Which type of transformation is shown?
• A. A rotation
• B. A dilation
O C. A reflection
• D. A translation

Answer:

(- 1, 9 )

Step-by-step explanation:

6x - y = - 15 → (1)

x + 2y = 17 → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

12x - 2y = - 30 → (3)

add (2) and (3) term by term to eliminate y

13x + 0 = - 13

13x = - 13 ( divide both sides by 13 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (2)

- 1 + 2y = 17 ( add 1 to both sides )

2y = 18 ( divide both sides by 2 )

y = 9

solution is (- 1, 9 )

Answer:

n+8+6

Sum means = and and means + so n+8+6

Answer:

\(f^{-1}\)(x) = 0.5x + 2

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = 2x - 4 ( add 4 to both sides )

y + 4 = 2x ( divide both sides by 2 )

\(\frac{y+4}{2}\) = x

Change y back into terms of x with x = \(f^{-1}\) (x)

\(f^{-1}\) (x) = \(\frac{x+4}{2}\) = 0.5x + 2

Answer: F -1(x)  = 0.5 x + 2

Step-by-step explanation:

Just took the test on edmentum and got a 100

Answer:

1.5 cm

Step-by-step explanation:

Triangles WTY and UTV are similar. Segment WT corresponds to UT and segment YT corresponds to VT. Thus we can create an equation knowing that the ratio of WT to UT must equal to the ratio of YT to VT.

WT = 7.5 cm

UT = ?

YT = 15 cm

VT = 12 cm

WT / UT = YT / VT

7.5 / UT = 15 / 12

UT = 6

WT = WU + UT

7.5 = WU + 6

WU = 1.5

The grandfather's age if he is 10 years more than thrice Kapil's age is

3x +10.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Kapil's age is m years.

His Grandfather is 10 years more than thrice Kapil's age.

Thrice Kapil's age = 3x

and, 10 years more than thrice Kapil's age = 3x + 10

Then, the age of Grandfather is

= 3x+ 10

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Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

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Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

y = -2/3x + 4

Comparing with the above formula

m / slope = - 2/3

Since the lines are parallel their slope are also the same

Thus

Slope of the parallel line = -2/3

Equation of the line using point ( - 2 , - 2) is

\(y + 2 = - \frac{2}{3} (x + 2)\)

\(y + 2 = - \frac{2}{3} x - \frac{4}{3} \)

\(y = - \frac{2 }{3} x - \frac{4}{3} - 2\)

We have the final answer as

\(y = - \frac{2}{3} x - \frac{10}{3} \)

Hope this helps you

The norm of the fitted vector y* in linear regression is generally smaller than the norm of the observed response y, but in some cases, it can be larger.

In linear regression, the goal is to find the best-fitting line or hyperplane that minimizes the sum of squared differences between the predicted values (y*) and the observed response values (y). The fitted vector y* represents the predicted values based on the regression model.

The geometry of orthogonal projection helps us understand this situation. Orthogonal projection involves finding the closest point on a line or hyperplane to a given point. In linear regression, the observed response y is a point in the data space, and the fitted vector y* lies on the regression line or hyperplane.

In certain cases, the observed response y may lie far from the regression line or hyperplane. This can happen when there are outliers or influential points in the data. In such situations, the orthogonal projection of y onto the regression line or hyperplane can result in a fitted vector y* that has a larger norm than the norm of the original response y.

However, in most cases, the fitted vector y* will have a smaller norm than the norm of the observed response y, as the regression model aims to minimize the differences between y* and y. So, while it is possible for the norm of y* to be larger than the norm of y, it typically occurs infrequently and is not the desired outcome in linear regression.

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Explanation:

The graph of y = -3/5x + 9 is a straight line, so to graph the function we need to identify two points of the line.

Then, we can find two points if we give a value to the variable x and calculate the value of y as:

If x = 5 then:

y = (-3/5)x + 9

y = (-3/5)*5 + 9

y = -3 + 9

y = 6

If x = 10 then:

y = (-3/5)*10 + 9

y = -6 + 9

y = 3

Therefore, we have the points (5, 6) and (10, 3), so the graph of the line is:

Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a Visual representation of the field, allowing for easier analysis and planning.

