The coordinates of the vertices of △ABC are A(3,0), B(2,−3), and C(0,3). The coordinates of the vertices of △XYZ are X(1,0), Y(0,3), and Z(−2,−3). Which series of transformations correctly shows that △ABC≅△XYZ?

A: a translation 2 units down and a reflection over the x-axis

B: a translation 2 units up and a reflection over the y-axis

C: a translation 2 units right and a reflection over the y-axis

D: a translation 2 units left and a reflection over the x-axis

Answer:20 feet

Step-by-step explanation:16 -12=4 and then take 16 divided by 4 which is 4 so u add 4 to 16 so the boxes will be 20 feet high

In order to estimate the population proportion within 5%, a sample size of at least 384 is needed.

The number of individuals or observations included in a study is referred to as the sample size. Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.

This can be calculated using the formula:

n = (z^2 * p * (1-p)) / (e^2)

where z is the z-score corresponding to a 95% confidence level, p is the estimated proportion of people in favor of legalizing marijuana, and e is the margin of error (5%).

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The slopes of the sides AB, BC and AC are - 1, - 3 and 5 / 3, respectively.

Triangles are generated by three distinct points known as vertices. The slopes of each side are determined by using each pair of vertices and the secant line formula:

Side AB

m = (- 4 - 3) / [5 - (- 2)]

m = - 7 / 7

m = - 1

Side BC

m = [8 - (- 4)] / (1 - 5)

m = 12 / (- 4)

m = - 3

Side AC

m = (8 - 3) / [1 - (- 2)]

m = 5 / 3

The slopes of the three sides of the triangle are - 1, - 3 and 5 / 3, respectively.

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Answer:

x = 1 student.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

irration minus rathional is a irrational number

Answer:

105

Step-by-step explanation:

1. x = mushroom he gather

2. he dry 2/5 from he gather, 2/5 from x

3. he pickled 5/9 of remaining mushroom

find the remaining mushroom value first, x-2/5x = 3/5x

then multiply with 5/9, 5/9(3/5x) = 15/45x

4. total mushroom - dry - pickled, he still have 28 to fry

5. write the equation like this

x - 2/5x - 15/45x = 28

45/45x - 18/45x -15/45x = 28

12/45x = 28

x = 28(45) / 12

x = 105

Answer: The coordinates of A = (-6,-3).

Step-by-step explanation:

The coordinates of image of point (x,y) after the dilation with scale factor of k given by :-

\((x,y)\to (kx,ky)\)

Given: Scale factor = 1.5

Coordiantes of A = (-4,-2)

The coordiantes of A' after a dilation with a scale factor of 1.5 will be

\((1.5\times-4, 1.5\times-2) = (-6,-3)\)

Hence, the coordinates of A = (-6,-3).

we can guess that the slope of the tangent line to the curve at P(3, 0.666666666666667) is also approximately 0.076.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To find the slope of the secant line PQ, we need to calculate the difference in y-coordinates divided by the difference in x-coordinates between points P and Q.

a. If x = 3.1:

Coordinates of point Q: (3.1, 2/3.1)

Slope of PQ: (2/3.1 - 0.666666666666667) / (3.1 - 3) ≈ 0.076

b. If x = 3.01:

Coordinates of point Q: (3.01, 2/3.01)

Slope of PQ: (2/3.01 - 0.666666666666667) / (3.01 - 3) ≈ 0.076

c. If x = 2.9:

Coordinates of point Q: (2.9, 2/2.9)

Slope of PQ: (2/2.9 - 0.666666666666667) / (2.9 - 3) ≈ 0.076

d. If x = 2.99:

Coordinates of point Q: (2.99, 2/2.99)

Slope of PQ: (2/2.99 - 0.666666666666667) / (2.99 - 3) ≈ 0.076

Based on the above calculations, we can observe that for all the given values of x, the slope of PQ is approximately 0.076.

Therefore, we can guess that the slope of the tangent line to the curve at P(3, 0.666666666666667) is also approximately 0.076.

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Answer:

1+2-3+4-5+6-7+8-9=3-3+4-5+6-7+8-9=-1+6-7+8-9=5-7+8-9=6-9=-3

Step-by-step explanation:

Answer: 45

Step-by-step explanation: Add all the digits

We are given the function, \(\underline{f(x)=x^3-9x^2+20x-12}\), and are asked to find the x and y intercepts of the function.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

What is an intercept?

An intercept is where the graph of a function cross either the x or y axis. The x-intercept(s) crosses the x-axis and the y-intercept(s) crosses the y-axis.

How do find the x-intercept(s)?

