use the substitution method

The function table for the function y=−2x+1 if given below so that Output of  y  could be –2, –1, 0, 1.

[tex]\left[\begin{array}{ccc}X&Y\\1/2&0\\1&1\\0&-1\\-1/2&-2\end{array}\right][/tex]

Here, Y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x). The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), other abbreviated symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or unspecified.

The function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences. German mathematician Peter Dirichlet first offered the modern definition of function in 1837.


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Answer and Step-by-step explanation:

You can start off your answer by comparing each gallon/mile of each car given. Compare the values that both cars have in common.

For Car M, the car drives a distance of 50.4 miles and used 2 gallons of gasoline.

For Car P, the car drives a distance of approximately 65 miles and used 2 gallons of gasoline.

For Car M, the car drives a distance of 80.5 miles and used 3 gallons of gasoline.

For Car P, the car drives a distance of approximately 90 miles and used 3 gallons of gasoline.

For Car M, the car drives a distance of 137.5 miles and used 5 gallons of gasoline.

For Car P, the car drives a distance of approximately 160 miles and used 5 gallons of gasoline.

After looking at the given information, we can conclude that for every gallon of gasoline used, Car P drives a farther distance than Car M.

We can see this at the points 2, 3, and 5 gallons, where Car M drives 50.4 miles, 80.5 miles, and 137.5 miles (respectively), and Car P drives 65 miles, 90 miles, and 160 miles (respectively).

Have a good day!

Answer:

14 3/10

Step-by-step explanation:

Divide 858 by 60 and get 14.3

14.3 in a mixed number form is 14 3/10

Therefore, one stone weighs 14 3/10 kilograms.

The equation of the line perpendicular to y = 1/3 x + 5 and passing through (2,6) is y = -3x + 12, which is option 3.

To find the equation of a line perpendicular to y = 1/3 x + 5 and passing through the point (2,6), we first need to determine the slope of the original line and the slope of y = 1/3 x + 5 is 1/3.

To find the slope of a line perpendicular to this, we can use the fact that the product of the slopes of two perpendicular lines is -1 and therefore, the slope of the line we want is the negative reciprocal of 1/3, which is -3.

Now that we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line passing through (2,6) with slope -3:

y - 6 = -3(x - 2)

y = -3x + 12

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The measure of the angle is 81 degrees, and the measure of its supplementary angle is 99 degrees.

Let x be the measure of the angle in question, and let y be the measure of its supplementary angle.

By definition, supplementary angles add up to 180 degrees, so we have:

x + y = 180

We also know from the problem statement that:

x = y - 18

We can substitute the second equation into the first equation to eliminate y, giving:

(y - 18) + y = 180

Simplifying this equation, we get:

2y - 18 = 180

Adding 18 to both sides, we get:

2y = 198

Dividing both sides by 2, we get:

y = 99

Finally, we can use the equation x = y - 18 to find the measure of the angle in question:

x = 99 - 18 = 81

Therefore, the measure of the angle is 81 degrees, and the measure of its supplementary angle is 99 degrees.

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h(2) = 3(2) = 6

The output is six

Using the data of interquartile range and median given, only option C is correct because approximately 50% of the days had a high temperature greater than 62°F.

We are given that the median high temperature is 62°F and the interquartile range is 32. The interquartile range is the difference between the first and third quartiles, which means that the first quartile is at 62 - 16 = 46°F and the third quartile is at 62 + 16 = 78°F.

Option A: approximately 25% of the days had a high temperature less than 30°F.

Since 30°F is much lower than the first quartile (46°F), it is unlikely that 25% of the days had a high temperature less than 30°F. Therefore, option A is not true.

Option B: approximately 25% of the days had a high temperature greater than 62°F.

This statement cannot be true because the median is already at 62°F, which means that 50% of the days had a high temperature greater than or equal to 62°F. Therefore, option B is not true.

Option C: approximately 50% of the days had a high temperature greater than 62°F.

This statement is true because the median high temperature is 62°F, which means that 50% of the days had a high temperature greater than or equal to 62°F, and the interquartile range is 32, which means that the third quartile is at 78°F. Since the third quartile is above 62°F, approximately 50% of the days had a high temperature greater than 62°F. Therefore, option C is most likely true.

Option D: approximately 57% of the days had a high temperature less than 94°F.

The maximum temperature that can be associated with the interquartile range of 32°F is the third quartile, which is at 78°F. Therefore, we cannot say that approximately 57% of the days had a high temperature less than 94°F. Therefore, option D is not true.

Hence, the most likely true statement is option C: approximately 50% of the days had a high temperature greater than 62°F.

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The best graphical representation for the given data would be a histogram. A histogram is a graph that displays the distribution of continuous numerical data. It consists of a series of bars, where each bar represents a range of values and the height of the bar represents the frequency or proportion of data points that fall within that range. Since the variable of interest in this case is the number of hours slept per night, which is a continuous numerical variable, a histogram would be an appropriate way to display the distribution of the data. A stem-and-leaf plot is another way to display numerical data, but it is better suited for smaller data sets. Circle graphs and bar graphs are used to display categorical data.