To create a scale drawing of a football field using a scale of 1:1,000, Mia can follow these steps:

1. Determine the dimensions: The football field's dimensions are given as 120 yards by 53 1/3 yards. Convert the fractional measurement to a decimal for simplicity. In this case, 1/3 yard is approximately 0.333 yards.

2. Decide on the units: Since the scale is 1:1,000, Mia needs to determine the unit of measurement she will use in her scale drawing. For consistency, she can choose to use feet as the unit.

3. Calculate the scaled dimensions: To create the scale drawing, Mia needs to scale down the dimensions of the football field. Since the scale is 1:1,000, she can divide the actual dimensions by 1,000 to obtain the scaled dimensions. The scaled dimensions would be 120 yards / 1,000 = 0.12 yards (or 0.36 feet) for the length and 53.333 yards / 1,000 = 0.053333 yards (or 0.16 feet) for the width.

4. Draw the scaled football field: Using a ruler and a grid paper, Mia can draw a rectangle with dimensions of 0.12 feet by 0.053333 feet (or inches, depending on the size of the grid paper). She can label the sides of the rectangle with the corresponding measurements in feet.

5. Add additional markings: Mia can add other markings to the scale drawing, such as the goal posts, yard markers, and any other important features of the football field. She can refer to the actual measurements and proportions of these elements to ensure accuracy.

By following these steps, Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a visual representation of the field, allowing for easier analysis and planning.

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Using the information provided, it appears that your neighbor will not save money by picking up the soil himself as its total cost is $103.86 as opposed to cost of delivery $30.

Here is a detailed breakdown of the calculations and assumptions made:

The area of the yard is estimated to be around 7,200 sq.ft. Assuming a 4 inch layer of topsoil, this requires 4 cubic yards (1 cubic yard = 27 cubic feet).

The cost of the soil delivery is $30 per truckload (up to 18 cubic yards). So the delivery cost for 4 cubic yards of soil would be $30.

The cost of topsoil per cubic yard is $18. Thus, the total cost of the topsoil is $72.

The weight of topsoil is 2000 pounds per cubic yard, so the total weight of the soil is 8,000 pounds (4 cubic yards x 2000 pounds).

The pickup truck's payload capacity is 1800 pounds, so the truck can only transport 1/4 of the total weight of the soil (1800/8000 = 0.225). Thus, it would require 4 trips to transport the soil, and the total trip distance is 36 miles (9 miles x 4 trips).

The truck gets 17 miles per gallon, so it would require 2.1 gallons of gas for each trip (36 miles/17 mpg = 2.12). The total amount of gas needed for the 4 trips is 8.4 gallons (2.1 gallons x 4 trips). The cost of gas per gallon is assumed to be $3.79, so the total cost of gas for the 4 trips is $31.86.

Thus, the total cost of picking up the soil himself is $31.86 + $72 = $103.86. This is higher than the cost of delivery which is only $30, so it would be better to pay for delivery.

To conclude, your neighbor will not save money by picking up the soil himself, and it is recommended that he pays for delivery.

Note: The question is incomplete. The complete question probably is: He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this. Here is (most of) the information you asked for:

Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery? Detail all your assumptions and calculations, and clearly write out your final conclusions.

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Intercept = 1

Equation - y = -(2/5)x + 1

Answer:

y - 12 = -5(x + 2)

Step-by-step explanation:

The option b "The area under the curve is 1." and the option d "It is symmetrical" are true about the probability function for a t distribution.

When the sample size is small and the population standard deviation is unknown, the t-distribution is used in statistics.

Option b confirms that the total area under the t-distribution curve is 1, indicating that the sum of probabilities for all possible outcomes is also equal to 1.

Option d confirms the symmetry of the t-distribution, implying that the curve is balanced on both sides of the mean. The mean, median, and mode of a symmetrical distribution are all equal.

To summarize, the t-distribution is a useful tool in statistics when working with small sample sizes because it accounts for the uncertainty in the population standard deviation.

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Answer:

you would have 8 oranges and 5 apples

The probability of all heads, all tails, exactly two tails, exactly one head will be 1/8, 1/8, 3/8, and 3/8 respectively.

