he triangles are congruent by SSS or HL.

Triangles P Q R and S T U are shown. Triangle P Q R is reflected across Q R and then is shifted up and to the right to form triangle S T U.

Which transformation(s) can map TrianglePQR onto TriangleSTU?

translation only
rotation only
rotation, then reflection
reflection, then translation

The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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Step-by-step explanation:

since it is in the same line as DE, both have the same slope.

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

and so by using the coordinates of D and E

x changes by +4 (from 8 to 12).

y changes by -8 (from 32 to 24).

the slope is therefore

-8/+4 = -2

Answer:

B. -2 *4

Step-by-step explanation:

Answer: \(312\times 412\times 2\)

Step-by-step explanation:

Given

The length of rectangular Prism is \(l=312\ m\)

The width of the rectangular prism is \(w=412\ m\)

The height of the rectangular prism is \(h=2\ m\)

The volume of the rectangular prism is given by \(l\times w\times h\)

Put values

Volume is \(V=312\times 412\times 2=2,57,088\ m^3\)

Answer: the answer is c

Step-by-step explanation:

The graph that represents the solution to the set of the inequality is -13 -14.

The graph that represent the solution to the inequality must contain numbers greater than negative 14.5 (-14.5). These numbers start from -14 to inifinity.

The given inequality; -14.5 < x

The possibles values in the solution of the inequality = -14, - 13, - 12, - 11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0. etc

Therefore, the graph that represents the solution to the set of the inequality is -13 -14.

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a) The first five terms of the sequence are 2, 12, 72, 432, 2592.
b) The first five terms of the sequence are -1, 2, -4, 8, -16.

c) The first five terms of the sequence are 2, -1, -3, -2, 1.

To find the first five terms of the sequence defined by each of these recurrence relations and initial conditions, we will use the given recurrence relation and initial conditions to find the next terms in the sequence.

a) an = 6an-1, a0 = 2

The first term is given as a0 = 2. We will use the recurrence relation to find the next terms.
a1 = 6a0 = 6(2) = 12
a2 = 6a1 = 6(12) = 72
a3 = 6a2 = 6(72) = 432
a4 = 6a3 = 6(432) = 2592

So, the first five terms of the sequence are 2, 12, 72, 432, 2592.

b) an = −2an-1, a0 = −1

The first term is given as a0 = -1. We will use the recurrence relation to find the next terms.
a1 = -2a0 = -2(-1) = 2
a2 = -2a1 = -2(2) = -4
a3 = -2a2 = -2(-4) = 8
a4 = -2a3 = -2(8) = -16

So, the first five terms of the sequence are -1, 2, -4, 8, -16.

c) an = an-1 – an-2, a0 = 2, a1 = −1

The first two terms are given as a0 = 2 and a1 = -1. We will use the recurrence relation to find the next terms.
a2 = a1 - a0 = -1 - 2 = -3
a3 = a2 - a1 = -3 - (-1) = -2
a4 = a3 - a2 = -2 - (-3) = 1

So, the first five terms of the sequence are 2, -1, -3, -2, 1.

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Answer:

44

Step-by-step explanation:

The point estimate of the population proportion is 0.515, with a margin of error of 0.253. The sample size is 1000, and the estimated number of individuals with the characteristic is 515.



To determine the point estimate of the population proportion, you can take the midpoint of the confidence interval, which is the average of the lower bound and upper bound.

Given:

Lower bound = 0.262

Upper bound = 0.768

n = 1000

Point estimate = (Lower bound + Upper bound) / 2

             = (0.262 + 0.768) / 2

             = 1.03 / 2

             = 0.515

The point estimate of the population proportion is approximately 0.515.

To calculate the margin of error, you can subtract the point estimate from the upper bound of the confidence interval.

Margin of error = Upper bound - Point estimate

              = 0.768 - 0.515

              = 0.253

The margin of error is approximately 0.253.

