Can you map shape I onto shape II by a sequence of transformations? If so, give a sequence of transformations that maps shape I onto shape II.

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

S cannot be a basis for \(R^{n }\)

What is Matrix ?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and other fields to represent systems of linear equations, transformations, and other mathematical objects and operations.

The statement "For each b in  \(R^{m }\), the equation Ax - b has a solution" is equivalent to the following statements:

A. The columns of A span \(R^{m }\)

B. Each b in \(R^{m }\) is a linear combination of the columns of A.

E. The matrix A has a pivot position in each column.

To explain why S cannot be a basis for  \(R^{n }\) , we can use the fact that a set of vectors S = {v1, ..., vk} is a basis for  \(R^{n }\) if and only if the matrix whose columns are the vectors in S is invertible. In this case, since k < n, the matrix whose columns are the vectors in S cannot be invertible because it has more columns than rows.

Therefore, S cannot be a basis for \(R^{n }\).

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The measure of angle BDC = 100°

The smallest polygon with three sides and three internal angles is known as a triangle. According to the triangle's "angle sum property," a triangle's internal angles add up to 180°.

Sum of angles in a triangle = 180°

Here we have

3 triangles in the given picture

As we know the Sum of angles in a triangle = 180°

From triangle CBD

∠CBD + ∠BDC + ∠DCB = 180°

From figure  ∠DCB = 40° and ∠CBD = 40°

=> 40° + ∠BDC + 40° = 180°  

=> ∠BDC = 180° - 80°

=> ∠BDC = 100°

Therefore,

The measure of angle BDC = 100°

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Answer:

i'm not sure if i messed up or not, but n can't equal -6?

Step-by-step explanation:

-4(-3(-6)-8)=10(6)+ 20

-4(18-8)=60+20

-4(10)=80

40=80

Answer:

12 feet

Step-by-step explanation:

Sometimes, a simple drawing is a great way to start! In the attached drawing, the red line represents the ladder, the brown represents the ground, and the black represents the building!

We want to find the side of the triangle from where the ladder meets the building to where the building meets the ground. This can be found using trigonometric identities, namely sine:

\(sin\theta=\frac{opposite}{hypotenuse}\)

Plug in known values:

\(sin(74^o)=\frac{x}{12}\)

Rearrange to isolate the variable:

\(x=12sin(74^o)\)

Simplify!

\(x=11.535140... ft\)

Round to the nearest foot:

\(x=12ft\)

Answer: True, if it is on a coordinate grid.

Step-by-step explanation:

\(\displaystyle\\Answer:\ \frac{7}{5}x +\frac{34}{5}\)

Step-by-step explanation:

\(\displaystyle\\(-7,-3)\ \ \ \ (-2,4)\\\\\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=-7\ \ \ \ \ x_2=-2\ \ \ \ y_1=-3\ \ \ \ \ y_2=4\\\\\frac{x-(-7)}{-2-(-7)} =\frac{y-(-3)}{4-(-3)}\\\\\frac{x+7}{-2+7}=\frac{y+3}{4+3} \\\\\frac{x+7}{5} =\frac{y+3}{7} \\\\\)

Multiply both parts of the equation by 7:

\(\displaystyle\\7(\frac{x+7}{5} )=y+3\\\\7(\frac{1}{5} x+\frac{7}{5} )=y+3\\\\\frac{7}{5}x +\frac{49}{5} =y+3\\\\\frac{7}{5}x +\frac{49}{5} -3=y+3-3\\\\\frac{7}{5}x +\frac{49}{5}-3=y\\\\\frac{7}{5}x +\frac{49-3(5)}{5} =y\\\\\frac{7}{5}x +\frac{49-15}{5} =y\\\\\frac{7}{5}x +\frac{34}{5} =y\\\\So,\ y=\frac{7}{5}x +\frac{34}{5}\)

Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

Answer: 24

Step-by-step explanation: 3*2*2*2=24

You can build 24 sundaes

The monthly repayment on the following hire-purchase agreement is £22.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a colour TV costs £640. The deposit was £200. The interest rate was 10% p.a. and it was paid off in two years.

The monthly repayment will be calculated as,

Total interest for two years = ( 640 - 200 ) x 1.2

Total interest for two years = ( 440 x 1.2 )

Total interest for two years = £528

The value of monthly repayment = 528 / 24 = £22

Therefore, the monthly repayment on the following hire-purchase agreement is £22.

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This is the same as the right side of the equation, the identity is verified. According to the given information, the identity is true.

