Which of the following describes the transformation from Figure 1 to Figure 2?

On a coordinate plane, figure 1 has points (negative 2, 5), (negative 2, 4), (negative 3, 4), (negative 3, 2), (negative 5, 2), (negative 5, 5). Figure 2 has points (2, negative 5), (2, negative 4), (3, negative 4), (3, negative 2), (5, negative 2), (5, negative 5).

Answer: x = 2, y = 0

Step-by-step explanation:

Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:

3x + y = 6

y + 2 = x

Substituting x for y + 2 gives us

3(y + 2) + y = 6

3y + 6 + y = 6

4y = 0

y = 0

Plugging y = 0 in for the second equation gives us

x = 0 + 2, or x = 2

Answer:

54°

Step-by-step explanation:

AB = BC = CD = AD (Because all sides of a rhombus are equal)

Let's consider the triangle DBC:

BC = DC => ∠DBC = 36°

The angle DCB is equal to:

180° - 36*2 = 180° - 72° = 108°

In a parallelogram, opposite angles are equal.

Then the angle DAB = DCB = 108°

Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.

So, the angle DAE = EAB = 108° / 2 = 54°

Answer:

going from left to right:

AA

BD

CB

DC

Answer:

60 - 10 = 50

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;

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;

;

Step-by-step explanation:

To find the range, we need to subtract the smallest value from the largest value in the dataset:

Range = Largest value - Smallest value

Range = 92 - 3

Range = 89

To find the variance and standard deviation, we need to calculate the mean first:

Mean = (Sum of all values) / (Number of values)

Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11

Mean = 45.09 (rounded to two decimal places)

Next, we need to calculate the variance:

Variance = (Sum of squared differences from the mean) / (Number of values - 1)

Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)

Variance = 1071.45 (rounded to two decimal places)

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = Square root of variance

Standard deviation = Square root of 1071.45

Standard deviation = 32.74 (rounded to two decimal places)

The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.

Answer:

6188 ways

Step-by-step explanation:

there ate 5 objects to be choosen and there is no replacement of the object therefore you got

17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection

totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188

note we used 5! cause there are 5 placed objects and 12! are unplaced objects

note

that you have used one so you have to deduct one every time you use one

The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.

Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.

The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.

Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.

The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:

6.8x + 4.2(35 - x) (35 - x)

When we simplify, we get:

6.8x + 147 - 4.2x

2.6x + 147

The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:

35(5.31) = 185.85

When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:

2.6x + 147 = 185.85

Subtractiοn οf 147 frοm bοth sides yields:

2.6x = 38.85

When we divide by 2.6, we get:

x ≈ 14.94

Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.

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With four decimal places added, we have P(2.04 Z 3.04) 0.0189.

To round a decimal value to two decimal places, use the hundredths place, which is the second place to the right of the decimal point.

Subtracting the area to the left of 1.25 from the area to the left of 2.15 will give us the standard normal area between 1.25 and 2.15.

The area to the left of 1.25 is 0.8944, and the area to the left of 2.15 is 0.9842, according to a conventional normal distribution table or calculator.

So, the standard normal area between 1.25 and 2.15 is:

P(1.25 < Z < 2.15) = 0.9842 - 0.8944 = 0.0898

Rounding to four decimal places, we get:

P(1.25 < Z < 2.15) ≈ 0.0898

We follow the same procedure as before to determine the standard normal region between 2.04 and 3.04:

P(2.04 < Z < 3.04) = P(Z < 3.04) - P(Z < 2.04)\

The area to the left of 2.04 is 0.9798, and the area to the left of 3.04 is 0.9987, according to a conventional normal distribution table or calculator.

So, the standard normal area between 2.04 and 3.04 is:

P(2.04 < Z < 3.04) = 0.9987 - 0.9798 = 0.0189

Rounding to four decimal places, we get:

P(2.04 < Z < 3.04) ≈ 0.0189

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The solution to the compound inequality -3+b> 7 OR b +9 <17 is given as follows:

b < 8 or b > 10.

