What is the congruence correspondence, if any, that will prove the given triangles congruent?

A. AAS
B. ASA
C. SSS
D. SAS

The length and width of the rectangle with perimeter of 24 cm are 8 cm and 4 cm respectively.

A rectangle is a quadrilateral with opposite sides equal to each other.

Opposite side are parallel to each other. The sum of angles in a rectangle

is 360 degrees.

Therefore, the perimeter of the rectangle ABCD is 24 cm. Let's find the sides.

AB = x + 2

BC = 5x - 2

CD = 2x

AD = 4x

Hence,

AB = CD

BC = AD

Therefore,

x + 2 = 2x

2 = 2x - x

x = 2

Hence,

AB = 2 + 2 = 4 cm

BC = 5(2) - 2 = 8 cm

CD = 2(2) = 4 cm

AD = 4(2) = 8 cm

Therefore,

length = 8cm

width = 4 cm.

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Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)

Answer:

The volume of the triangular prism is 677.6 cubic meters.

Step-by-step explanation:

The formula for the volume of a triangular prism is:

\(\sf\qquad\dashrightarrow Volume \: (V) = \dfrac{1}{2} \times b\times h \times l \)

where:

Substituting the given values, we have:

\(\sf:\implies Volume \: (V) = \dfrac{1}{2} \times 11 \times 11 \times 11.2\)

\(\sf:\implies \boxed{\bold{\:\:Volume \: (V) = 677.6\: meters^3\:\:}}\:\:\:\green{\checkmark}\)

Therefore, the volume of the triangular prism is 677.6 cubic meters.

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Solution

To solve this problem, we only need to equate and solve for H

Answer:

15

Step-by-step explanation:

suppose x is the no. of cloth that can be bought in rs 727.5

then cost of 1meter cloth is rs 727.5×.....(i)

and cost of 40mtr cloth is rs 1940

then 1mtr cloth is 1940/40....(ii)

so from i and ii

we get

727.5/x = 1940/40

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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Answer:

A≈676.2

Step-by-step explanation:

1. Exponentially solve equation

A=249e-0.0015t as t = 43 years (Unless conversion to seconds)

A≈676.2

2. Solve graphically = intersect = (43, 676.2) x axis is time y axis is amount.

The golfball may be as tall as 64 feet. The greatest or minimum means that potential on whether the quadratic function has a vertex. The graph exhibits a minimum when the primary coefficient is in the positive range. A maximal condition is when it is negative.

The x-coordinate of the vertex may be determined by using the equation, and the y-coordinate can be obtained by substituting the vertices into to the primary purpose.

Given :

      \(h=-16t^{2} +64t\)

Let's start by describing the generic formula for a quadratic function:

                   \(y=ax2+bx+c\)

So,

      \(a=-16\)

        \(b=64\)

\(a\) is the learning coefficient, \(b\) is the linear coefficient, and \(c\) is the constant term.

To find the maximum of the given function, we find it through the vertex. We use the following formula for the \(t\)

coordinate:

                      \(Vt= \frac{-b}{2a}\)

When we substitute the values of \(a\) and \(b\) , we get:

                                       \(Vt= \frac{- 64}{2 (-16)}\)

The result of solving is:

                        \(Vt=\frac{- 64}{-32} = 2\)

In the original code, we replace the discovered value for the vertex's t coordinate to determine the height which the golf ball needs to reach:

                          \(h=-16(2)^{2} +64(2)\)

By condensing, we arrive at:

               \(h=-16(4)+128=64-128=64\)

 The golf ball may rise up to 64 feet in height.                          

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                              "Complete question"

The height in feet of a golfball hit into the air is given by h= -16t^2 + 64t, where t is the number of seconds elapsed since the ball was hit. What is the maximum height of the ball?

The partition of matrix B into 2x2 blocks is:

B = [1 2 | 3 4 ;

3 4 | 5 6 ;

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

1 3 | 4 1 ;

3 4 | 6 3]

To construct the partition of the matrix B into 2x2 blocks, we divide the matrix into smaller submatrices. Each submatrix will be a 2x2 block. Here's how it would look:

B = [B₁ B₂;

B₃ B₄]

where:

B₁ = [1 2; 3 4]

B₂ = [3 4; 5 6]

B₃ = [1 3; 3 4]

B₄ = [4 1; 6 3]

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Answer:

Neither

Step-by-step explanation:

Parallel lines don't intersect

Answer:

Neither parallel or perpendicular.

Step-by-step explanation:

For AB A(-1,-4) and B(2, 11)

x1,y1 x2,y2

Gradient = (y2 - y1)/(x2 - x1)

= (11 - (-4))/(2 - (-1))

= 15/3 = 5.

For CD C(1 , 1) and D(4 , 10)

x1, y1 x2, y2

Gradient = (y2 - y1)/(x2 - x1)

= (10 - 1)/(4 - 1)

= 9/3 = 3

from the above they are neither parallel or perpendicular.

324 miles can Mario drive with 9 gallons of gas.

The term "proportional" refers to any connection where the ratio and amount fluctuate directly with one another.

