please help fill these in..​

The AA criterion for the similarity between two triangles means that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar.

The steps to prove the AA criterion for similarity using GeoGebra is as follows:

Open GeoGebra and select the "Geometry" option to create a new geometry file.

From the toolbar on the left, select the "Triangle" tool and create two triangles by clicking on three points on the screen.

Use the "Measure" tool to measure the angles in both triangles. To do this, select the "Measure" tool from the toolbar, click on one of the angles in the first triangle, and then click on the corresponding angle in the second triangle.

Record the measurements of the two corresponding angles and calculate their values.

Use the "Move" tool to adjust the position of one of the triangles. Make sure that the two corresponding angles are still the same size.

Observe the triangles to see if they still appear to be similar, even after the movement.

Repeat the process several times, each time moving one of the triangles and observing if they are still similar.

Draw a conclusion based on your observations. Can you prove that the two triangles are similar based on the AA criterion?

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The depreciation expense for each year is 1,000,000 shs.

Accumulated depreciation up to year 6 is 6,000,000 shs.

The depreciation using the straight line method is given by the formula:

Depreciation expense per year = (Initial cost - Salvage value) / Useful life

Initial cost = 5,000,000 + 800,000 + 1,500,000 = 7,300,000 shs.

Salvage value = 1,300,000 shs.

Depreciation expense per year = (7,300,000 - 1,300,000) / 6

                                                    = 6,000,000 / 6

                                                    = 1,000,000 shs.

Thus, the depreciation expense for each year is 1,000,000 shs.

Accumulated depreciation up to year 6 = Depreciation expense per year * Number of years

Accumulated depreciation up to year 6 = 1,000,000 * 6 = 6,000,000 shs.

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The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.

Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.

cos(35°) = adjacent side (FH) / hypotenuse (GH)

We know that FH = 18.4 in. So, we can write the equation as:

cos(35°) = 18.4 / GH

GH = 18.4 / cos(35°)

GH = 18.4 / 0.81915

=  22.46 inches

So, the length of GH, the hypotenuse, is approximately 22.46 inches.

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Let [tex]x[/tex] be the unknown side of the triangle. Find the length of this side from the Pythagorean Theorem;

Another root of the equation is also negative, but we've eliminated it because length can't be a negative value.

To find the area of a triangle, we multiply the height of the triangle by the base length and take half.

Answer:

Trapezoid

Step-by-step explanation:

It's a quadrilateral and it only has one pair of parallel sides.

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

The truth table for the given expression can be given using p= T q = T, p^q = T, ~p = F, ~q = F, ~q v ~p = T, and  (p ^ q) =~p v ~q = T, thus proving the required.

The field of symbolic logic known as propositional logic, also referred to as sentential logic or statement logic, is concerned with propositions or statements, which are declarative phrases that can be true or untrue. To represent propositions and their relationships, propositional logic employs symbols and operators.

Many disciplines, including mathematics, computer science, philosophy, and others, employ propositional logic as a tool for debating the truth or falsity of propositions and analysing arguments.

The truth table for the given expression can be given as:

p  |  q  |  p ^ q  |  ~p  |  ~q  |  ~q v ~p  |  (p ^ q) =~p v ~q

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

T  |  T  |    T    |   F  |  F   |    T     |         T

T  |  F  |    F    |   F  |  T   |    T     |         T

F  |  T  |    F    |   T  |  F   |    T     |         T

F  |  F  |    F    |   T  |  T   |    T     |         T

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La velocidad requerida para que una partícula de 6 kg alcance una energía cinética de 20 joule es de aproximadamente 2.58 m/s. La respuesta es A.

Velocidad

La fórmula para calcular la energía cinética es:

E_cinética = 1/2 * m * v^2

Donde m es la masa de la partícula y v es su velocidad.

Dado que la energía cinética y la masa de la partícula son conocidas, podemos despejar la velocidad de la siguiente manera:

20 J = 1/2 * 6 kg * v^2

20 J = 3 kg * v^2

v^2 = 20 J / 3 kg

v = √(20 J / 3 kg)

v ≈ 2.58 m/s

Por lo tanto, la velocidad requerida para que una partícula de 6 kg alcance una energía cinética de 20 joule es de aproximadamente 2.58 m/s. La respuesta es a).