To verify the identity

\(1 - sin \theta / cos  \theta = cos  \theta / 1 + sin  \theta\),

we can simplify both sides of the equation.

Starting with the left side:
\(1 - sin \theta / cos \theta = (cos \theta / cos \theta) - (sin \theta / cos \theta) \\=(cos \theta - sin \theta) / cos \theta\)

Next, we simplify the right side:
\(cos \theta / 1 + sin \theta = cos \theta / (1 + sin \theta) \\= (cos \theta) / (1 + sin \theta)\)

To check if the identity holds true, we can cross-multiply:
\((cos \theta - sin \theta) / cos \theta = (cos \theta) / (1 + sin \theta)\\(cos \theta - sin \theta)(1 + sin \theta) = (cos \theta)(cos \theta)\)
Expanding and simplifying:
\(cos \theta - sin \theta + cos \theta sin \theta - sin^2 \theta = cos^2 \theta\)

Rearranging the terms:
\(cos \theta + cos \theta sin \theta = cos^2 \theta+ sin^2 \theta\)

Using the Pythagorean identity \(cos^2 \theta + sin^2 \theta = 1\), we get:
\(cos \theta + cos \theta sin \theta = 1\)

Factoring out cos θ on the left side:
\(cos \theta(1 + sin \theta) = 1\)

Since this is the same as the right side of the equation, the identity is verified.

In conclusion, the given identity is true.

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It would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

Dennis' reasoning is incorrect.

To determine the rate of picking apples per minute, Dennis correctly divided the total number of apples (24) by the time it took (6 minutes), resulting in 4 apples per minute. However, his approach to calculating the number of apples that could be picked in 8 minutes is flawed.

Dennis multiplied the rate of picking apples per minute (4 apples) by the given time (8 minutes), assuming that the rate remains constant. This approach would be valid if the rate of picking apples per minute were constant, but in this scenario, it is not necessarily the case.

The rate of picking apples could vary depending on factors such as fatigue, efficiency, or other variables. Therefore, it is not accurate to assume that the rate of picking apples per minute remains the same over a longer duration of time.

To determine the number of apples that could be picked in 8 minutes, it would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

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The rate of change for Function A (35 or 3.5) is greater than the rate of change for Function B (1). This means that Function A increases at a faster rate than Function B.

what is rate of change ?

Rate of change refers to the speed at which a quantity changes with respect to another quantity. In mathematics, rate of change is often referred to as slope and is a measure of how steep a line is.

In the given question,

The rate of change, also known as the slope, of a linear function is constant and can be determined by calculating the change in y divided by the change in x.

For Function A, y = 35x, the rate of change is 35, which means that for every increase of 1 in x, y increases by 35. This can also be written as the fraction 35/1 or as a decimal, 3.5.

For Function B, y = x, the rate of change is 1, which means that for every increase of 1 in x, y increases by 1. This can also be written as the fraction 1/1 or as a decimal, 1.

Therefore, the rate of change for Function A (35 or 3.5) is greater than the rate of change for Function B (1). This means that Function A increases at a faster rate than Function B.

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Answer:

Step-by-step explanation:

The resulting reflection will be (4,-5) and will be followed by (-4,-5).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. A series of data indicating a precise position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is 12 units long and 5 units high.

Here,

given coordinates=(4,5)

Firstly, reflecting across x axis, point (x,y) turns to (x, -y).

=(4,-5)

Secondly, reflecting (x,-y) across y-axis, point (x,-y) turns to (-x,-y).

=(-4,-5)

The resultant reflection will lead (4,-5) followed by (-4,-5).

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We can use the formula for gravitational potential energy (GPE) to find the height at which Jessie is off the ground:

GPE = mgh

where m is the mass of the object (in kg), g is the acceleration due to gravity (9.8 m/s² on Earth), h is the height (in meters) above some reference point where the GPE is defined.

In this case, we know that Jessie has a mass of 50 kg and 4,900 joules of GPE. Plugging these values into the formula, we get:

4900 = (50 kg)(9.8 m/s²)(h)

Solving for h, we get:

h = 4900 J / (50 kg x 9.8 m/s²)

h = 10 meters

Therefore, Jessie is 10 meters off the ground at the point where she has 4,900 joules of GPE.

Answer:

10 meters

Step-by-step explanation:

P.E = mgh

4900 = 50 × 9.8 × h

4900 = 490 × h

h = 10 m

Answer:

(x+2,y-4)

Step-by-step explanation:

The correct answer is (x+2, y-4)

The translation of ABCD to A'B'C'D' is given by (x + 2,y - 4).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Translation is the movement of a point either up, left, right or down.

