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The reflected figure is labeled figure C is B: A is congruent to A, B is congruent to B, C is congruent to C. The correct answer is B: A is congruent to A, B is congruent to B, C is congruent to C.

To explain why figure A is congruent to figure C, we need to understand the transformations that were applied to create each figure.

In the given scenario, figure A was translated 3 units to the right and 2 units up to create figure B. This means that every point in figure A was shifted horizontally by 3 units to the right and vertically by 2 units up to obtain the corresponding points in figure B.

Next, figure B was reflected over the x-axis to create figure C. This reflection flips the figure vertically, so the y-coordinates of each point are negated while the x-coordinates remain the same.

Now, if we compare the coordinates of figure A and figure C, we can see that the x-coordinates of each point in figure C are the same as in figure A, while the y-coordinates are negated. This means that the two figures have the same shape and size, just positioned differently on the coordinate plane.

Therefore, we can conclude that figure A is congruent to figure C because they have the same shape and size, even though they are located in different positions on the coordinate plane.

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Answer:

im study about history it was my favourite subject!

Answer:

5x + 7x = 1,224

12x = 1,224

x = 102

5(102) = 510 men, 7(102) = 714 women

You will pay S/.80 for 2 bananas, 3 peaches, and a pineapple.

Let the price of a banana be b, a peach p, a medlar m, and a pineapple P in Peruvian soles.

From the information, 8b=6p, 4p=10m, 12m=2P, and 10P=S/.320.

From these equations, we have p=4b/3, m=p/2=2b/3, and P=6m=4b.

Substituting for P, 10(4b)=320, so b=8. Hence, p=32/3, m=16/3, and P=32.

For 2 bananas, 3 peaches and a pineapple, the total cost is 2b+3p+P = 2(8) + 3(32/3) + 32 = 16 + 32 + 32 = S/.80.

Therefore, you will pay S/.80 for 2 bananas, 3 peaches, and a pineapple.

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The Question in English

At a fair they sell 8 bananas at the same price as 6 peaches, 4 peaches the same as 10 medlars. A dozen medlars at the same price as 2 pineapples, if 10 pineapples cost S/.320, how much will I pay for 2 bananas, 3 peaches and a pineapple?

Option A. c - 0 = b - a is the missing statement in Step 4 of the proof.

To determine the missing statement in Step 4 of the proof, let's examine the given table and image related to the relationship between the slopes of two parallel lines.

Step 1: Given the slopes of two parallel lines, m₁ and m₂.

Step 2: Assume two points on each line: (0, a) and (c, b).

Step 3: Calculate the slopes using the slope formula: m₁ = (b - a) / (c - 0) and m₂ = (d - a) / (0 - c).

Step 4: ??? (Missing Statement)

Step 5: Since the lines are parallel, the slopes are equal, so m₁ = m₂.

By analyzing the given information, we can identify the missing statement by comparing the calculated slopes:

From Step 3, we have:

m₁ = (b - a) / (c - 0)

m₂ = (d - a) / (0 - c)

Comparing the two slopes, we can see that (b - a) / (c - 0) = (d - a) / (0 - c).

To express this relationship, the missing statement in Step 4 should be:

A. c - 0 = b - a

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The correct option is the third one.

The new vertices are:

(-4, -1), (0, -1). (-4, -3)

For a point (x, y), a rotation of 90° counterclockwise changes a quadrant, and changes the coordinates to (-y, x)

So, for the point (-1, 4) which is on the second quadrant, it will move it to the third quadrant, so the new point is (-4, -1)

For the second point:

(-1, 0)

It is on the second quadrant, and we go to the third one again, the new point is (0, -1)

Finally_

(-3, 4) --> (-4, -3)

Then the correct option is the third option.

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The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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The distance along the ground between the building and the pilot is approximately 92.19 feet (rounded to the nearest tenth).

To find the distance along the ground between the building and the pilot, we can use trigonometry.

We have the following information:

Angle of elevation (θ) = 38°

Distance from the building to the pilot (opposite side) = 72 ft

We need to find the adjacent side, which represents the distance along the ground.

Using the trigonometric function tangent (tan), we can set up the following equation:

tan(θ) = opposite/adjacent

tan(38°) = 72/adjacent

To find the adjacent side, we rearrange the equation:

adjacent = 72 / tan(38°)

Using a calculator, we can evaluate this expression:

adjacent ≈ 72 / 0.7813 ≈ 92.19 ft

Therefore, the distance along the ground between the building and the pilot is approximately 92.19 feet (rounded to the nearest tenth).

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The inverse statement is false.

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The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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The exponential equation to model Puerto Rico's population in millions after t years is:

[tex]P(t) = 3.72 \times e^(^-^0^.^1^1^8^t^).[/tex]

To model Puerto Rico's population in millions after t years using an exponential equation, we can use the following formula:

[tex]P(t) = P₀ \times e^(^r^t^),[/tex]

where:

P(t) is the population at time t,

P₀ is the initial population (in 2010),

e is the base of the natural logarithm (approximately 2.71828), and

r is the growth rate.