To find the x-intercepts let y in your function equal zero, then solve for x.

How do find the y-intercept(s)?

To find the y-intercepts let x in your function equal zero, then solve for y.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Refer to the attached image for the rest.

We will repeat the exact same procedure. Something may have gone wrong.                                                                                                    

The special theory of relativity by German-born scientist Albert Einstein contains the equation \(E=mc^{2}\), which conveys the idea that mass and energy are one and the same physical substance and may be transformed into one another. The kinetic energy (E) of a body is equal to its increased relativistic mass (m) multiplied by the square root of the speed of light.

Because the mass and the speed of light are both constants, we are unable to test a new variable. Since our findings don't match the accepted formula, we cannot share them.

The result obtained is wrong we cannot apply it to another experiment. The only way we can find the correct result is by repeating the experiment. Because something may have gone wrong on the first attempt.

Therefore, the correct answer is

d) Repeat the exact same procedure.  

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The correct question is: Suppose you conduct one experiment and find that the \(E=mc^{3}\), rather than the historically accepted formula, \(E=mc^{2}\). What should you do next?

a.Test a new variable

b.Share your findings

c.Apply your results to a new experiment

d.Repeat the exact same procedure                                                                                                                                                                                                                                                                                                                                                                                      

Answer:

D. 10^10

Step-by-step explanation:

Multiplying numbers with exponents rule : \(a^b*a^c=a^b^+^c\)

explanation of rule : we simply keep the bases the same and add the exponents.

10^3 • 10^7

keep the base as 10 and add the exponents

\(10^3 * 10^7 =10^3^+^7=10^1^0\)

Keep in mind that this only works when the bases are the same.

Answer:

\(\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: ANSWER : \: \: \: \: 10^{10} }}}}}}}}\)

Step-by-step explanation:

The given expression, 10³ • 10⁷ has the same base but different exponential values. We know that,

So,

\(\large{\mathfrak{10^{3} * 10^{7} }}\)

= \(\large{\mathfrak{10^{3 + 7} }}\)

= \(\huge{\boxed{\mathfrak{10^{10} }}}\)  (3rd option)

_____

Hope it helps!

\(\mathfrak{Lucazz}\)

Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

The Price of the guitar is $ 1418.03

In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to calculate a percentage of a number, multiply it by 100 after dividing it by its whole.

To find the percentage multiply the ratio of the actual value by the total value with 100.          

Here given

Gerardo works in a music store and earns a 6.1% commission on each sale.

Gerardo sells a guitar and earns $86.50  

Here we need to find the Price of the guitar

Since we don't know the price of the guitar

Let's assume that the Price of the guitar is $ x

From the given data,

The commission earned on the guitar = 6.1% of x

=> \(\frac{6.1}{100} \times x\)  

=>  0.061x

Given that

The amount earned by Gerardo on guitar = $86.50  

=> 0.061x = $86.50  

=> x = (86.50)/0.061

=> x = 1418.03

Therefore,

The Price of the guitar is $ 1418.03

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Answer:

1418.03

Step-by-step explanation:

Explanation:

From 9:24 AM to 10:24 AM is 60 minutes (aka 1 hour)

Then from 10:24 AM to 10:43 AM is another 19 minutes (because 43-24 = 19)

The full duration is 60+19 = 79 minutes

The answer of the given question based on the right angle triangle is , the height of the light pole to the nearest tenth of a foot is 9.3 feet.

A right-angled triangle, also known as a right triangle, is a triangle that has one angle equal to 90 degrees. The side opposite right angle is called hypotenuse, and other two sides is called legs. The leg opposite to a particular acute angle is known as the opposite side, and the leg adjacent to it is known as the adjacent side.

The Pythagorean theorem is a fundamental theorem that applies to all right-angled triangles. It states that square of hypotenuse of right-angled triangle is equal to sum of squares of its two legs

To determine the height of the light pole, we can use similar triangles.

Let's call height of light pole be  "x". Then we have:

(height of stop sign) / (length of stop sign's shadow) = (height of light pole)/(length of light pole's shadow)

Substituting the given values, we have:

8/12 = x/14

Simplifying this equation, we get:

x = (8/12) * 14 = 9.33 feet

Therefore, the height of the light pole to the nearest tenth of a foot is 9.3 feet.

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The total line integral over c is: ∫c xy dx + (x − y) dy = ∫c1 xy dx + (x − y) dy + ∫c2 xy dx + (x − y) dy = 0 + 15√5/5 = 3√5.