The inequality for this problem is defined as follows:

-3+b> 7 OR b +9 <17.

The or operation means that the we must solve each operation separately, and then the solution set to the compound inequality is given by the union of the solution set of each of the inequalities.

The solution set for the first inequality is given as follows:

-3+b> 7

b > 10.

The solution set for the second inequality is given as follows:

b + 9 < 17

b < 8.

Hence the solution for the entire inequality is of:

b < 8 or b > 10.

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Answer:

19782m

Step-by-step explanation:

1  revolution = circumference

circumference = π * diameter

π = 3.1416

Then

circumference = 3.1416 * 63

= 197.92m

1 revolution = 197.82m

100 revolutions = 100*197.82m

= 19782m

Answer:

19.8 km

Step-by-step explanation:

To find:-

Answer:-

We are here given that,

We can first find the circumference of the wheel using the formula,

[tex]:\implies \sf C = 2\pi r \\[/tex]

Here radius will be 63/2 as radius is half of diameter. So on substituting the respective values, we have;

[tex]:\implies \sf C = 2\times \dfrac{22}{7}\times \dfrac{63}{2} \ m \\[/tex]

[tex]:\implies \sf C = 198\ m \\[/tex]

Now in one revolution , the cycle will cover a distance of 198m . So in 100 revolutions it will cover,

[tex]:\implies \sf Distance= 198(100)m\\[/tex]

[tex]:\implies \sf Distance = 19800 m \\[/tex]

[tex]:\implies \sf Distance = 19.8 \ km\\[/tex]

Hence the bicycle would cover 19.8 km in 100 revolutions.

Answer:

[tex]{ \sf{a = \frac{0.012}{0.633 -0.063 } }} \\ \\ { \sf{a = \frac{0.012}{0.57} }} \\ \\ { \sf{a = 0.021 \: (2 \: s.f)}}[/tex]

The required value of the function  (f + g)(x) for given f(x) and g(x) as ( 3 / √x )  - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

Function f(x) is equals to,

( 3 / √x )  - ( 2 / x³ ) for all x > 0

Function g(x) is equals to,

g(x) = √(5x - 7)

To get the value of (f + g)(x),

Substitute the value of f(x) and g(x) and  add the functions f(x) and g(x) together,

Sum of f(x) and g(x) is equals to,

(f + g)(x)

= f(x) + g(x)

= ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7)

Therefore, value of the function (f + g)(x) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

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The above question is incomplete, the complete question is:

The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).

The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.

Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.

The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.

Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:

CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees

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_____The given question is incomplete, the complete question is given below:

Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI

Answer:

invertible

Step-by-step explanation:

If A is invertible then ∣A∣ =0

Students were asked to simplify the expression using trigonometric identities:

 A.  student A is correct; student B was confused by the division

 B.  3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names.

Each student correctly made use of the trigonometric identities

cosec(θ) = 1/sin(θ)

1 -sin²(θ) = cos²(θ)

A.

Student A's work is correct.

Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.

The transition from Step 2 can look like:

[tex]\frac{(\frac{1-sin^2\theta}{sin\theta} )}{cosec\theta} =\frac{1-sin^2\theta}{sin\theta} .\frac{1}{cosec\theta} =\frac{cos^2\theta}{(sin\theta)(cosec\theta)}[/tex]

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Complete question:

Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)

Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)

Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)

Answer:

13/8

Step-by-step explanation:

You first find the lcm of 8 and 4 which is 8

Then make a dividing line (/) with the lcm as the numerator.