The relative frequency of a class is computed by dividing the frequency of the class by the total number of observations in the data set. This statement (C) is true.

What is the relative frequency?

The relative frequency is a statistical term that represents the percentage of times a certain event occurs in an experiment or study. It is calculated by dividing the number of times an event occurred by the total number of trials in the experiment or study.

The class width is the difference between the upper limit and lower limit of a class. Class width is used to construct frequency histograms, cumulative frequency curves, and frequency polygons.The frequency of a class is the number of times the data falls within a certain class.

So, to compute the relative frequency of a class, divide the frequency of the class by the total number of observations in the data set. Therefore, option c, "dividing the frequency of the class by the total number of observations in the data set," is correct.

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Answer:

  x² -6x +22 = 0

Step-by-step explanation:

You want to write the quadratic equation that has roots x = 3±4i, starting from x -3 = ±4i.

The next step would be to square both sides of the equation:

  (x -3)² = (±4i)²

  (x -3)² = 16i² = -16

  (x -3)² +16 = 0 . . . . . . add 16

  x² -6x +22 = 0 . . . . .  expand the square

Answer:

6

Step-by-step explanation:

Put the numbers in order and find the number in the middle

2,4,6,10,15  The number in the middle is 6.

Helping in the name of Jesus.

Answer: 6

Step-by-step explanation:

the median is the middle number to put it in an easy explanation. Since there are 5 numbers the 3rd one would be the middle one since there would be 2 numbers of the left and 2 number on the right!!!

sorry I forgot to put them in order so

2,4,6,10,15

out of those 6 is the one in the middle

Therefοre, The similarity statement is ΔBAT ~ ΔDER, and the reasοn fοr the similarity is by SSS similarity since the cοrrespοnding sides are in prοpοrtiοn.

Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal. Sο yοu can find the dimensiοns οf a triangle using anοther triangle. If ABC and XYZ are twο similar triangles, yοu can find the assοciated angles and side lengths using the fοrmulas belοw.

Tο determine whether the twο triangles BAT and DER are similar, we can use the similarity criteria. Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are in prοpοrtiοn.

Let's check if the triangles satisfy the similarity criteria:

Angle BAT is cοngruent tο angle DRE, bοth being right angles.

Angle BTA is cοngruent tο angle EDR, bοth being acute angles.

Angle A is cοngruent tο angle E, bοth being acute angles.

Therefοre, the twο triangles have cοrrespοnding angles that are cοngruent.

Next, we can check if their cοrrespοnding sides are in prοpοrtiοn:

BA/BT = 48/84 = 4/7

ED/DR = 8/14 = 4/7

AT/ER = 72/12 = 6/1

We can see that the ratiοs οf the cοrrespοnding sides are equal, which means that the twο triangles are similar.

Therefοre, The similarity statement is ΔBAT ~ ΔDER, and the reasοn fοr the similarity is by SSS similarity since the cοrrespοnding sides are in prοpοrtiοn.

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Answer:

100

Step-by-step explanation:

[tex]\frac{40}{6} = \frac{x}{15}[/tex]

x = (40 x 15) / 6

x = 100

Answer:

2/5

Step-by-step explanation:

2/5 x 7/8 = 7/8 x 2/5

14/40 = 14/40

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Answer:

X= -2x - 1,2x + 3

Step-by-step explanation:

1)Break down the problem into these 2 equations.

(2x-3) - X+ 1 = 4x − 1

-(-(2x-3) - X + 1) = 4x − 1

2)Solve the 1st equation: (2x-3) - X + 1 = 4x − 1.

X=-2x 1

3)Solve the 2nd equation: -(-(2x-3) − X + 1) = 4x – 1.

X = 2x + 3

4)Collect all solutions.

X= -2x - 1,2x + 3

Outside of this range, the relationship's range may differ, and outliers or other significant points may also have an impact.

A variable in mathematics is a symbol or letter that designates a number or value that is subject to change or variation. In order to solve problems and generate expressions and equations that represent the relationships between different quantities, variables are employed. X and Y are variables in the equation y = 3x + 2, for instance. The variable value of x determines the value of y. In order to express unknown numbers that we want to solve for, we can also utilize variables.

given

The scatterplot's depicted relationship is a positive linear relationship. These are some possible descriptions of the relationship's scope:

As the independent variable (x-axis) rises, so too does the dependent variable (y-axis).

There is not much scatter around the trendline, suggesting that the link is reasonably strong. From the lowest value on the y-axis to the greatest value on the y-axis, the relationship's range is defined.

The scatterplot only depicts the relationship between the two variables within the observed range of the data, it is crucial to remember this. Outside of this range, the relationship's range may differ, and outliers or other significant points may also have an impact.

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The probability that at least 4 of the 10 selected employees are women is approximately 0.671.

Let the probability that a randomly selected employee is a woman is "p",

The 120 employees are men and rest 80 are women,

We have,

⇒ p = (number of women)/(total number of employees),

⇒ p = (200 - 120)/200,

⇒ p = 0.4,

Let X = number of women among the 10 employees selected.