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One per 2,500 can be used to represent the rate of 80cm to 2km.

To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):

80 cm/100,000 = 0.0008 km

Now we can express the rate as:

0.0008 km per 2 km

Or we can simplify it by dividing both the numerator and denominator by 0.0008:

1 per 2,500

Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.

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Answer:

  (d)  25 feet and 20 feet​

Step-by-step explanation:

You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.

The area is the product of the length and width. The area of the pools offered in the answer choices are ...

  (a)  15·30 = 450 . . . square feet

  (b)  10·35 = 350 . . . square feet

  (c)  50·10 = 500 . . . square feet

  (d)  25·20 = 500 . . . square feet

The area requirement eliminates answer choices A and B.

The perimeter is twice the sum of length and width. The perimeters of the possible pools are ...

  (c) 2(50 +10) = 120 . . . feet

  (d) 2(25 +20) = 90 . . . feet

The perimeter requirement eliminates answer choice C.

The pool's possible length and width are 25 feet and 20 feet, choice D.

__

Additional comment

You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.

If x is the width, then 45-x is the length, and the area is ...

  x(45 -x) = 500

  x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square

  x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension

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The correct option -D. 5;  Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

A line that precisely intersects a circle at two points is said to be a secant.

The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.

Using the Theorem:

The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:

4(4 + x) = 6²

16 + 4x = 36

4x = 36 - 16

4x = 20

x = 20/4

x = 5

Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

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Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

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The requried quantity of drug that remains in the body, in the long run, is 220 mg.

Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:

[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]

We can see that the formula for [tex]D_n[/tex] is:

[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]

Simplifying this formula, we get:

[tex]D_n = 220 * (1 - 0.95^n)[/tex]

Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex]  as n goes to infinity. Using the formula above, we can see that:

[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]

Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.

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Answer:

Tyshawn would have to sell 6 computers on a given day to get paid $225

Step-by-step explanation:

We can use the information in the table to find the equation of the linear relationship between a (the number of computer sales) and p (Tyshawn's total pay):p = 75 + 25aThis equation tells us that Tyshawn's total pay is $75 plus $25 for each computer he sells.To find out how many computers Tyshawn would have to sell in order to get paid $225 on a given day, we can substitute p = 225 into the equation and solve for a:225 = 75 + 25a150 = 25aa = 6

The histogram should be modified as follows:

A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.

Then the height of the histogram gives the number of observations into each data interval.

Hence the histogram should be modified as follows:

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Answer:

33 thats with the 1 dollar subtracted for the entry fee

Step-by-step explanation:

first you add all the number of marbles you have then you get 41 then divide it by 12 because you have 2 gold and 10 silver and you get 3.4 and multiply that by 10 because its 6 and 4 and you get 34 subtract the entry fee

In a a case whereby factory that has 6 X 10³ workers makes 2.4 X 105 products each day, the average amount of products made per worker is 4 *10^1 products per worker

The term "average" in mathematics typically refers to a measure of central tendency, which is a way to describe the typical or common value in a set of numbers. There are several types of averages.

We can calculate the required value as

( 2.4 X 10^5 )/ (6 X 10³)

=4 *10^1 products per worker

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Answer:

D

Step-by-step explanation:

A rotation and translation preserves the length measures of the sides, so FD is equal to 7 inches

Answer: D

Step-by-step explanation:

If  Lee has a catering company. His staff is making pies for an event.  there are 41 pies that have only rhubarb filling.

To find the number of pies that have only rhubarb filling, we need to subtract the pies that have rhubarb filling and another filling(s) from the total number of pies that have rhubarb filling.

We can use the given information to create a Venn diagram to visualize the relationships between the different fillings:

        _______________

         /      (3)      \

        /______ 14 ______\

       /       /    \      \

      /  (1) / (5)  \ (2)  \

     /_____/_______ \______\

          /         \       \

         /     (4)     \______\

(1) represents the number of pies that have only cherry filling,

(2) represents the number of pies that have only strawberry filling,

(3) represents the number of pies that have only rhubarb filling,

(4) represents the number of pies that have cherry and strawberry filling, but not rhubarb filling,

(5) represents the number of pies that have rhubarb and strawberry filling, but not cherry filling.

