Name the vertex of ∠2.

Answer:

140 degrees

Step-by-step explanation:

first start by making the given angles equal each other because they are congruent.

2x+28=6x+4

Subtract 4 on both sides

2x+24=6x

subtract 2x on both sides

24=4x

divide both sides by 4 to get x

24/4=4x/4

6=x

next to find the actual number of the angle, plug 6 back into either one of the equations. Im gonna use the first one.

2x + 28

2(6) + 28

12+28= 40

Now that we have the number, we already know that a full circle is 360 degrees so half a circle is 180.

Take 40 and subtract from 180

180-40= 140

Well, m∠1 and m∠3 are congruent by the Vertical Angle Congruent Theorem (VACT). This means that because the angles are opposite of each other, their angles are the same because they are formed by the same two intersecting lines.

Because of this, we can set m∠1 and m∠3 equal to each other:

m∠1 = m∠3

(2x + 28) = (6x + 4)

2x + 28 = 6x + 4

-4x + 28 = 4

-4x = -24

-x = -6

x = 6

Knowing that x equals 6, we can use this to find m∠2. By the Supplementary Angles Theorem (SAT), angles that are on the same line add up to equal 180°. To use the SAT, we need to plug x in to find m∠1 or m∠3, because they are both the same:

x = 6

m∠1 = (2x + 28)

m∠1 = 2(6) + 28

m∠1 = 12 + 28

m∠1 = 40°

m∠3 also equals 40°.

Now that we have the value for ∠1 (or ∠3), we can use the SAT:

m∠2 + m∠3 = 180 ← You could also use m∠1, because they both equal the same!

m∠2 + 40 = 180

m∠2 = 140°

So, the measure of ∠2 is 140°.

If you have any questions, feel free to ask! :)

Answer:

180°

Step-by-step explanation:

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

22! / 20! × 2!

\(21 \times 11 = 231 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

Answer:

21

Step-by-step explanation:

We know that the total number of students has to be divisible by 3. So to solve this specific problem, you can either use a guess and check system, prior knowledge, or by using a factoring method.

If we try to divide all four answer choices evenly by 3, only 21 leaves us with a whole number. Therefore, there could be 21 students participating.

25/3 = 8.33

21/3 = 7

23/3 = 7.667

26/3 = 8.667

Answer:

16

Step-by-step explanation:

Area of a triangle = 1/2(b×h)

b or l = x+4

h = x

a = 40

1/2(x+4 × x) = 40

1/2(x+4 × x) = 40x + 4 × x / 2 = 40

4 × x = 4x

4x + x = 5x

5x/2 = 40

cross-multiply

40 × 2 = 5x

40 × 2 = 5x80 = 5x

divide both sides by 5

5x/5 = 80/5

5x/5 = 80/5x = 16

The correct answer is (D) If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

Mathematically, assume that B = {v₁, v₂, v₃, ........} is the set of vectors. Then B will be linearly independent if the vector equation

y₁v₁ + y₂v₂ + y₃v₃ + ........ = 0 possesses the trivial solution such that

y₁ = y₂ = y₃ = ........ = 0.

Let A be a matrix, then columns of A will be linearly independent if the equation Ax = 0 possesses the trivial solution. In other words, The row space of matrix A is the span of its rows. The column space denoted by

C(A) is the span of A’s columns. The dimension of the row and column spaces is always the same, which is known as the rank of A.

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The domain and range of the given function are equal to (0, 3.85) and (0, 18.75) respectively.

In this exercise, you're given the following function h(t) = -4.87t² + 18.75t. Next, we would equate the function to zero (0) to determine its domain as follows:

0= -4.87t² + 18.75t.

4.87t(-t + 3.85) = 0

t = 0 or t = 3.85.

Therefore, the domain is 0 ≤ t ≤ 3.85 or (0, 3.85).

h(t) = -4.87t² + 18.75t

h(t) = -4.87(t² - 3.85t + 3.85 - 3.85)

h(t) = -4.87(t - 1.925)² + 18.05

Therefore, the range is 0 ≤ h ≤ 18.05 or (0, 18.75).

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Answer:

A on EDGE 2022

Step-by-step explanation:

A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

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The correct option is "None of the answers".