To find the number of individuals in the sample with the specified characteristic, you can multiply the point estimate by the sample size.

Number of individuals = Point estimate * Sample size

                    = 0.515 * 1000

                    = 515

The number of individuals in the sample with the specified characteristic is approximately 515.

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Explanation:

Think of a Rubik's cube. Each face is composed of 9 small squares, in which the goal is to get each side to have the same color of 9 squares.

Since we have 9 squares on one face, this means we have each side that is sqrt(9) = 3 units long. Each little square is 1 unit by 1 unit.

The volume of the Rubik's cube is 3*3*3 = 27 cubic units. Meaning that we need 27 small cubes to build up the entire device. We can think of it like saying there are 9 cubes in the top row, 9 in the middle row, and 9 in the bottom row to give 9+9+9 = 27 total cubes.

This figure shows 7 such cubes, so we need 27-7 = 20 more cubes to form a complete Rubik's cube.

Answer:

1,050 miles

Step-by-step explanation:

First: Convert any mixed numbers to fractions.

Then your initial equation becomes: Applying the fractions formula for multiplication,

2/14×200/1

Applying the fractions formula for multiplication,

21×200

 4×1

=42004

Simplify

1,050

The work required to pump the water out of the full hemisphere tank is given by 1000 * V * 9.8 * r joules.

To calculate the work required to pump the water out of the full hemisphere tank, we need to determine the gravitational potential energy of the water being lifted. The work done is equal to the change in potential energy.

First, let's calculate the volume of the hemisphere tank. The volume of a hemisphere is given by the formula:

V = (2/3) * π * \(r^{3}\)

Where r is the radius of the hemisphere.

Next, we need to find the height from which the water is lifted. Since the tank is a full hemisphere, the height is equal to the radius of the hemisphere.

Once we have the volume and the height, we can calculate the mass of the water lifted using the density of water:

m = density * V

Finally, we can calculate the work done using the formula:

Work = m * g * h

Where g is the acceleration due to gravity (approximately 9.8 m/\(s^{2}\) ) and h is the height.

Let's assume the radius of the hemisphere tank is given as 'r'. Then we can calculate the work required as follows:

Step 1: Calculate the volume of the hemisphere tank

V = (2/3) * π * \(r^{3}\)

Step 2: Calculate the mass of water lifted

m = density * V

m = 1000  kg/\(m^{3}\)  * V

Step 3: Calculate the work done

Work = m * g * h

Work = 1000 kg/\(m^{3}\) * V * 9.8 m/\(s^{2}\) * r

Therefore, the work required to pump the water out of the full hemisphere tank is given by 1000 * V * 9.8 * r joules.

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Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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Answer:

16, 32, 64

Step-by-step explanation:

There is a common ratio between consecutive terms, that is

2 ÷ 1 = 4 ÷ 2 = 8 ÷ 4 = 2

Thus to obtain any term in the sequence multiply the previous term by 2

a₅ = a₄ × 2 = 8 × 2 = 16

a₆ = a₅ × 2 = 16 × 2 = 32

a₇ = a₆ × 2 = 32 × 2 = 64

Answer: (x-2),(2x+3), and (2x-1)

Step-by-step explanation: I just took the test and guessed but now I know the answer, so I'm helping everyone :)

Answer:

10

Step-by-step explanation:

The median is arranged in numerical value.

it goes: 4, 5, 9, 11, 12, 13. The median is basically the number in-between. you would cross out 4 and then 13. next, 5 and 12. Now there's 9 and 11 in the middle and that is what's left. the number in between of 11 and 9 is 10. 10 would be the median of the data set.

Answer:

the answer would be 9 I think

Hi~!

Answer:

843

Step-by-step explanation:

We know that 58 is a even number, and so is 48,894. So we can  check this by multiplying 843, which is th number I got when I divided it, and multiply that by 58, then we get 48,894.