Given that the population of Puerto Rico in 2010 was approximately 3.72 million people, we can substitute P₀ = 3.72 into the equation.

Now, to determine the growth rate (r), we need to consider the population decrease of 11.8% since 2010. We can convert this percentage into a decimal by dividing it by 100, so 11.8% becomes 0.118.

Since the population decreased, we use a negative growth rate, so r = -0.118.

Therefore, the exponential equation to model Puerto Rico's population in millions after t years is:

[tex]P(t) = 3.72 \times e^(^-^0^.^1^1^8^t^).[/tex]

This equation takes into account the initial population in 2010 and the negative growth rate to project the population in millions for any given year (t) after 2010.

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The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

The initial number of people on the bus was 39.

To find out how many people were on the bus initially, we can work backwards from the given information. If 22 people got off the bus and 17 people remained on the bus, we can assume that the total number of people who got off and those who remained accounts for the entire initial number of people on the bus.

Let's denote the initial number of people on the bus as 'x'. According to the information provided, 22 people got off the bus, so the number of people who remained on the bus is 'x - 22'. We are also given that 17 people remained on the bus, so we can set up the equation:

x - 22 = 17

To solve this equation, we can add 22 to both sides:

x - 22 + 22 = 17 + 22

This simplifies to:

x = 39

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The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.

To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.

Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.

Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).

Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).

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Answer:

The answer is $3.91 hope it is help you

Angle a + Angle d = 180 degreesAngle b + Angle c = 180 degrees.

In a parallelogram, adjacent angles are supplementary. As a result, we can express c in terms of the angles adjacent to it as follows: Angle a + Angle c = 180 degreesAngle c + 46 degrees = 180 degreesAngle c = 180 degrees - 46 degrees = 134 degreesTherefore, the size of angle c is 134 degrees.

A parallelogram is a four-sided quadrilateral that has opposite sides parallel and equal in length. Each of the opposite angles is also equal in size.In general, if we label the angles of a parallelogram as follows: Angle a, Angle b, Angle c, and Angle d,.

we have the following:Angle a = Angle c (opposite angles are equal)Angle b = Angle d (opposite angles are equal)Adjacent angles in a parallelogram are supplementary, which means they add up to 180 degrees.

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The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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Answer:

[tex]\frac{30meters}{second}[/tex]

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

[tex]\frac{108km}{1hour}[/tex] · [tex]\frac{1hour}{60 minutes}[/tex] · [tex]\frac{1minute}{60seconds}[/tex] ·[tex]\frac{1000meters}{1 km}[/tex]

[tex]\frac{108000meters}{3600seconds}[/tex]

[tex]\frac{30meters}{second}[/tex]

[tex]\frac{30meters}{second}[/tex] ·[tex]\frac{20seconds}{1}[/tex]

600 meters

Helping in the name of Jesus.

Trapezoid 1 is similar to trapezoid 2 because trapezoid 1 can be mapped onto trapezoid 2 by a series of transformations.

In Mathematics and Geometry, two geometric figures such as trapezoids are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

This ultimately implies that, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar;

Scale factor = √10/√2 = 5/2.5 = 7/3.5

Scale factor = 2.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The value of x is 70 degrees.

To find the value of x, we can use the properties of angles in a circle.

In the given circle, we have a diameter AB passing through the center of the circle, labeled as point C. Point D is located at 2 o'clock, point B at 3 o'clock, and point A at 9 o'clock.

We are given that angle ABD is labeled as 70 degrees. Since angle ABD is an angle formed by a chord (AB) and a tangent (BD), we can apply the property that the measure of an angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.

In this case, angle ABD intercepts the arc AB. Since AB is a diameter, it subtends a 180-degree arc. Therefore, the measure of angle ABD is equal to half the measure of the intercepted arc AB, which is 180 degrees divided by 2, resulting in 90 degrees.

Now, let's focus on angle DAB, labeled as x. Since angle DAB and angle ABD are vertical angles (angles formed by the intersection of two lines), they have the same measure. Therefore, x is also equal to 70 degrees.

In conclusion, the value of x is 70 degrees.

