Match the formula with the solid

According to the information we can infer that the single transformation that maps triangle A onto triangle B is a reflection.

To determine the transformation that maps triangle A onto triangle B, we can observe the changes in the coordinates.

We can see that the x-coordinates remain the same for all three vertices, indicating that there is no horizontal shift or change in position along the x-axis.

However, there is a vertical shift or translation between the two triangles. The y-coordinates of triangle B are greater than the y-coordinates of triangle A.

By comparing the y-coordinates, we can determine that triangle B is obtained by moving triangle A 5 units in the positive y-direction.

So, the single transformation that maps triangle A onto triangle B is a translation of 5 units in the positive y-direction. Additionally, according to the image, we can infer that is reflection.

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Answer:

1) 2 should be added with 12 only and not with 6x as 6x and 2 are not like terms.

2) When adding polynomials, You should add only like terms.

Step-by-step explanation:

The steps done are:

Step 1: y-2=6x+12

Step 2: Add 2 on both sides

y-2+2=6x+12+2

Answer : y=8x+14

1) What mistake did I made?

You made a mistake in step 2,

When adding polynomials, you add only like terms. i.e

y-2+2=6x+12+2

y=6x+14

2 should be added with 12 only and not with 6x as 6x and 2 are not like terms.

2) Suggestion to avoid Such mistake in the future.

When adding polynomials, You should add only like terms.

Like terms are those that have same degree of variables i,e

2x and 3x, 2x^2 and 3x^2, 2 and 3 they all are like terms.

You can add 2x and 3x but can't add 2x and 2x^2 as they are not like terms.

So, while solving polynomials always add like terms.

Answer:

If AR = 26, find AD = 13

If BD = 9, find BQ = 18

If MQ = 35, find LQ = 17.5

If LP = 13.25, find NP = 26.50

Step-by-step explanation:

For the first question which is finding AD, is basically half the line of AR. So it's half of AR.

26 ÷ 2 = 13

For the second question which is finding BQ, the line is just 2x the line of BD. So it's 2 times of BD.

9 x 2 = 18

For the third question which is finding LQ, it's half the line of MQ. So it's half of MQ.

35 ÷ 2 = 17.5

For the fourth question which is finding NP, it's 2 times of LP. So it's 2 times of LP.

13.25 x 2 = 26.50

To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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In rounding a number to nearest multiple of 10, look at the digit to the right of the number to be rounded:

402053 rounded to the nearest thousand

　　　　‎‎\( \tt 3 \: - Ones \\ \tt 5 \: - Tens \\ \tt 0 \: - Hundreds \\ \tt 2\: - Thousands \\ \tt 0 \: - Ten \: Thousands \\ \tt 4 \: - Hundred \: Thousands\)

Since, 2 is on hundreds place look at the right digit to be rounded. So, 0 si on right digit let's round off from 2 let's keep it 2 then replace the other digits of zero.

Therefore, 402053 is now 402000

When rounded to the nearest thousand, the number 402053 becomes 400000.

Rounding a number to the nearest thousand means finding the closest multiple of 1000 to the given number. Let's work with the number 402053 and round it to the nearest thousand.

First, let's look at the digit in the thousands place, which is the digit in the "hundreds of thousands" position. In 402053, this digit is 4.

Next, look at the digit immediately to the right of the thousands place, which is the hundreds place. In 402053, this digit is 0.

Since the hundreds place is 0, we don't need to round up. So, the nearest thousand to 402053 is simply 400000.

Therefore, when rounded to the nearest thousand, the number 402053 becomes 400000.

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Answer:

Step-by-step explanation:

S and T are supplementary angles

Answer:

could you take a screen shot and link the graph pls?

Step-by-step explanation:

Answer:

Hmmmm...I believe the answer is letter D.