We can use the given information to fill in the values in the Venn diagram:

68 pies have cherry filling (1) + (4) + (6) + (7) + (8) + (9) + (10) + (14) = 68

73 pies have strawberry filling (2) + (4) + (5) + (7) + (8) + (9) + (10) + (14) = 73

30 pies have rhubarb and cherry filling (6) + (7) + (10) + (14) = 30

23 pies have rhubarb and strawberry filling (5) + (7) + (9) + (10) + (14) = 23

12 pies have only strawberry and cherry filling (7) = 12

14 pies have all three fillings (14) = 14

To find the number of pies that have only rhubarb filling, we can start by adding up the pies that have rhubarb filling and no other fillings: (3) + (6) + (9) + (10).

(3) is already the number of pies that have only rhubarb filling. For the other three regions, we need to use the values in the Venn diagram to calculate the number of pies with the given combinations of fillings:

Adding up the number of pies that have only rhubarb filling from each region, we get:

Number of pies that have only rhubarb filling = (3) + (24) + (14) + (0) = 41.

Therefore, there are 41 pies that have only rhubarb filling.

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a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]

b)  the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

What is exponential equation?

An exponential equation is one in which the exponent contains a variable.

(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation

log8 1/64 = 2

means that 8 raised to the power of 2 is equal to 1/64:

[tex]8^2 = 1/64[/tex]

Thus, we can write the exponential equation as:

[tex]1/64 = 8^{(-2)}[/tex]

Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]

(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation

[tex]3^0 = 1[/tex]

means that the logarithm of 1 to the base 3 is equal to 0:

log3 1 = 0

Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

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The surface soil of the entire garden within the fencing that needs to be turned prior to planting is approximately 176.625 square feet.

Radius is a mathematical term that refers to the distance from the center of a circle, sphere, or other curved object to any point on its circumference or surface. It is typically denoted by the letter "r".

Let's call the radius of the circular garden "r". We know that the circumference of the garden (the length of the fence) is 47.1 feet, so we can set up the equation:

2πr = 47.1

Simplifying this equation by dividing both sides by 2π, we get:

r = 47.1/(2π)

Using 3.14 as a substitute for π, we can calculate:

r ≈ 7.5 feet

Now that we know the radius of the garden, we can calculate the area of the garden by using the formula for the area of a circle:

A = πr²

A = 3.14 * 7.5²

A ≈ 176.625 square feet

Therefore, the surface soil of the entire garden within the fencing that needs to be turned prior to planting is approximately 176.625 square feet.

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Finally, the number is divisible by 9 because the sum of its digits is 27, which is a multiple of 9 is 7,983.

In mathematics, a number is a quantity or value used to represent a quantity or a position in a sequence. Numbers are used to quantify things and to perform mathematical operations such as addition, subtraction, multiplication, and division. There are many different types of numbers, including natural numbers (1, 2, 3...), integers (..., -2, -1, 0, 1, 2, ...), rational numbers (numbers that can be expressed as a ratio of two integers), irrational numbers (numbers that cannot be expressed as a ratio of two integers), and real numbers (all rational and irrational numbers). Numbers can also be classified as positive, negative, or zero. Positive numbers are greater than zero, negative numbers are less than zero, and zero represents a neutral or null value. Numbers are used extensively in many fields of study, including science, engineering, economics, and statistics. They are used to quantify measurements, represent data, and make predictions based on patterns and relationships.

Here.

It is odd and between 3,000 and 8,000.

The largest digit in our number system is 9, which is in the one's place.

Two of the digits in the number are the same digit, which is 8 in the thousand's and ten's place.

The hundred's digit and ten's digit are both 8, so the difference is zero.

The digit in the thousand's place is 4 less than the one's place, which is 5.

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[tex]\sqrt{363}-3\sqrt{27} ~~ \begin{cases} 363=3\cdot 11\cdot 11\\ \qquad 3\cdot 11^2\\ 27=3\cdot 3\cdot 3\\ \qquad 3\cdot 3^2 \end{cases}\implies \sqrt{3\cdot 11^2}-3\sqrt{3\cdot 3^2} \\\\\\ 11\sqrt{3}-3(3)\sqrt{3}\implies 11\sqrt{3}-9\sqrt{3}\implies 2\sqrt{3}[/tex]

One such tool that enables us to visualise the given math issue using various-sized rectangles or bars is the bar model.