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Answer:

x = 150 , y = 30 , z = 60

Step-by-step explanation:

x and 30° are same- side interior angles and sum to 180° , that is

x + 30 = 180 ( subtract 30 from both sides )

x = 150

-------------

x and y are a linear pair and sum to 180° , that is

x + y = 180

150 + y = 180 ( subtract 150 from both sides )

y = 30

----------------

since EF and EG are congruent then Δ EFG is isosceles with base angles congruent , then

2 = y = 30

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

z is an exterior angle of Δ EFG , then

z = ∠ 2 + ∠ y = 30 + 30 = 60

Answer:

hikers can travel before they have to turn around be "d" days. Also, let's represent the supplies the hikers have with "s."Given that after three days the hikers used 2/5 of their supplies, we can say that they have 3/5 of their supplies left. Hence,3/5s = Supplies remaining after 3 days, which means that2/5s = Supplies used in the first 3 daysWe need to find the number of days the hikers can travel before they have to turn around. So, we can say that the ratio of supplies used to the number of days traveled will be equal to the ratio of supplies remaining to the number of days remaining.2/5s ÷ 3 = (3/5s) ÷ dWe can simplify the above expression to find d as:d = (3/2) × 3/5 = 9/10 daysTherefore, the hikers can go forward for 9/10 days before they have to turn around.

Answer: The caret symbol (^) represents a power.

Step-by-step explanation:

In short, a power or an exponent indicates the number of times a number needs to be multiplied by itself. The caret can be used to represent a number that is to be used as an exponent.

For example, 5^2 is the same thing as [tex]5^2[/tex]. [tex]5^{2} =[/tex] 5 x 5 = 25.

In the example you provided, 1200 x (1.0041666667) ^ 48, the caret means that you need to raise 1.0041666667 to the power of 48.

The Laplace transform of the given function is L{(2+6)te^((2+0)t)+(3+0)sin3t}. Simplifying the expression inside the Laplace transform, we get L{8te^(2t)+3sin3t}.

The Laplace transform of te^(at) is (s-a)^(-2) and the Laplace transform of sin(at) is a/(s^2+a^2). Substituting these values into the expression, we get:

L{8te^(2t)+3sin3t} = 8(s-2)^(-2) + 3(3/(s^2+9)) = 8/(s-2)^2 + 9/(s^2+9)

This is the simplified form of the Laplace transform of the given function.

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The system of linear inequalities that represent the graph is y ≥ -4x + 1 and y > -x - 2

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

Graph 1: (1, -3) and (0, 1)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 1

Using the other points, we have

m + 1 = -3

So, we have

m = -4

So, we have

y = -4x + 1

As an inequality, we have

y ≥ -4x + 1

Also, we have

Graph 2: (1, -3) and (0, -2)

So, we have

y = mx - 2

Using the other points, we have

m - 2 = -3

So, we have

m = -1

So, we have

y = -x - 2

As an inequality, we have

y > -x - 2

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If two different signs are multiplied, the product obtained should be multiplied by another negative sign. We would then get the last sign as positive.

When two different signs are multiplied, the product obtained should be multiplied by another negative sign. When two different signs are multiplied, we obtain either a positive or negative product depending on the signs. If both signs are positive, the product is positive. If both signs are negative, the product is also positive.

However, if two different signs are multiplied, the product is negative. This is the first step in answering the question.

After we obtain a negative product by multiplying two different signs, we are to multiply this product with another negative sign. Multiplying a negative product with another negative sign would yield a positive result. This is because the product of two negatives is positive.

To understand this concept, we can use numbers as examples. Let us say we want to multiply -5 and 7. The product of -5 and 7 is -35 since we are multiplying two different signs. Now we are to multiply this product with another negative sign, say -1. Multiplying -35 and -1, we obtain +35, which is the answer to the problem.
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A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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The y-intercept of line ↔AB is 56/5.

The equation of line ↔CD is y = (-7/5)x + 12.

To find the y-intercept of line ↔AB, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

Given the coordinates of point A (8, 0) and point B (3, 7), we can calculate the slope of line ↔AB:

slope (m) = (y₂ - y₁) / (x₂ - x₁)

= (7 - 0) / (3 - 8)

= 7 / -5

= -7/5

Now, we can substitute the slope (-7/5) and the coordinates of point A (8, 0) into the slope-intercept form to find the y-intercept:

0 = (-7/5)(8) + b

Simplifying:

0 = -56/5 + b

To isolate b, we can add 56/5 to both sides:

b = 56/5

Therefore, the y-intercept of line ↔AB is 56/5.

Moving on to line ↔CD, given the coordinates of point D (5, 5), we can use the point-slope form of a linear equation to find the equation of the line:

y - y₁ = m(x - x₁)

Substituting the coordinates of point D (5, 5) and the slope from the previous calculation (-7/5), we have:

y - 5 = (-7/5)(x - 5)

Expanding and simplifying:

y - 5 = (-7/5)x + 7

Rearranging the equation to slope-intercept form:

y = (-7/5)x + 7 + 5

y = (-7/5)x + 12

Therefore, the equation of line ↔CD is y = (-7/5)x + 12.

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When m = -4, the expression 8100.3m evaluates to -24300.12.

To evaluate the expression 8100.3m for m = -4, we substitute the value of m into the expression:

8100.3m = 8100.3(-4)

Now, we can calculate the value:

8100.3(-4) = -24300.12

Therefore, when m = -4, the expression 8100.3m evaluates to -24300.12.

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