To find the derivative ds/dt of the function s = \((tan^2(t) - sec^2(t))^5\), we'll use the chain rule.
Step 1: Differentiate the outer function with respect to the inner function. The outer function is s(u) = \(u^5,\) so ds/du = \(5u^4\).
Step 2: Differentiate the inner function with respect to t. The inner function is u(t) = \(tan^2(t) - sec^2(t)\), so du/dt = \((2tan(t).sec^2(t)) - (-2sec(t).tan(t).(sec^2(t)))\).
Step 3: Apply the chain rule by multiplying the derivatives from steps 1 and 2: \(ds/dt = ds/du * du/dt = 5u^4 * ((2tan(t)(sec^2(t))) - (-2sec(t)tan(t)(sec^2(t)))).\)

Now, substitute u(t) back into the equation:
\(ds/dt = 5(tan^2(t) - sec^2(t))^4 * (2tan(t)(sec^2(t)) + 2sec(t)tan(t)(sec^2(t)))\)

Therefore, the derivative ds/dt of the function \(s = (tan^2(t) - sec^2(t))^5 is 5(tan^2(t) - sec^2(t))^4 * (2tan(t)(sec^2(t)) + 2sec(t)tan(t)(sec^2(t))).\)

This does not match any of the given options, so the correct answer is "None of the other answers."

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Answer:

152%

Step-by-step explanation:

There is one whole grid shaded = 100%

The other grid has 13/25 shaded.  This is the same as 52/100=52%

100+52=152%

Answer: 152%

Step-by-step explanation: To easy please like

There are no other numbers that always work for dissecting a triangle into similar triangles. For other numbers, you can dissect a triangle into infinitely many similar triangles by recursively applying the above methods. However, four and six are the most basic and common dissections that result in similar triangles.

(a) To prove that any triangle can be dissected into four similar triangles, we can start by drawing an altitude from one vertex of the triangle to the opposite side, dividing the triangle into two smaller right triangles. We can then draw another altitude from the same vertex to the opposite side, dividing one of the smaller right triangles into two similar right triangles. This gives us a total of three similar triangles. Finally, we can draw a line from the vertex to the midpoint of the hypotenuse of one of the smaller right triangles, dividing it into two similar triangles.

To dissect any triangle into four similar triangles by connecting the midpoints of each side. When you connect these midpoints, you form a smaller triangle within the original one, and three additional triangles around it. Since all midpoints divide the sides in half, the ratios of corresponding side lengths are equal, which makes all four triangles similar.

(b)  To prove that any triangle can be dissected into six similar triangles, we can start by drawing a line from one vertex of the triangle to the midpoint of the opposite side, dividing the triangle into two smaller triangles. We can then draw another line from the same vertex to the midpoint of one of the sides of one of the smaller triangles, dividing it into two similar triangles. This gives us a total of three similar triangles. We can repeat this process for the other smaller triangle, dividing it into three similar triangles.

To dissect any triangle into six similar triangles, first draw an altitude from any vertex to the opposite side. Then, draw the midpoints of the two other sides and connect them to the intersection point of the altitude and the base. This creates six smaller triangles. The altitudes and midpoints preserve the angles, and the ratios of corresponding side lengths are equal, making all six triangles similar.

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On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

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The incenter is the intersection of the angle bisectors, the distances from the incenter to the sides are proportional to the lengths of the adjacent sides, which gives the desired proportionality.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

To sketch the segments representing the distance from the incenter to the sides of a triangle, we draw perpendiculars from the incenter to each of the sides, as shown in the attached image.

The segments representing the distances from the incenter P to the sides of the triangle are the inradii.

Let r1, r2, and r3 be the lengths of the inradii corresponding to sides AB, BC, and AC, respectively.

Then, we have:

r1 = distance from P to AB

r2 = distance from P to BC

r3 = distance from P to AC

To compare these distances, we use the fact that the incenter is the intersection of the angle bisectors of the triangle.

Therefore, the distance from the incenter to each side is proportional to the length of the corresponding side. More precisely, we have:

r1 : r2 : r3 = AB : BC : AC

This proportionality can be proved using the angle bisector theorem, which states that the length of the segment of an angle bisector in a triangle is proportional to the lengths of the adjacent sides.

Hence, the incenter is the intersection of the angle bisectors, the distances from the incenter to the sides are proportional to the lengths of the adjacent sides, which gives the desired proportionality.

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Answer:

x=−y+2

Step-by-step explanation:

Answer: 18.84

Step-by-step explanation:

Answer:

La fracción de bombones que se comieron entre los dos es \(\frac{7}{10}\)

La caja tenía 40 bombones.