After which you start diviing the lcm by each denominator of the two terms, and then multiplying with their numerators:

8/8 x 7 + 8/4 x 3 all over the lcm which is 8

(1 x 7 + 2 x 3)/8

(7 + 6)/8

13/8

Answer:

To solve the quadratic equation 9×^2-15×-6=0, we can use the quadratic formula, which is given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = 9, b = -15, and c = -6, so we can substitute these values into the quadratic formula:

x = (-(-15) ± sqrt((-15)^2 - 4(9)(-6))) / 2(9)

Simplifying this expression gives:

x = (15 ± sqrt(225 + 216)) / 18

x = (15 ± sqrt(441)) / 18

x = (15 ± 21) / 18

So the two solutions to the quadratic equation are:

x = (15 + 21) / 18 = 2

x = (15 - 21) / 18 = -1/3

Therefore, the solutions to the quadratic equation 9×^2-15×-6=0 are x = 2 and x = -1/3.

The probability of obtaining a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.

Probability is the branch of mathematics concerned with the occurrence of a random event, and there are four types of probability: classical, empirical, subjective, and axiomatic.

The readings at freezing on a set of thermometers are normally distributed, with a mean () of 0°C and a standard deviation () of 1.00°C. We want to know how likely it is that we will get a reading between -0.08°C and 1.68°C.

To solve this problem, we must use the z-score formula to standardise the values:

z = (x - μ) / σ

where x is the value for which we want to calculate the probability, is the mean, and is the standard deviation.

The lower bound is -0.08°C:

z1 = (-0.08 - 0) / 1.00 = -0.08

1.68°C is the upper bound:

z2 = (1.68 - 0) / 1.00 = 1.68

We can now use a standard normal distribution table or calculator to calculate the probabilities for each z-score.

The probability of obtaining a z-score of -0.08 or less is 0.4681, and the probability of obtaining a z-score of 1.68 or less is 0.9535, according to the table. We subtract the probability associated with the lower bound from the probability associated with the upper bound to find the probability of obtaining a reading between -0.08°C and 1.68°C:

P(-0.08°C x 1.68°C) = P(z1 z z2) = P(z 1.68) minus P(z -0.08) = 0.9535 - 0.4681 = 0.4854

As a result, the chance of getting a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.

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Random sampling is crucial when surveying as it ensures that the sample selected is representative of the population.

By randomly selecting participants from the population, the sample is likely to be unbiased on average, which means that the results of the study can be generalized to the entire population. Without random sampling, the results of the study may be skewed or biased towards a certain group, which can lead to incorrect conclusions and poor decision-making. Therefore, it is essential to use random sampling when surveying to obtain accurate and reliable results.

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The total amount of money Carol originally invested is £22,000 in the bank account.

Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.

This results in exponential growth or accumulation of interest over time.

Let X be the amount that Carol originally invested in the account.

After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).

After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.

After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).

We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:

(X(1.025) - £1000)(1.025) = £23,517.60

Expanding the left-hand side and simplifying, we get:

X(1.025)² - £1000(1.025) = £23,517.60

X(1.025)² = £24,567.63

Dividing both sides by (1.025)², we get:

X = £22,000 (rounded to the nearest pound)

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The complete question is -

On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?

By answering the presented questiοn, we may cοnclude that Since a line equatiοn parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.

When twο expressiοns are equal, a mathematical equatiοn is a statement stating that equality. Twο sides are jοined by the algebraic symbοl (=), and tοgether they make up an equatiοn. Fοr instance, the claim that "2x + 3 = 9" means that "2x plus 3" equals the number "9" is made in this argument. Finding the value(s) οf the variable(s) necessary fοr the equatiοn tο be true is the gοal οf sοlving equatiοns.

There are variοus types οf equatiοns, including regular and nοnlinear οnes with οne οr mοre elements. "x² + 2x - 3 = 0" is an equatiοn that raises the variable x tο the secοnd pοwer. Mathematical disciplines like algebra, calculus, and geοmetry all make use οf lines.

the given equatiοn:

[tex]$\begin{array}{c}{{5x-6y=30}}\\ {{-6y=-5x+30}}\\ {{y=(5/6)x-5}}\end{array}$[/tex]

Sο the slοpe οf the given line is 5/6.