Then X follows a binomial distribution with parameters "n = 10" and "p = 0.4".

The probability of "at-least-4" selected employees are women is expressed as⇒ P(X ≥ 4) = 1 - P(X ≤ 3),

⇒ P(X ≤ 3) = [tex]\[ \sum_{k=0}^{3} \][/tex] C(10,k) × 0.4^k × 0.6^(10-k),

We can then subtract this value from 1 to obtain P(X ≥ 4),

⇒ P(X ≥ 4) = 1 - P(X ≤ 3),

⇒ P(X ≥ 4) ≈ 0.671

Therefore, the required probability is approximately 0.671.

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Answer: 43

43 x 0.7 = 30.1

Answer:

70 % is salty water and 30% IS DRINKING WATER in which 2.1% comes from glaciers

As we know consecutive angle of parallelogram are supplementary then the sum m∠JLM = 22°.

Let the m∠JLM be x.
Thus, x+56+27+75 = 189
x = 180 - 158
x = 22

Hence the angle m∠JLM would be 22°

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are supplementary to the transversal on the same side. 360 degrees is the total of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

The properties of a parallelogram are shared by the shapes of a square and a rectangle.

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Answer: the answer to the question is A.

The final equation of the line is   y = (-2/3)x - 3   in the coordinate system.

what is coordinate system?

A coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the position of a point or an object in space. In mathematics, the most common coordinate system is the Cartesian coordinate system

what is equation ?

In mathematics, an equation is a statement that shows the equality between two expressions. It contains an equals sign (=) between the two expressions that are being compared. Equations can be used to describe relationships between variables, to solve problems, or to represent real-world situations.

In the given question,

To draw the line going through (-6,1) with a slope of -2/3, we can follow these steps:

Plot the point (-6,1) on a coordinate system. This will be one point on the line.

From that point, use the slope to find another point on the line. A slope of -2/3 means that for every 3 units to the right we move, we must move 2 units down. So starting from (-6,1), we can move 3 units to the right and 2 units down to get to the point (-3,-1). This is another point on the line.

Draw a straight line through the two points to represent the line going through (-6,1) with a slope of -2/3.

To write the equation of the line, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1,y1) is one point on the line, m is the slope, and (x,y) are the coordinates of any other point on the line. Let's choose (-6,1) as our point:

y - 1 = (-2/3)(x - (-6))

Simplifying, we get:

y - 1 = (-2/3)x - 4

Adding 1 to both sides, we get the final equation of the line:

y = (-2/3)x - 3

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Answer:

x = 6

Step-by-step explanation:

4x - 2x= 2x

15-3= 12

2x=12

12/2=6

6=x

Answer:

x<6<6

Step-by-step explanation:

4+3<2+15.

4x+3−3< 2x+15−3

4<2+12

4x−2x<2x+12−2x4−2<2+12−2

2x<122<12

2x2<12222<122

x<6

Answer:

Step-by-step explanation: First, you need to convert the width of the mural from feet to meters.

1 meter = 3.28084 feet (approximately)

So, 1 foot is approximately 0.3048 meters.

13 feet x 0.3048 meters/foot = 3.9624 meters (rounded to four decimal places)

Therefore, the width of the mural on the scale drawing would be 3.9624 meters.

Next, you need to convert the height of the mural from feet to meters.

24 feet x 0.3048 meters/foot = 7.3152 meters (rounded to four decimal places)

Therefore, the height of the mural on the scale drawing would be 7.3152 meters.

So, the measurements of the mural on a scale drawing using the scale 3m: 2ft would be 3.9624 meters wide and 7.3152 meters tall.

Answer:

A) Red

Step-by-step explanation:

We can find the probability of the spinner landing on each color by dividing the number of sections for that color by the total number of sections.

Probability of landing on red: 3/6 = 1/2

Probability of landing on yellow: 1/6

Probability of landing on blue: 1/6

Probability of landing on purple: 1/6

The spinner is most likely to land on red because it has the highest probability, 1/2 or 50%. Therefore, the answer is A. Red.

A, red

It would frequently land on 3 because 3 takes up the bigger portion of the spinner

18:8, 27:12 and 45:20 are ratios are equivalent to 9:4.

A ratio is a mathematical comparison between two or more quantities that indicates how many times one quantity is contained within another. Ratios are expressed in the form of a fraction, with the first quantity being the numerator and the second quantity being the denominator.

three ratios that are equivalent to 9:4

All of these ratios are equivalent to 9:4, because they represent the same ratio of 9 parts to 4 parts.

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Varying 'a' in the equation og graph [tex]y = a(x-2)^2 + 5[/tex] changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).

A graph is a visual representation of data or information that displays a relationship or pattern between two or more variables.

The graph of [tex]y = a(x-2)^2 + 5[/tex] is a quadratic function that has been shifted 2 units to the right and 5 units up from the standard form of [tex]y = x^2.[/tex] The variable 'a' represents the vertical stretch or compression factor of the parabola.

In summary, varying 'a' in the equation [tex]y = a(x-2)^2 + 5[/tex] changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).

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