Answer:

Step-by-step explanation:

y = x/4 - 12

x = y/4 - 12

y/4 - 12 =x

y/4 = x + 12

y = 4x + 48

h(x) = 4x + 48

y = 3x - 122

x = 3y - 122

3y - 122 = x

3y = x + 122

y = x/3 + 122/3

f^-1(x) = x/3 + 122/3

Answer:

y=f(x+9)-5

Step-by-step explanation:

to move the graph 9 units to the left, you would need to add 9 to the variable (which is x) - so that transformation for y=f(x) would look like this:

y=f(x+9)

then, to move the graph 5 units down, you would need to subtract 5 from f(x), so the transformation for y=f(x) that moves the graph 5 units down would be:  

y=f(x)-5

now, you would put that all together and it would look like this:

y = f (x+9) -5

i hope this helps.

The probability distribution of the number of cards dealt that are either face cards or aces can be shown as  P(X = 7) = C(4, 7) * C(48, 0).

To find the probability distribution of the number of cards dealt that are either face cards or aces, we can calculate the probability for each possible outcome (0, 1, 2, 3, 4, 5, 6, 7) and construct a probability distribution table.

Let's denote the number of face cards or aces dealt as X.

To calculate the probability distribution, we need to determine the total number of possible outcomes (combinations) and the number of favorable outcomes (combinations with face cards or aces).

Total number of possible outcomes:

Since there are 52 cards in a standard deck, the total number of possible outcomes is given by the binomial coefficient (52 choose 7), which is calculated as:

C(52, 7) = 52! / (7! * (52-7)!) ≈ 133,784,560

Number of favorable outcomes:

We need to consider that there are 4 face cards (Jack, Queen, King, and Ace) in each suit, and 4 aces (one for each suit).

Now, let's calculate the probabilities for each possible outcome:

P(X = 0) - Probability of not getting any face cards or aces:

Number of favorable outcomes: C(48, 7)

Probability: P(X = 0) = C(48, 7) / C(52, 7)

P(X = 1) - Probability of getting exactly 1 face card or ace:

Number of favorable outcomes: 4 * C(48, 6)

Probability: P(X = 1) = 4 * C(48, 6) / C(52, 7)

P(X = 2) - Probability of getting exactly 2 face cards or aces:

Number of favorable outcomes: C(4, 2) * C(48, 5)

Probability: P(X = 2) = C(4, 2) * C(48, 5) / C(52, 7)

P(X = 3) - Probability of getting exactly 3 face cards or aces:

Number of favorable outcomes: C(4, 3) * C(48, 4)

Probability: P(X = 3) = C(4, 3) * C(48, 4) / C(52, 7)

P(X = 4) - Probability of getting exactly 4 face cards or aces:

Number of favorable outcomes: C(4, 4) * C(48, 3)

Probability: P(X = 4) = C(4, 4) * C(48, 3) / C(52, 7)

P(X = 5) - Probability of getting exactly 5 face cards or aces:

Number of favorable outcomes: C(4, 5) * C(48, 2)

Probability: P(X = 5) = C(4, 5) * C(48, 2) / C(52, 7)

P(X = 6) - Probability of getting exactly 6 face cards or aces:

Number of favorable outcomes: C(4, 6) * C(48, 1)

Probability: P(X = 6) = C(4, 6) * C(48, 1) / C(52, 7)

P(X = 7) - Probability of getting all 7 face cards or aces:

Number of favorable outcomes: C(4, 7) * C(48, 0)

Probability: P(X = 7) = C(4, 7) * C(48, 0)

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A distance-time graph below shows a car travelling then the Speed of the car is 8.88 miles per hour

Speed is the time rate at which an object is moving along a path,

A distance-time graph below shows a car travelling

We know that speed is distance by time

From the graph the distance is 80 and time is 9

Speed= 80/9

=8.88 miles per hour

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Answer:

r=7

Step-by-step explanation:

Using the formula

d=2r

Solving for r

r=d/ 2=14/ 2=7

Hope this helped!!!

Answer:

0.4

Step-by-step explanation:

1.6 - 1.2 = 0.4

As shown in the graph above, the point G is in the interior of the right angled triangle. Angle ABG measures (x^2 + 3x) while angle CBG measures 40x.

Angles ABG and CBG add up to 90 and that gives you;

Knowing that we are dealing with a positive angle measure, we shall take x = 2 (and not x = -45)

Therefore, x = 2, and angle ABG measures

Also angle CBG measures;

Answer:

the population variance is 2 and the population standard deviation is approximately 1.41.