ABCD has vertices at A(-6, 2), B(-5, 4), C(-2, 4) and D(1, 2). If ABCD is translated 4 units down and 2 units right, the new point is A'(-4, -2), B'(-3, 0), C'(0, 0) and D'(3, -2)

The translation of ABCD to A'B'C'D' is given by (x + 2,y - 4).

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Answer:  There is a total of 900 seats in the auditorium.

Step-by-step explanation:

there is a formula for this

t - n = a + ( n - 1) d

It is called a Arithmetic Progression.

We use this to find the number of seats in the last row first.

a = initial value, 12

d = common difference for each successive term

n = is the number of terms in the sequence

t - 25 = 12 + (25 -1) * 2

We ignore the left side for now, just solve the right and we get 60.

Now we use the equation,

n / 2 (2a + n -1 * d)

So,

25/2 ( 24 + 24 * d)

The answer is 900

A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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Answer:

4).

Step-by-step explanation:

sin A = cos B

Because sin A = CB/AB and cos B = CB/AB.

Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The correct option is d. Neither Type I nor Type II error.  The concepts of Type I and Type II errors, and to use appropriate methods and sample sizes to minimize the risk of making such errors.

To understand why, let's first define Type I and Type II errors. Type I error is rejecting a true null hypothesis, while Type II error is failing to reject a false null hypothesis.

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The required dimensions are 500 meters and 250 meter for the fencing to be minimum.

If a rectangle has dimensions x and y, then its area is equal to x and y, and its perimeter is equal to 2(x + y). The edge of a figure has anything to do with fencing. Use the idea of maxima and minima by combining all the variables into a single variable.

Let the dimensions of the rectangular pasture be x and y.

Equate the area of the rectangle to 125,000 and solve for y.

Where:

xy = 125000

y = 125000/x

If one side of the rectangle is left out, figure out how much fencing or perimeter is needed.

P = 2(x + y) - x

= x + 2y.

Set y = 125000/x into obtained perimeter.

P = x + 2(125000/x).

= x + (2,50,000/x)

Differentiate P with respect to x.

dP/dx = 1 - (2,50,000/x²)

Equate the obtained derivative to 0 and solve for x (can not be negative).

1 - (2,50,000/x²) = 0

(2,50,000/x²) = 1

x² = 2,50,000

x = 500

Calculate the second derivative of P and set x = 500.

d²P/dx² = 1 - (2,50,000/x³)

= (2,50,000/x³)>0

Calculate y by setting x=500 into y = 125000/x .

y =  125000/x

y =  125000/500

y = 250

The required dimensions are 500 meters and 250 meter for the fencing to be minimum.

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Answer:

$1278.23

Step-by-step explanation:

Answer:

2/4

Step-by-step explanation:

i think its 2 gallons

Answer:

The segment that connects the midpoints of the legs of a trapezoid is called the median of the trapezoid.

Step-by-step explanation:

Answer:

Fourth Graph

Step-by-step explanation:

\(2x - y = -1\)

\(2x + 1 = y\)

\(y = 2x + 1\)

Approximately 19.9919 pounds of bananas are removed from the display table during the first 2 hours the store is open.

The function has a constant term 10, which represents the minimum rate of banana removal even if no customers are present.

The second function is g(t), which models the rate at which bananas are added to the display table.

Now, to answer the question, we need to find out how many pounds of bananas are removed from the display table during the first 2 hours. We can do this by integrating the function f(t) from 0 to 2, which gives us the total amount of bananas removed during this time interval. Using the integral notation, we have:

Total amount of bananas removed = ∫₀² f(t) dt

Using the formula for f(t), we can evaluate this integral as follows:

∫₀² [10 + (0.81)sin(100t)] dt = [10t - (0.81/100)cos(100t)] from 0 to 2

Plugging in the limits of integration, we get:

[10(2) - (0.81/100)cos(200)] - [10(0) - (0.81/100)cos(0)] = 20 - 0.0081 ≈ 19.9919 pounds

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Complete Question:

When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove bananas from the display table at a rate modeled by

f(t) = 10 + (0.81)sin 100 for 0

where f(t) is measured in pounds per hour and is the number of hours after the store opened. After the store has been open for three hours, store employees add bananas to the display table at a rate modeled by

8(t) = 3 + 2.4 In (12 + 2+) for 3

where g(t) is measured in pounds per hour and is the number of hours after the store opened.

(a) How many pounds of bananas are removed from the display table during the first 2 hours the store is open?