The table of values represents a linear function.
X Y
-2. 1
0. -9
2. -19
4. -29
6. -39
Complete the equation below to represent the function defined by the table in the form
y = mx + b.

The slope of the line is -1/4, So correct option is B.

It is defined as the ratio of the change in the vertical coordinate (y) to the change in the horizontal coordinate (x) between any two points on the line or curve. The letter m is typically used to indicate a line's slope.

The formula for the slope of a line between two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

The slope can be positive, negative or zero, depending on the direction of the line. A positive slope indicates that the line is moving upwards from left to right, while a negative slope indicates that the line is moving downwards from left to right. A slope of zero indicates that the line is horizontal.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1)/(x2 - x1)

Using the coordinates (-4, 2) and (4, 0), we have:

slope = (0 - 2)/(4 - (-4)) = -2/8 = -1/4

Therefore, the answer is option B, -1/4.

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Answer: 9/56

Step-by-step explanation:

Yes, the table represents the proportional relationship.

The proportional relationship between the variables {x} and {y} is such that -

y/x = K {constant}

y = Kx

y₁/x₁ = y₂/x₂ = k  

A proportional relationship is represented by a straight line {where K is the slope}. It is concluded from the fact that the equation of the straight line passing through origin is of the form y = mx.

Given is a table as shown in the image.

For a direct or proportional  variation -

y₁/x₁ = y₂/x₂ = k                                                {k is constant parameter}

1/2 = 2/4 = k {constant}

1/2 = 1/2 = k {constant}

Therefore, yes, the table represents the proportional relationship.

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The graph of a piecewise-defined function y=c is a horizontal line reaching height c from the x-axis.

A piecewise function is arithmetic that is constructed from bits of various functions across various time intervals.

To determine which of the above intervals (as well as inequalities) -

Keep in mind that the function is represented by the line y=1 and is from -∞ to 0, or the left side.

Similar to that, the function is y=-1 from 0 to ∞ (doesn't include) .

Hence, the rule provides the function:

y=1, for x≤0,

y=-1, for x>0.

Thus, the graph of a function y=c is a horizontal line reaching height c from the x-axis.

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The complete question is-

The graph of a piecewise-defined function is shown below.

Check the correct option-

On the interval (x≤0, x≤1, x<1, x<0) the function is given by the rule (x= - 1, y= - 1, y=1, x=1), and on the interval (x≥0, x>1, x≥1, x>0) the function is given by the rule (y= - 1, x= - 1, y= 1, x= 1).

The weight 69.9 kg is equal to approximately 154.32 pounds. This conversion was done using the formula 69.9 kg x 2.20462 lbs/kg = 154.32478 lbs.

We know that 1 kg is equivalent to 2.20462 pounds, which means that we can convert kilograms to pounds by multiplying the weight in kilograms by the conversion factor 2.20462.

So to convert 69.9 kg to pounds, we can use the following formula:

69.9 kg x 2.20462 lbs/kg = ? lbs

Multiplying 69.9 by 2.20462 gives us:

69.9 x 2.20462 = 154.32478

Therefore, 69.9 kg is equivalent to 154.32478 pounds.

Finally, we can round this result to two decimal places to get:

69.9 kg is approximately equal to 154.32 pounds.

So the final answer is that 69.9 kg is equivalent to approximately 154.32 lbs.

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The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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The boys will have same the height after 48 months.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, two boys are increasing with the rate of 1/4 and 1/2 of an inch every month, they have height 60 in and 48 in, will need to find that when will they have equal height,

The height increased in x month of them is given by,

x/4 + 60 or x/2 + 48

Let they have equal height after y months,

y/4 + 60 = y/2 + 48

y/4 = 12

y = 48

Hence, the boys will have same the height after 48 months.

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This is not a random sample of the restaurant's customers.

The offer of a coupon in exchange for completing a brief survey about favorite desserts may bias the sample and result in a non-random sample of the restaurant's customers.

Only those customers who were interested in the coupon may have participated in the survey, which may not be representative of the overall customer population. Additionally, those who chose to participate may have different tastes and preferences compared to those who did not participate.

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Answer:

Step-by-step explanation:

The area of a round pizza with a 17 inch diameter is:

A = πr^2 = π(8.5)^2 ≈ 226.98 square inches

To find the length of the sides of a triangle with the same area, we can use the formula for the area of a triangle:

A = (1/2)bh

where b is the base of the triangle and h is the height.

Since the triangle is equilateral (i.e., all sides are equal), the base and height are the same. Let's call this length x. Then:

A = (1/2)bh = (1/2)x(x/2) = x^2/4

Setting this equal to the area of the round pizza, we get:

x^2/4 = 226.98

Multiplying both sides by 4, we get:

x^2 = 907.92

Taking the square root of both sides, we get:

x ≈ 30.13

So the sides of the equilateral triangle should be about 30.13 inches long to have the same area as a round pizza with a 17 inch diameter. Rounded to the nearest inch, the sides of the triangle should be 30 inches long.