To evaluate the line integral of the given curve, we need to split the integral into two parts corresponding to the line segments. Let's denote the first line segment as C1 and the second as C2. For C1, the curve goes from (0, 0) to (3, 0). Since y is constant (y = 0) along this segment, dy = 0, and the integral simplifies to:
∫(C1) xy dx = ∫(0 to 3) x*0 dx = 0 (because y = 0)
For C2, the curve goes from (3, 0) to (4, 2). We can parameterize this segment as x = 3 + t, y = 2t, where t goes from 0 to 1. Then, dx = dt and dy = 2 dt. Now, we can rewrite the integral:
∫(C2) xy dx + (x - y) dy = ∫(0 to 1) [(3 + t)(2t) dt + ((3 + t) - 2t)(2 dt)]
Now, evaluate the integral:
= ∫(0 to 1) [6t² + t³ + 2(3 + t - 2t) dt]
= ∫(0 to 1) [6t² + t³ + 6 dt - 2t dt]
= ∫(0 to 1) [6t² + t³ + 6 - 2t] dt
Finally, integrate with respect to t and evaluate the limits:
= [2t³ + (1/4)t⁴ + 6t - t²] (from 0 to 1)
= (2 + 1/4 + 6 - 1) - (0)
= 7.25
So, the total line integral is the sum of the integrals along the two line segments:
∫C = ∫(C1) + ∫(C2) = 0 + 7.25 = 7.25

To evaluate the line integral ∫c xy dx + (x − y) dy, where c consists of line segments from (0, 0) to (3, 0) and from (3, 0) to (4, 2), we need to break up the curve c into two line segments and apply the line integral formula for each segment.
First, consider the line segment from (0, 0) to (3, 0). This segment lies along the x-axis and is parameterized by x = t and y = 0, where 0 ≤ t ≤ 3. Thus, dx = dt and dy = 0, and we have:
∫c1 xy dx + (x − y) dy = ∫0^3 t(0) dt + (t − 0)(0) dt = ∫0³ 0 dt = 0
Next, consider the line segment from (3, 0) to (4, 2). This segment is parameterized by x = 3 + t/√5 and y = 2t/√5, where 0 ≤ t ≤ √5. Thus, dx = dt/√5 and dy = 2dt/√5, and we have:
∫c2 xy dx + (x − y) dy = ∫0√5 (3 + t/√5)(2t/√5)(dt/√5) + (3 + t/√5 − 2t/√5)(2dt/√5)
= ∫0√5 (6t/5) dt/5 + (3 + t/√5 − 2t/√5)(2dt/√5)
= ∫0√5 (6t/25) dt + (6/√5)(dt/√5)
= (3/25)(√5)² + (12/5)(√5)
= 3√5/5 + 12√5/5
= 15√5/5
Therefore, the total line integral over c is: ∫c xy dx + (x − y) dy = ∫c1 xy dx + (x − y) dy + ∫c2 xy dx + (x − y) dy = 0 + 15√5/5 = 3√5

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Answer:

y = (x + 3)^2 + 1

Step-by-step explanation:

100% on edge

Have a nice day :]

The equation in vertex form is \(y = (x + 3)^2 + 1\), and the values of h & k are -3 and 1

The vertex form of an equation is a quadratic equation, written in the form of a parabola

The equation is given as:

\(y = x^2 + 6x + 10\)

Write out the constant

\(y = (x^2 + 6x) + 10\)

Take the coefficient of x

\(k = 6\)

Divide by 2

\(k/2 = 3\)

Square the expression

\((k/2)^2 = 9\)

So, we have:

\(y = (x^2 + 6x + 9 - 9) + 10\)

Rewrite as:

\(y = (x^2 + 6x + 9) -9+ 10\)

\(y = (x^2 + 6x + 9) + 1\)

Express as a perfect square

\(y = (x + 3)^2 + 1\)

Hence, the equation in vertex form is \(y = (x + 3)^2 + 1\), and the values of h & k are -3 and 1

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The correct answer is a. the inclusion-exclusion principle must be used to find the number of bit strings of length seven that either begin with two Os or end with three 1s.

This is because we need to subtract the number of bit strings that both begin with two Os and end with three 1s (which are counted twice if we simply add the number of bit strings that begin with two Os and the number that end with three 1s). The inclusion-exclusion principle allows us to do this by first adding the number of bit strings that begin with two Os and the number that end with three 1s, and then subtracting the number of bit strings that both begin with two Os and end with three 1s.

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3(u-6) = 3u-18

Step-by-step explanation:

The question is 3(u-6).