Step-by-step explanation:

Sabes que Andrés se comió 1/5 de los bombones de una caja y Ana 1/2 de la misma. Para conocer la fracción de bombones que se comieron entre ambos, debes sumar las fracciones que comieron cada uno:

\(\frac{1}{5} +\frac{1}{2}\)

Para hacer suma de fracciones con distinto denominador, lo primero que hay que hacer es determinar un denominador común. Para eso debes calcular el mínimo común múltiplo (mcm) entre los denominadores.

En este caso, el mcm entre 5 y 2 es 10.

Ahora tienes que multiplicar cada numerador por el número que hayas multiplicado el denominador. Para ello, dividís el m.c.m entre el denominador inicial y el resultado se multiplica por el numerador de esa fracción:

Entonces:

\(\frac{1}{5} +\frac{1}{2}=\frac{2}{10} +\frac{5}{10}\)

Ahora  simplemente sumas los denominadores:

\(\frac{1}{5} +\frac{1}{2}=\frac{2}{10} +\frac{5}{10}=\frac{7}{10}\)

La fracción de bombones que se comieron entre los dos es \(\frac{7}{10}\)

Sabes que quedaron 12 bombones en la caja. Representando 1 la cantidad total de bombones, y si se comieron 7/10 de la caja, entonces quedaron:

\(1-\frac{7}{10}\)

Restando de manera similar al procedimiento usado para la suma se obtiene:

\(1-\frac{7}{10}=\frac{3}{10}\)

Finalmente podes aplicar la siguiente regla de tres: si 3/10 representa los 12  bombones que quedaron en la caja, entonces en 1 (que representa la cantidad total de bombones) cuantos bombones hay?

\(cantidad total de bombones=\frac{1*12}{\frac{3}{10} }\)

cantidad total de bombones=40

La caja tenía 40 bombones.

Answer:

scorpion -_-

Step-by-step explanation:

Answer:

Scopion

Step-by-step explanation:

Answer:

3 + 2k

Step-by-step explanation:

1/5(15+10k)

distribute

1/5 * 15 + 1/5 * 10k

3 + 2k

Answer:

3 + 2k

Step-by-step explanation:

First, I am going to explain what the distributive property is. Lets say he had the expression a(b + c). We can "distribute" the a to the b and c:

a(b + c) = ab + ac

We can apply the distributive property to the expression 1/5(15 + 10k):

1/5(15 + 10k)

= (1/5)(15) + (1/5)(10k)

= 3 + 2k

By using the distributive property, we found the expression 3 + 2k.

I hope you find my answer helpful.

The z-score is -0.933 and the interpretation is that Andy's score is -0.933 standard deviations away from the mean.

From the question, the given parameters about the distribution are

Mean value of the set of data = 100

Standard deviation value of the set of data = 15

The actual data value = 86

The z-score of the data value is calculated using the following formula

z = (Actual data - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (86 - 100)/15

Evaluate the difference

z = -14/15

Evaluate the quotient

z = -0.933

This means that the score is -0.933 standard deviations away from the mean.

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Complete question

The Wechsler IQ test is normally distributed with mean 100 points and standard deviation 15 points.

Andy Warhol was found to have an IQ of 86 on the Wechsler IQ test. What was his z-score and what does that mean in context?

a. (i) 4/5 + 1/3 = 17/15
  (ii) 4/5 + 1/3 = 0.933 (Three-digit chopping)
  (iii) 4/5 + 1/3 = 0.933 (Three-digit rounding)
  (iv) Relative error in (ii) = |(17/15) - 0.933| / (17/15) = 0.039
      Relative error in (iii) = |(17/15) - 0.933| / (17/15) = 0.039

b. (i) 4/5 x 1/3 = 4/15
  (ii) 4/5 x 1/3 = 0.267 (Three-digit chopping)
  (iii) 4/5 x 1/3 = 0.267 (Three-digit rounding)
  (iv) Relative error in (ii) = |(4/15) - 0.267| / (4/15) = 0.272
      Relative error in (iii) = |(4/15) - 0.267| / (4/15) = 0.272

c. (i) (1/3-3/11)+3/20 = -11/220
  (ii) (1/3-3/11)+3/20 = -0.050 (Three-digit chopping)
  (iii) (1/3-3/11)+3/20 = -0.051 (Three-digit rounding)
  (iv) Relative error in (ii) = |(-11/220) - (-0.050)| / (-11/220) = 0.077
      Relative error in (iii) = |(-11/220) - (-0.051)| / (-11/220) = 0.068

d. (i) (1/3+3/11)-3/20 = 19/220
  (ii) (1/3+3/11)-3/20 = 0.086 (Three-digit chopping)
  (iii) (1/3+3/11)-3/20 = 0.086 (Three-digit rounding)
  (iv) Relative error in (ii) = |(19/220) - 0.086| / (19/220) = 0.554
      Relative error in (iii) = |(19/220) - 0.086| / (19/220) = 0.554

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The correct answer is: The confidence interval from the first simulation is (0. 149, 0. 195), and the confidence interval from the second simulation is (0. 180, 0. 230). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 149 and 0. 195. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 180 and 0. 230.