The speed of the river is given as follows:

4 kilometers per hour.

The lowest speed that can be assumed by the boat is given as follows:

8 - r.

In which r is the speed of the river.

The lowest velocity is of 4 kilometers per hour, hence the speed of the river is obtained as follows:

8 - r = 4

r = 8 - 4

r = 4 kilometers per hour.

Then the maximum velocity is of:

8 + 4 = 12 kilometers per hour.

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Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

Answer:

90, 90, 90, 90

Step-by-step explanation:

This is because a squares angles are ALWAYS 90

Answer: All 90 degrees

Step-by-step explanation:

The number of unit cubes whose dimensions are 3/5 inch fill up the rectangular prism is (125/27)abc.

The total volume, in cubic inches, is represented in the diagram n cubic inches.

A cube is a three-dimensional object who has six faces.

Since each side of the unit cube has a length of 1 inch, the number of unit cubes that fill up the rectangular prism is equal to its volume in cubic inches. If the rectangular prism has dimensions a x b x c inches, then its volume is V = abc cubic inches.

Now, we need to find how many unit cubes whose dimensions are 3/5 inch fill up the rectangular prism. First convert the dimensions of the unit cube and the rectangular prism to a common unit, such as inches. Since 1 inch = 5/3 unit cubes, each side of the unit cube has a length (3/5) inch. Therefore, each side of the rectangular prism has dimensions (5a/3) x (5b/3) x (5c/3) unit cubes.

To find the number of unit cubes that fill up the rectangular prism, we can divide its volume (abc cubic inches) by the volume of each unit cube, which is (3/5)³ cubic inches. Thus, the number of unit cubes whose dimensions are 3/5 inch that fills up the rectangular prism is:

(abc) / [(3/5)³] = (125/27)abc

To find the total volume represented in the diagram, we need to add up the volumes of all the unit cubes shown in the diagram. Since we don't know the dimensions of the rectangular prism, we can't calculate its volume directly.

Therefore, the total volume represented in the diagram is n cubic inches.

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44 °F was found out to be equivalent to approximately 6.67 °C using conversion formula of Fahrenheit to Celsius.

To convert a temperature from Fahrenheit to Celsius, you can use the following formula:

°C = (°F - 32) x 5/9

where °C is the temperature in Celsius, and °F is the temperature in Fahrenheit.

Using this formula, we can convert 44 °F to Celsius as follows:

°C = (44 - 32) x 5/9

= 12 x 5/9

= 6.67 °C (rounded to two decimal places)

Therefore, 44 °F is equivalent to approximately 6.67 °C.

On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.

On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.

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The value of x in the triangle is 10 units

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

The triangle

On the triangle, we have the following equivalent ratio

x : 15 = 4 : 6

Express as fraction

So, we have

x/15 = 4/6

This gives

x = 15 * 4/6

Evaluate

x = 10

Hence, the value of x is 10

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The point (- 1, 2) lies on the new graph.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The graph of f(x) = |x| has been translated left 2 units and up 1 unit.

Now, The function is,

⇒ f (x) = |x|

After translated 2 unit left we get;

⇒ f (x) = |x + 2|

And, After translated 1 unit down we get;

⇒ f (x) = |x + 2| + 1

Now, We can check all the given points as;

For point (- 1, 2);

Put x = -1 , f (x) = 2;

⇒ f (x) = |x + 2| + 1

⇒ 2 = |- 1 + 2| + 1

⇒ 2 = 1 + 1

⇒ 2 = 2

Thus, The point (- 1, 2) lies on the new graph.

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The quadrilateral with diagonals that are always perpendicular bisectors of each other is a square. Correct option is 1.

In a square, the diagonals bisect each other at right angles, which means they intersect at a 90-degree angle. Moreover, since a square has four congruent sides and four right angles, the diagonals are also congruent. Thus, each diagonal is a perpendicular bisector of the other diagonal, splitting it into two equal segments.

In contrast, a rectangle has diagonals that bisect each other, but they are not always perpendicular. A trapezoid has only one pair of opposite sides that are parallel, and its diagonals do not bisect each other.

A parallelogram has opposite sides that are parallel, but its diagonals do not necessarily bisect each other or intersect at a right angle.

Therefore, the correct answer is a 1 (square).

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An exponential function of the form y = 20aˣ can be 20 at the y-intercept

when a = 1.

An exponential function in which the independent variable is the exponent.

An exponential function can be written in the form as, y = aˣ, where a is a constant and 'x' is the variable.

We know, the y-intercept is when the value of x = 0.

Therefore, An exponential function of the form y = 20aˣ can be 20 at y-intercept when a = 1.

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Hence, combine all the solutions we get,

[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].

Trigonometric identities are equalities which involves trigonometric functions which are true for every value of variables that occur on both sides of the identities.