Since a line parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.

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For the equations 2xy - y^2 = 1 and xy + x + y = x^2y^2 using implicit differentiation the value Dxy is given by Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3  respectively.

Equation 2xy - y^2 = 1,

Differentiate both sides of the equation with respect to x,

Treating y as function of x and then differentiate again with respect to x.

Using implicit differentiation,

First, differentiate both sides with respect to x,

2y + 2xy' - 2yy' = 0

Next, solve for y',

⇒2xy' - 2yy' = -2y

⇒y' (2x - 2y) = -2y

⇒y' = -y/(x - y)

Now, differentiate again with respect to x,

y''(x - y) - y'(2x - 2y) = y/(x - y)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - y) - (-y/(x - y))(2x - 2y) = y/(x - y)^2

Simplify and solve for y'',

y''(x - y) + (2xy - 3y^2)/(x - y)^2 = 1/(x - y)^2

The expression for Dxy is,

Dxy = (1 - 2xy + 3y^2)/(x - y)^3

For the equation xy + x + y = x^2y^2,

Differentiate both sides of the equation with respect to x,

Using implicit differentiation,

First, differentiate both sides with respect to x,

⇒y + xy' + 1 + y' = 2xyy'

Solve for y',

⇒xy' - 2xyy' + y' = -y - 1

⇒y' (x - 2xy + 1) = -y - 1

⇒y' = -(y + 1)/(x - 2xy + 1)

Now, differentiate again with respect to x,

y''(x - 2xy + 1) - y'(2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - 2xy + 1) - (-y - 1)/(x - 2xy + 1)^2 (2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Simplify and solve for y''

y''(x - 2xy + 1) - (2y^2 - 2xy - 2y)/(x - 2xy + 1)^2 = (y + 1)/(x - 2xy + 1)^2

The expression for Dxy is,

Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

Therefore , the value of Dxy using implicit differentiation for two different functions is equal to

Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

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x = 4.9

Solution:

We can use the intersecting chords formula:

[tex]7\times7 = 10x[/tex]

[tex]49 = 10x[/tex]

[tex]49\div10=10x\div10[/tex]

[tex]4.9 = x[/tex]

Therefore, x = 4.9.

Therefore , the solution of the given problem of unitary method comes out to be  the attraction sold 943 child tickets and 736 adult tickets on that particular day.

It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.

Here,

Assume the attraction sold x tickets for adults and y tickets for kids.

Based on the supplied data, we can construct the following two equations:

=>  x + y = 1679 (equation 1, representing the total number of tickets sold)

=>  35x + 20y = 44620 (equation 2, representing the total revenue generated)

Using the elimination technique, we can find the values of x and y.

When we divide equation 1 by 20, we obtain:

=>  20x + 20y = 33580 (equation 3)

Equation 3 is obtained by subtracting equation 2 to yield:

=>  15x = 11040

=>  x = 736

When we enter x = 736 into equation 1, we obtain:

=>  736 + y = 1679

=> y = 943

As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.

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The perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.

The whole distance encircling a form is referred to as its perimeter. It is the length of any two-dimensional geometric shape's border or outline. Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance. If all the sides are the same length, the same wire can be used to create a square.

The perimeter of a figure is the sum of all the segments of the figure.

The perimeter of triangle is:

P = 2x - 5 + x + x + 3 = 4x - 2

The perimeter of rectangle is:

P = 2(l + b)

P = 2(3x + 1 + x - 5)

P = 2(4x - 4)

P = 8x - 8

The perimeter of square is:

P = 4(s)

P = 4(3x - 2y)

P= 12x - 8y

Hence, the perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.

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Answer:

Relating SSE to Other Statistical Data



Step-by-step explanation:

So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered

Answer:

Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.

Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.

Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.

Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.

Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.

Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

m = 0

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,2) (1,2)

We see the y stay the same and the x increase by 1, so the slope is

m = 0/1 = 0

So, the slope is 0