The confidence interval is a range of values that is likely to contain the true proportion of wins with the new game strategy based on the sample data.

A 95% confidence interval means that if the simulation is repeated many times, the proportion of wins with the new game strategy will fall within this range 95% of the time.

The correct interpretation of the confidence intervals is that for the first simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.149 and 0.195.

This means that if we were to repeat the simulation many times, we would expect the true proportion of wins to fall between these values in 95% of the trials.

Similarly, for the second simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.180 and 0.230.

Therefore, the correct answer is an option (b).

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11.4 centimeters is the radius of the cylinder .

What does volume mean in plain terms?

The capacity of a solid shape is determined using volume, a three-dimensional quantity.

                     It implies that a closed figure's volume determines how much three-dimensional space it can fill.

The volume of a cylinder is given by

   v = πr²h

The total volume of the two hemispheres is given by

   v' = 2× 2/3 πr³

    v' = 4/3 πr³

Now, the total volume of the solid is given by:

  \(V_{T}\) = πr²h + 4/3 πr³

  Now, substitute the value of the total volume in the above expression and then solve for h.

       12 = πr²h + 4/3 πr³

        h = 12/πr² - 4r/3

Now, the surface area of the curved surface is given by:

        A = πrh

Now, the surface area of the two hemispheres is given by

      A' = 2 × (2πr² )

      A' = 4πr²

Now, the total area is given by

    \(A_{T}\) = 2πr ( 12/πr² - 4r/3) + 4πr²

 Simplify the above expression.

  \(A_{T} =\)  24/r + 4πr²/3

Now, differentiate the total area with respect to 'r'.

      \(\frac{dA_{T} }{dr}\) = -24/r² + 8πr/3

Now, equate the above expression to zero.

     0 = -24/r² + 8πr/3

Simplify the above expression in order to determine the value of 'r'.

        8πr³  =  60

         r =  11.4

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Answer:

the answer is y=6x-6

Step-by-step explanation:

hope this helps

Answer: y = 6x-6

Step-by-step explanation:

The area of the quadrilateral ABCD is 4 square units

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

The figure

The quadrilateral ABCD is a polygon that is formed from two congruent triangles with the following dimensions

Base = 2

Height = 2

So, we have

Area = 2 * 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * 1/2 * 2 * 2

Evaluate

Area = 4

Hence, the area is 4 square units

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Answer:

A

Step-by-step explanation:

Heron's formula finds the area of any triangle.

Area = sqrt(s*(s - a)*(s-b)*(s-c) )

s = (a + b + c)/2

a = 8

b = 16

c = 12

s = 36/2 = 18

s-a = 18 - 8 = 10

s-b = 18 - 16 = 2

s-c = 18 - 12 = 6

Area = sqrt(18*10*2*6) = sqrt(2160)

Area = 12*sqrt(15)

Area = 46.4758

Now x is easily found. It is the altitude to 16

Area = 1/2 16 * h

46.4758 * 2 / 16 = h

h = 3*sqrt(15)/2

h= 5.81

Answer:

Step-by-step explanation:

Fins the similar diagram attached;

The sum of the angles is 180 degree since they lie on the same straight line. Hence;

3x - 13 + x - 3 = 180

Collect the like terms;

3x+x -13 - 3 = 180

4x - 16 = 180

4x = 180 + 16

4x = 196

x = 196/4

x = 49

Hence the value of x is 49

Note that the values in question is different from that of diagram but the diagram is similar to what we need

Answer: B (26)

Step-by-step explanation:

i did math

Answer:  26 square meters (choice B)

Work Shown:

\(A = h*\frac{b_1+b_2}{2}\\\\A = 4*\frac{5+8}{2}\\\\A = 4*\frac{13}{2}\\\\A = 4*6.5\\\\A = 26\\\\\)

Answer:

As a rule of thumb, if you know only the two shorter side, their ratio is the tangent of the angle opposed to the side you use as a numerator.

If you know one side and the hypotenuse, the ratio side/hypotenuse is either the sine of the opposite angle, or the cosine of the adjacent angle.