Given,[tex]3\sin \left(2x\right) = 2\cos \left(x\right)[/tex]

[tex]3\sin \left(2x\right)-2\cos \left(x\right)=0[/tex]

Using trigonometric identities, [tex]sin2x= 2sinx cosx[/tex]

we get,[tex]-2\cos \left(x\right)+6\cos \left(x\right)\sin \left(x\right)=0[/tex]

Taking [tex]2cos(x)[/tex] as factor, we get,

⇒[tex]2cos(x)(3sin(x) -1)[/tex]

⇒[tex]2cos(x) = 0 , (3sin(x) -1)=0[/tex]

⇒[tex]cos (x)= 0[/tex] for x= [tex]x=\frac{\pi}{2} +2n\pi,\frac{3\pi}{2} +2\pi n[/tex] and

[tex](3sin(x) -1)=0 for x= sin^{-1} (\frac{1}{3} )+ 2\pi n , sin^{-1 }(\frac{1}{3})+2\pi n[/tex]

Hence, combine all the solutions we get,

[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].

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The required values are;

(2). x = 88°

(3). x = 5.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:

(2). The exterior angle is 52°.

So, the sum of all the interior angles in the polygon = (5 - 2)180

x + (180 - 52) + 2x + x + 2 + 90 = 560

4x + 208 = 560

4x = 352

x = 88

(3). From the diagram of the triangle,

12x - 20 = 2 (3x + 5)

12 x - 6x = 10 + 20

6x = 30

x = 5

Therefore, the values are x = 88 and x = 5.

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The linear equation is f(x) = 2^2 + x, while the other two functions are nonlinear functions

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

The three equations

A linear equation is any equation that has a degree of 1

From the three equations, we can see that

Degree = 1

Degree = 2

Degree = 3

Hence, the linear function is f(x) = 2^2 + x

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Answer:

50.24

Step-by-step explanation:

c=[tex]2\pi R[/tex]=[tex]d\pi[/tex]=16*3.14=50.24

The wavelength will be "0.125 m".

The wavelength, as well as frequency, have an inverse relationship. It shows  that whenever a short wavelength exists, a high frequency exists, and when a big wavelength exists, a lower frequency exists.

The distance of a single wave-particle travels after completing one oscillation would be its wavelength.

According to the given information,

Speed of transverse, s = 25 m/s

Frequency, f = 200 Hz

We know the formula,

→ Wavelength, λ = velocity/ frequency

By substituting the values, we ger

λ = 25/200

 λ = 0.125

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Answer:

2,735 yes votes

Step-by-step explanation:

First we have too determine the ratio of yes votes to the total number of votes.

We can rationalize thus

If there are 5 yes votes and 4 no votes, the total number of votes = 5+ 4 = 9

So 5/9th of the total votes are yes votes

If the total number of votes = 4923 , number of yes votes = 5/9 x 4923

= 2,735 yes votes       ANSWER

We can check to see if our reasoning is correct:

Total number of no votes = 4923 - 2735 = 2188

Yes votes to Nay votes = 2735 : 2188

As a fraction:
2735 / 2188 = 1.25

1.25 = 1 1/4 = 5/4 which is the ratio of yes to no votes and tallies with the question data

Answer:

Axis of Symmetry is 3 or x=5

vertex is (3,5)

Step-by-step explanation:

the vertex is either the highest or the lowest point on a quadratic function's graph, here (3,5) is the highest point, therefore it is the vertex.

Axis of symmetry is usually always the x value of the vertex, that is that in (3,5). 3 is the axis of symmetry. This is because along the line x=5 the graph shows perfect symmetry

please do say thanks.

The length of MK is given as follows:

MK = 36.

Similar triangles are triangles that share these two features presented as follows:

The similar triangles for this problem are given as follows:

MNO and MKL.

Hence the proportional relationship for the side lengths is given as follows:

15/MK = 20/48

Applying cross multiplication, the length MK is given as follows:

20MK = 15 x 48

MK = 15 x 48/20

MK = 36.

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Answer:

it is 60

Step-by-step explanation:

you add all the numbers than you round it, the number is 0 so it stays the same, hope it helps, murdle

The inequality that  this situation, where s is the number of shirts she can buy is S>81.5.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

We are given that;

Budget of lelah for clothes= $135

For shoes= $35.25

For shirts= $18.25

Now,

S+$18.25+35.25>135

S>135-18.25-35.25

S>135-53.5

S>81.5

Therefore, the inequality will be S>81.5.

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Andrea has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 8 mph and walks back at a speed of 2 mph, she will spend 72 minutes walking back.

This is referred to as the measured period during which an action, process, or condition exists or continues .

'x' rill represent the amount of time spent running in hours, then 3-x represents the time spent walking in hours.

Distance = Speed × time

Distance = 8x

Speed = 2mph

Time = (6-x)hours

Substitute the values

8x = 2 (6-x)

8x = 12 - 2x

10x = 12

x = 12/10 = 6/5

6/5 × 60 = 72minutes.

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