=14 in equation (II), we get

x=182-11(14)

x=28

Therefore, the number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.

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"Your question is incomplete, probably the complete question/missing part is:"

Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories. Carmel has 1 cup of popcorn and 11 oz of soda for a total of 182 calories. Determine the number of calories per cup of popcorn and per ounce of soda

The examples of horizontal symmetry is B, C, H, E.

The term horizontal symmetry is defined as is a line about which the object is symmetric.

Here we know that the symmetry line or horizontal axis of a shape which divides the shape into two identical halves is known as horizontal line of symmetry.

Which defines that  the axis here crosses across the shape to cut it into two equal parts.

Therefore, the English alphabets such as B, C, H, E, are the examples of horizontal symmetry.

In this case, here we have a horizontal line passing through the middle of the image and when the image is folded along this line, then we get the two halves overlapping and coinciding perfectly.

Therefore, this one is also an example for this could be a square or a rectangle or any other object that is symmetric horizontally.

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The error interval for the length ,x, of the material is [8.25, 8.35)

We know that error interval is nothing but the limits of accuracy when a number has been rounded.

It is the range of possible values that a number could have been before a number was rounded.

Here, The length L of a some material is 8.3 meters.

The length of the material has been rounded to 8.3 to one decimal place.

The number below 8.3 is 8.2 and the number above is 8.4

Consider a half way between 8.2 and 8.3 for the lower bound and half way between 8.3 and 8.4 for the upper bound.

This means, the length of the material must have been between 8.25 meters and 8.35 meters to round to 8.3 meters to one decimal place.

Therefore, the required error interval would be 8.25 ≤ x < 8.35

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The inequality representing s, the number of sets of glasses Julia should buy is 286 + 6s ≥ 316.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Since Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, the number of sets will be:

286 + 6s ≥ 316

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Answer:

65.6488549618 %

Step-by-step explanation:

total left = 131

left who have artistic ability = 86

proportion of left who have artistic ability = number of favorable outcomes/total outcomes = 86/131 = 0.65648854961

mutliply by 100 to convert to a percent

65.6488549618 %