A bar model in mathematics is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes. To answer issues involving the four operations of addition, subtraction, multiplication, and division, bar models are most frequently utilised.

To help kids "see" mathematical structure, the bar model is utilised in teaching for mastery. It is not a method for solving issues, but rather a strategy to uncover the mathematical underpinnings of a problem and obtain knowledge and clarity to aid in its resolution.

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Image attached below,

George's kitten is approximately 15.23 yards away from its bed

What is distance?

Distance is a measure of the length or spatial separation between two points. It is a scalar quantity, which means it has magnitude but not direction. In physics, distance is often measured in units such as meters (m), feet (ft), kilometers (km), or miles (mi).

We can use the Law of Cosines to solve this problem. Let's call the distance from the kitten's final position to the bed "d". Then, we have:

d² = 23² + 14² - 2(23)(14)cos(140°)

d² = 529 + 196 + 644cos(140°)

d² = 529 + 196 - 644(0.766)

d² = 529 + 196 - 493.304

d² = 231.696

d = sqrt(231.696)

d ≈ 15.23

Therefore, George's kitten is approximately 15.23 yards away from its bed

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Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

In the Euclidean plane, a rectangle is a quadrilateral with four right angles.

A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.

A rectangle with four equal-length sides is a square.

Squares are not always rectangles, but rectangles are always squares.

So, the pool and walkway together have a 360 square foot total space.

Assume that the walkway is w feet in width.

Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).

Thus, we can construct the following equation:

(8 + 2w) x (10 + 2w) = 360

By enlarging and condensing the left side, we obtain:

4w² + 36w - 80 = 0

Using the quadratic formula, we can find w:

w = (-b ± √(b² - 4ac)) / 2a

Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:

w = (-36 ± √(36² - 4(4)(-80))) / 8

w = (-36 ± √(1872)) / 8

w ≈ -5.6 or w ≈ 3.6

We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.

Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

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The expression (23,000-789) * 19 = = 421409.

An expression can contain variables, constants, and mathematical operations, and it can be used to represent a wide variety of mathematical concepts and relationships.

According to given information:

To solve the expression (23,000-789) * 19, we need to perform the subtraction operation inside the parentheses first and then multiply the result by 19.

(23,000-789) equals 22,211.

So, we have:

(23,000-789) * 19 = 22,211 * 19

Now, we can multiply the two numbers using the standard multiplication method. We multiply each digit of 19 with the digits of 22,211 starting from the right and then add the results.

22,211 x  19 =

444422  (19 x 1 = 19, write 9 and carry 1) + 420789  (19 x 1 = 19, write 9 and carry 1, 19 x 2 = 38, write 8 and carry 3)

= 421409

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a) The angular velocity = 0.4π rad/s b) The linear velocity of the hamster = 4π cm/s.

Linear velocity is the rate of change of an object's position with respect to time. It measures how fast an object is moving in a straight line, and is often expressed in units of distance per time, such as meters per second or kilometers per hour.

a) The angular velocity of the wheel can be calculated as follows:

Angular velocity = (2π * number of revolutions) / time

Here, the wheel completes one revolution in 5 seconds, so the number of revolutions is 1 and the time is 5 seconds. Therefore,

Angular velocity = (2π * 1) / 5

Angular velocity = 0.4π rad/s (or approximately 1.26 rad/s)

b) The linear velocity of the hamster can be calculated as follows:

Linear velocity = radius * angular velocity

Here, the radius of the wheel is 10 cm, and the angular velocity we found in part (a) is 0.4π rad/s. Therefore,

Linear velocity = 10 cm * 0.4π rad/s

Linear velocity = 4π cm/s (or approximately 12.57 cm/s)

So the hamster is running at a linear velocity of approximately 12.57 cm/s.

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Answer:

$3.25

Step-by-step explanation:

An ice cream cone that has x scoops of ice cream costs 1 + 0.75x.

So an ice cream cone that has 3 scoops of ice cream costs
1 + 0.75×3 = 3.25 (dollars)