Step-by-step explanation:

To calculate the variance and standard deviation of a population, you can use the following formulas:

Population variance = (Σ(x - μ)²) / N

Population standard deviation = √(Σ(x - μ)² / N)

Where:

Σ is the sum of

x is each individual score in the population

μ is the population mean

N is the number of scores in the population

To begin, we need to find the population mean (μ):

μ = (6 + 2 + 3 + 0 + 4) / 5 = 3

Next, we can calculate the variance:

Population variance = ((6-3)² + (2-3)² + (3-3)² + (0-3)² + (4-3)²) / 5

Population variance = (9 + 1 + 0 + 9 + 1) / 5

Population variance = 2

Finally, we can calculate the standard deviation:

Population standard deviation = √((6-3)² + (2-3)² + (3-3)² + (0-3)² + (4-3)²) / 5

Population standard deviation = √(9 + 1 + 0 + 9 + 1) / 5

Population standard deviation = √2

Therefore, the population variance is 2 and the population standard deviation is approximately 1.41.

The variance of the given set of scores is 4 and the standard deviation is 2. Both are measures of how spread out the data is in statistics. The variance is calculated by acquiring the average squared deviation from the mean, while the standard deviation is the square root of the variance.

This is a question about the notions of variance and standard deviation in statistics. Variance is a measure of how spread out the numbers in a data set are. Standard deviation, on the other hand, is the square root of the variance, indicating the amount of deviation (or variation) you can expect in your data.

Here are the steps for calculating variance and standard deviation for given set of scores: 6, 2, 3, 0, 4

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The height of the building is approximately 62.4369 feet. The solution involves using trigonometry and solving for the opposite side of the triangle using the tangent function.

Let h be the height of the building, and x be the distance between the first point and the base of the building. Then we have:

tan(26.8°) = h/x ----(1)

tan(19.5°) = h/(x + 43.9) ----(2)

From equation (1), we have x = h/tan(26.8°)

Substituting this value of x in equation (2) and solving for h, we get:

h = (43.9 tan(19.5°) tan(26.8°))/(tan(26.8°) - tan(19.5°))

Plugging in the values, we get:

h ≈ 62.4369 feet

Therefore, the height of the building is approximately 62.4369 feet.

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Answer:

\(\frac{y-b}{x}\)=m

Step-by-step explanation:

y=mx+b

-b          -b

y-b=mx

\(\frac{y-b}{x}\)     =  \(\frac{mx}{x}\)

\(\frac{y-b}{x}\)=m

Answer:

25 students in each bus, 16 students in each van

Step-by-step explanation:

x = vans

y = buses

\(3x + 10y = 298\\\\12x + 7y = 367\)

Multiply the top equation by -4 to turn 3x into -12x

\(-12x - 40y = -1192\\12x + 7y = 367\)

Cancel out -12x and 12x

\(-40y = -1192\\7y = 367\)

Add the terms together

\(-33y = -825\\y = 25\)

We know that 25 students can fit in each bus

\(3x + 10(25) = 298\\3x + 250 = 298\\3x = 48\\x = 16\)

16 students can fit in each van

The total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

1 mass of a paperclip = 8.0 × 10−4 mg

But there are 7.68 × 104 paperclips = x mg

cross multiply

x = 7.68 × 104 × 8.0 × 10−4 mg

Multiply through

x = 61. 44 × 10^ 4 -4

x = 61. 44 × 1

x = 6. 144 × 10^1 mg

Thus, the total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

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Answer: 1,800

Step-by-step explanation: At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert was 360, what was the total number of audience members? x = ? If you divide 360 by 20% it will give you 1,800 audience members.