We simply multiply 3*u=3u and 3*6=18, so we will get

3(u-6) = 3u-18

Answer:

\(d = 5\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point A (1, 2)

Point B (5, 5)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

(6-√21,  6+√21)

Step-by-step explanation:

x^2 - 12x = -15

(x - 6)^2 - 36 = -15

(x - 6)^2 = 21

x - 6 = ± √21

x = 6  ± √21

The solution set of the given equation is (6-√21,  6+√21)

Given is an equation, x² - 12x = -15 we need to solve it by completing the square.

Solving the equation,

x² - 12x = -15

(x - 6)² - 36 = -15

(x - 6)² = 21

x - 6 = ± √21

x = 6  ± √21

Therefore, the solution set is (6-√21,  6+√21)

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The average is calculated by adding up all the data sets, then dividing that total by the total number of data points. She used 6 gallons of gas on her trip.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The two unit rates of (30 miles per gallon) and can be used to convert three hours to gallons of gas (60 miles per hour).

30 miles = 1 gallon of gas used

For (30 × 2) 60 miles = 2 gallons of gas used

2 gallons of gas she used per hour.

Susan goes 180 miles in 3 hours (60 miles per hour).

Therefore,

For 3 hrs = 3 × 2 = 6 gallons of gas used.

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As per the 95% confidence interval, the margin of error is 22.0495

The term confidence interval is known as a probability that a population parameter will fall between a set of values for a certain proportion of times.

Here we have given that  in order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. the average weight was 18 pounds and the sample variance is 56.25 pounds.

And we need to find at 95% confidence, what is the margin of error.

While we looking into the given question, we have identified that the following values are given,

=> Sample size = 25

=> average weight = 18

=> sample variance = 56.25

=> confidence interval = 95%

Then the margin of error is calculated as,

First, find the critical value: is calculated as,

=> z = 1.9599

Then next, we have to find the standard error of the mean:

=> SE = σ/√n = 45/4

Here finally, the margin of error is

=> ME = z x SE

=> ME = 1.9599 x (45/4) ≈22.0495

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The confidence level used for the margin of error was 95%.

The margin of error (MOE) is calculated by dividing the critical value (z*) of the confidence level by the square root of the sample size (n). For a 95% confidence level, the critical value (z*) is 1.96. MOE = 1.96 / sqrt(350) = 4.382% Therefore, the confidence level used for the margin of error was 95%. To calculate the margin of error, we must first determine the confidence level. For a 95% confidence level, the critical value (z*) is 1.96. The margin of error (MOE) is then calculated by dividing the critical value (z*) by the square root of the sample size (n). In this case, the MOE is 1.96 / sqrt(350) = 4.382%. This means that the confidence level used for the margin of error was 95%.

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Answer:

y = 3x + 7

Step-by-step explanation:

Using the formula y = mx + b we can create this equation.

m = slope

b = y -intercept

based on the information provided I know that

Slope = 3

and

y-intercept = 7

Substitute:

y = mx + b

y = 3x + 7

y = 3x + 7 is the equation when the slope is 3 and the y intercept is 7.

Let us use the slope-intercept form for this, with m as the slope and b as a constant.

y = mx + b

7 = 3(0) + b  [since the y-int is 7, the x value will be zero]

b = 7

y = 3x + 7

Answer:

150.5 is median

148 is your mean

and 60 is a range

Finding the volume of a cylinder is similar to finding the volume of a prism because both structures have congruent and parallel bases. In both cases, the volume is obtained by multiplying the area of the base (a polygon for a prism and a circle for a cylinder) by the height of the figure.

The volume of a cylinder is determined by multiplying the area of its base, which is a circle, by its height. Similarly, the volume of a prism is found by multiplying the area of its base, which is a polygon, by its height.

In both cylinders and prisms, the bases are congruent, meaning they have the same shape and size. The bases are also parallel, as they lie in parallel planes. This similarity allows for the application of the same formula to calculate their volumes.

By multiplying the area of the base by the height, we are essentially stacking identical cross-sectional areas (the base) along the height of the figure to form a solid shape. This process accounts for the three-dimensional space occupied by the figure and provides an accurate measure of its volume.

Therefore, despite their different cross-sectional shapes, cylinders and prisms share the same approach to finding volume, emphasizing the congruence and parallelism of their bases and the multiplication of base area by height.

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Answer:

\(K' = 83^o\)

Step-by-step explanation:

Given

\(K = 83^o\)

Reflection: \(y= 2\)

Required

K'

The general rule is that, reflection does alter measurements (angles or lengths).

So, this means that K' will have the same measure as K.

i.e.

\(K' = K\)

\(K' = 83^o\)