The complete question is given below.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Then the total number of the event will be

Total event = 2³

Total event = 8 {HHH, HHT, HTH, THH, HTT, THT, HHT, TTT}

Then the probability of all heads will be

⇒ 1/8

Then the probability of all tails will be

⇒ 1/8

Then the probability of exactly two tails will be

⇒ 3/8

Then the probability of exactly one head will be

⇒ 3/8

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Answer:

one solution

Step-by-step explanation:

that was easy

Answer:

a

Step-by-step explanation:

22.978 rounded is 23

Answer:

2x

Step-by-step explanation:

aka 2

Answer: 2

Step-by-step explanation:

I did this question before

Therefore, the distance d(P₁, P₂) between the points P₁ = (3, 3) and P₂ = (-6, 5) is approximately 9.22.

To find the distance between two points in a two-dimensional Cartesian coordinate system, you can use the distance formula. The formula is given by:

d(P₁, P₂) = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the distance using the given coordinates:

P₁ = (3, 3)

P₂ = (-6, 5)

Substituting the values into the formula:

d(P₁, P₂) = √((-6 - 3)² + (5 - 3)²)

= √((-9)² + 2²)

= √(81 + 4)

= √85

≈ 9.22

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Given that the first two sides of a triangle are 8 cm and 10 cm in length, the third side's range of potential lengths will be [2,18].

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself. The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range can also be thought of as the distance between the highest and lowest observation.

Here,

The minimum length can be,

=10-8

=2 cm

The maximum length can be,

=10+8

=18 cm

(10-8)<x<(10+8)

2<x<18

The range of possible lengths for the third side will be [2,18] as The lengths of two sides of a triangle are 8 cm and 10 cm.

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Answer:

Step-by-step explanation:

Term            Coefficient

3a                    3

-8n                   -8

Expressions that are tested by the 'if' statement is called conditions.

A condition is an expression that evaluates to either 'True' or 'False', and it determines whether the code block within the 'if' statement is executed. The 'if' statement allows the program to make decisions and execute different codes based on whether the condition is 'true' or 'false'. For example, in Python, an 'if' statement might look like this:

if x > 10:

   print("x is greater than 10")

In this example, the condition being tested is 'x > 10', which will evaluate as 'True' or 'False' depending on the value of x. If the condition is 'True', then the code block within the 'if' statement (in this case, the print statement) will be executed. If the condition is 'False', then the code block within the 'if' statement will be skipped.

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Answer:

A) √3/4

Step-by-step explanation:

Eccentricity describes how closely a conic section resembles a circle:

\(e=\sqrt{1-\frac{b^2}{a^2}}\\\\e=\sqrt{1-\frac{52}{64}}\\\\e=\sqrt{\frac{12}{64}}\\\\e=\sqrt{\frac{3}{16}}\\\\e=\frac{\sqrt{3}}{4}\)

Note that \(a^2 > b^2\) in an ellipse, so the decision of these values matter.

The number of possible k-lists (x₁, x₂, ..., xₙ) where each xₙ is a positive integer and 1 ≤ x₁ ≤ x₂ ≤ · · · ≤ xₙ ≤ n is given by the formula n choose k, or (n choose k) = n!/(k!(n-k)!)

First, let's consider the case when k = 1. In this case, there is only one integer in the list, and it must be a positive integer between 1 and n inclusive. Therefore, there are n possible k-lists when k = 1.

We can continue this process for larger values of k.

In general, the number of possible k-lists is the number of ways we can choose k positive integers between 1 and n inclusive such that the first integer is less than or equal to the second integer, the second integer is less than or equal to the third integer, and so on up to the kth integer being less than or equal to n.

Using the formula for combinations, this is equal to n choose k, or (n choose k) = n!/(k!(n-k)!), where n! is the factorial of n.

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You should do 585 × 0.50 to find the markdown. Then subtract the markdown from the selling price to find the sale price.

Step-by-step explanation:

The probability to select $5 bill when the first selected bill is $10 is given by 1/2.

Probability is the possibility to occur of an event.

In mathematical terms, probability can be defined as,

\(\text{Probability}=\frac{\text{The number of favorable case}}{\text{The total number of case}}\)

Given that, the number of total $5 bills = 3

the number of $10 bills = 4

Total number = 3+4 = 7

If the first drawn bill is $10, then the number of $10 bills = 4-1 = 3

Total number of bills =7-1 = 6

So the probability to select $5 bill when the first selected bill is $10 = 3/6 = 1/2

Hence, the probability to select $5 bill when the first selected bill is $10 is given by 1/2.

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