Answer:

Mean = 125.136

Median = 110

Mode = 180

Step-by-step explanation:

Given the data:

75 95 180 136 89 75 110 180 100 136 180 95 180 136 75 100 110 180 180 136 75 90

Frequency distribution:

Value(X) ___freq (F) ____cumm frequency

85 _________ 4 _______ 4

89 _________ 1 _______5

90 __________1 _______6

95 __________2 ______ 8

100 _________ 2 ______10

110 __________2______ 12

136 __________4 _____ 16

180 __________6______22

2) Using the frequency distribution :

Mean = Σfx / Σf

[(85*4) + (89*1) + (90*1) + (95*2) + (100*2) + (110*2) + (136*4) + (180*6)]/ 10

= 2753 / 22

= $125.136

Median of grouped data :

Frequency + 1 / 2 = 23/2 = 11.5 th term

The median value = $110

Mode of the data:

Most frequently occurring = 180 (frequency of 6)

The mean of the frequency distribution is $125.136, the median of the frequency distribution is $110, and the mode of the frequency distribution is $180.

Given :

a) The frequency distribution is given below:

Prices              Frequency       Cumulative Frequency

85                           4                                 4

89                            1                                 5

90                            1                                  6

95                            2                                  8

100                           2                                 10

110                            2                                  12

136                            4                                 16

180                            6                                 22

b) The mean is calculated as:

\(\rm Mean = \dfrac{85\times4 + 89\times1 +90\times1 +95\times 2+100\times2 +110\times2 +136\times4 +180\times6 }{10}\)

Simplify the above expression.

Mean = $125.136

c) The median of the frequency distribution is calculated as:

\(\rm Term= Frequency + \dfrac{1}{2}=11.5\)

So, the median is $110.

The mode of the frequency distribution is $180.

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Answer: 1.704 x 10^9

Step-by-step explanation: Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

angle ABC is parallel to angle DEF

Step-by-step explanation:

...

The planes DEF and ABC are parallel planes. Then the correct option is C.

When the distance between the planes is constant then the planes are called parallel planes. The lines do not intersect when they are separated from each other. And the slope of the planes is equal.

A closed solid with two parallel triangle bases joined by a rectangle surface is known as a triangular prism.

The triangle prism is shown below.

The slope of plane ABC and the slope of plane DEF are congruent.

From the figure, the planes DEF and ABC are parallel planes. Then the correct option is C.

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Graphing the function is the process of drawing the graph ( curve ) of the corresponding function.

Given :

Graph of a function :

Graphing functions is drawing the curve that represents the function on the coordinate plane.

If a curve ( graph ) represents a function, then every point on the curve satisfies the function equation.

Example :

f ( x ) = -x + 2

take x = 0

y = -0 + 2

y = 2

( x , y ) = ( 0 , 2 )

take x = 2

y = -2 + 2

y = 0

( x , y ) = ( 2 , 0 )

Graph is in the image uploaded.

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The gradient of a function is a vector that points in the direction of the greatest rate of change of the function. The differential of a function is a linear approximation of the function near a point. The gradients and differentials of the three functions are as follows:

fi: (x, y) → x cos(y) defined on R²

Gradient: (cos(y), x sin(y))

Differential: dx * cos(y) + dy * x sin(y)

f2: (x, y, z) → 1 + x + xy + xyz defined on R³

Gradient: (1 + y, x + z, xy)

Differential: dx + dy + (x + z) * dx + xy * dy

f3: (x, y, z) → ² defined on {(x, y, z) € R³ | z ‡ 0}

Gradient: (0, 0, 2z)

Differential: 0 * dx + 0 * dy + 2z * dz

The gradient of a function is a vector that points in the direction of the greatest rate of change of the function. The differential of a function is a linear approximation of the function near a point.

In the first case, the gradient of fi is (cos(y), x sin(y)) because the greatest rate of change of fi is in the direction of (cos(y), x sin(y)). The differential of fi is dx * cos(y) + dy * x sin(y) because this is the linear approximation of fi near the point (x, y).

In the second case, the gradient of f2 is (1 + y, x + z, xy) because the greatest rate of change of f2 is in the direction of (1 + y, x + z, xy). The differential of f2 is dx + dy + (x + z) * dx + xy * dy because this is the linear approximation of f2 near the point (x, y, z).

In the third case, the gradient of f3 is (0, 0, 2z) because the greatest rate of change of f3 is in the direction of (0, 0, 2z). The differential of f3 is 0 * dx + 0 * dy + 2z * dz because this is the linear approximation of f3 near the point (x, y, z).

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