I hope this helps!~ :)

Answer:

843

Step-by-step explanation:

In long division, first take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top as the quotient. After, subtract the result from the digit and write the difference below. Bring down the next digit of the dividend (if present). Lastly, repeat the same process.

    00,843
58)48,894
   - 464 ↓↓
----------------
        249 ↓
      - 232 ↓
----------------

           174
         - 174
-----------------
              0

From this, we can see that 58 goes into 48,894 843 times. In other words, 48,894 ÷ 58 is 843.

hope this helps!

Answer:

500

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

add them together lol

Answer:

1. = 96

2. = -158

Step-by-step explanation:

When you multiply two negatives the answer is positive, and when you multiply one negative and one positive the answer is negative

Answer:

14/9 or 1.555556

Step-by-step explanation:

1) Simplify 1 + 1/3 to 4/3.

(4/3)^2 - 2/9

2) Use Division Distributive Property: (x/y)^a = x^a/y^a.

4^2/3^2 - 2/9

3) Simplify 4^2 to 16.

16/3^2 - 2/9

4) Simplify 3^2 to 9.

16/9 - 2/9

5) Simplify.

14/9

(Decimal form: 1.555556)

Thanks, Eddie

Answer:

Step-by-step explanation:

-1, -0.5, 1/4

Answer:

Option (D)

Step-by-step explanation:

Given inequalities are,

\(y>-\frac{1}{3}x+2\) --------(1)

y > 2x - 3 ------(2)

Inequality (1) will be represented by a dotted line having negative slope and y-intercept = 2 → (blue line)

And the solution set will lie in the region left to the dotted line.

Similarly, inequality (2) will be represented by a dotted line with positive slope and y-intercept = (-3) → (red line)

Area above the red line will be the solution set for this inequality.

And the common area of both the inequalities will be solution area to the system of linear inequalities.

Option (D) will be the answer.

According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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Answer:

HCF = 6.

Step-by-step explanation:

The Highest Common factor is 6.

Other common factors are 1, 2 and 3.

The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.

The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated  instead of the radius, we have  to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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Answer:

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction 37° north of east.

In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates (x, y). In a similar fashion, a vector

→

A

in a plane is described by a pair of its vector coordinates. The x-coordinate of vector

→

A

is called its x-component and the y-coordinate of vector

→

A

is called its y-component. The vector x-component is a vector denoted by

→

A

x. The vector y-component is a vector denoted by

→

A

y. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x– and y-axes, respectively. In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:

Step-by-step explanation:

Answer:

approximately 85 m

Step-by-step explanation:

use the law of cosines

x²=120²+90²-2(120)(90)cos(45)

*120 & 90 are given values

*45 is from 25+20; bcuz of alternate interior angles, the other angle from mirror 1 is 25 degrees, making the total 45 degrees

x=√120²+90²-2(120)(90)cos(45)

x=85, the distance btwn origin point and mirror 2

There are variations in the participation prices of boys and girls across unique sports, with boys having decreased representation in varsity soccer, better representation in freshman basketball, and identical illustration in varsity tennis compared to ladies.

Based on the given statements:

The percentage of boys who play varsity soccer is much less than the share of ladies who play varsity football.

The share of boys who play freshman basketball is extra than the share of girls who play freshman basketball.

The percentage of boys who play varsity tennis is the same as the variety of women who play varsity tennis.

We can finish subsequent:

Boys have a lower representation in varsity football as compared to ladies.

Boys have a higher representation in freshman basketball in comparison to ladies.

The percentage of boys playing varsity tennis is identical to the proportion of women playing varsity tennis.

These statements suggest differences in participation fees and proportions between boys and women in unique sports activities.

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The correct question is:

"The percentage of boys who play varsity soccer is ✔ less than the percentage of girls who play varsity soccer. the proportion of boys who play freshman b-ball is ✔ greater than the proportion of girls who play freshman b-ball. the percentage of boys who play varsity tennis is ✔ the same as the number of girls who play varsity tennis.

What can you conclude from the above statements?"