As per the details share in the above question we get,

The data are as follow,

Mario has a driving range of 18 miles  ½ gallon of gas.

Here we have to find how many miles can mario drive with 9 gallons of gas.

Thus we know that,

He can travel 18 miles on just half a gallon of fuel.

Let x be the amount of miles that 9 gallons of gas will cover.

Thus, if we use the notion of proportion, we obtain

⇒ 18 / (1/2) = x / 9

⇒ 18 × 2 = x / 9

⇒ 36 × 9 = x

⇒ x = 324 miles

Mario can travel 324 miles on 9 gallons of gas.

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===========================================================

Work Shown:

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

Extra info (optional section)

If you want to solve for h, then you could follow these steps.

9.80h+10 = 88.40

9.80h = 88.40-10 ... subtract 10 from both sides

9.80h = 78.40

h = 78.40/9.80 .... divide both sides by 9.80

h = 8

Valerie worked 8 hours on Friday.

As a check,

9.80h + 10 = 88.40

9.80*8 + 10 = 88.40

78.40 + 10 = 88.40

88.40 = 88.40

The answer is confirmed.

The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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Question options:

A. Yes, Walter is correct.

B. No 3.612 is less than 13.

C. No, both 3.612 and 3.622 are greater than

D. No, both 3.612 and 3.622 are less than 13

Answer:

C. No, both 3.612 and 3.622 are greater than the square root of 13

Explanation:

13 is a prime number and must have a decimal number as its square root and so the square root should be between √9 and √16

Using the Newton Raphson method to estimate the square root of 13 with the formula: ai +1= ai²+n/2ai

We get square root of 13 = 3.6055512

This is the same result we get using a calculator to calculate square root of 13= 3.6055512

So yes Walter is not correct

Answer:

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

Translate

Solution

Option B is the closest one.

Answer:

b) n - 6 > 2 ; n > 8

Step-by-step explanation:

Given statement,

→ The result of 6 subtracted from a number n is at least 2.

Forming the inequation,

→ n - 6 > 2

Now the value of n will be,

→ n - 6 > 2

→ n > 2 + 6

→ [ n > 8 ]

Hence, the value of n is 8.

a)Pˣ =  \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\)  in matrix form, using eigen-values.

b)state 2 is 0.75; state 5 is 0 and ;state 6 is 0.25.

a)In order to calculate the value of Pˣ, follow the below-given steps:

Step 1: Compute the eigen-values of the matrix P.

Here, we get λ = 1, λ = 0.6, λ = 0.4, λ = 0.1, λ = 0, λ = 0.

Step 2: Compute the eigen-vectors corresponding to each eigenvalue of the matrix P.

Step 3: Compute the diagonal matrix D and the transition matrix T. \(\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\end{matrix}0.6\)

\(\begin{matrix}0.58 & 0.25 & 0.72 & 0 & 0 & 0\end{matrix}0.4.\)

\(\begin{matrix}0.07 & 0 & 0.04 & 0.7 & 0 & 0\end{matrix}0.1.\)

\(\begin{matrix}0.35 & 0.75 & 0.56 & 0 & 1 & 0\end{matrix}0.\)

\(\begin{matrix}0 & 0 & 0 & 0.3 & 0 & 1\end{matrix}\)

Pˣ = T . Dˣ . T⁻¹

We get the following matrix as a result.  

Pˣ =  \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\)  

b)If the process starts in state 3,

the probability that it will be absorbed in state 2 is 0.75,

the probability that it will be absorbed in state 5 is 0, and

the probability that it will be absorbed in state 6 is 0.25.

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The exponents' best option will be determined by

a + b's value is seven.

How often a number is multiplied by itself is indicated by the exponent.

For instance

In this case, 2 is multiplied by 4

Now in ( m times)

The base is designated as a, and the power is designated as m.

There are some indexing laws.

\(1)a^m \times a^n = a^{m+n}\\2)\frac{a^m}{a^n} = a^{m-n}\\3) (a^m)^n = a^{mn}\\4) (ab)^m = a^mb^m\\5) a^0 = 1\\6) a^{-m} = (\frac{1}{a})^m\)

Here,

\((2^a)(2^b) = 128\\\)

\(2^{a+b} =2^7\) [According to laws of indices]

\(a + b = 7\)

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Complete Question

If \((2^a)(2^b) = 128\\\), then a  + b is equal to?

The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.

The surface area of a cone is calculated using the following formula:

Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.

In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.

l² = 12² + 42²

l² = 1764

l = 42.01 meters

The surface area of the cone is then calculated as follows:

Surface area = πr² + πrl

Surface area = 3.14 * 12² + 3.14 * 12 * 42.01

Surface area = 1,670.5 square meters

Here are some additional explanations:

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Based on the correlation coefficient between sodium and the calories in the meal, we can say that there is a strong positive correlation, and it is not likely causal.

Correlation coefficients are used to show the strength of a correlation between two variables. They go from -1 to 1 and the closer to figure is to 1, the stronger the correlation between the two.

If the figure is close to 1 (instead of -1) as is the case here it means that there is a positive correlation.

Correlation however, does not mean causation which is why there is a strong positive correlation between Sodium and calories with a coefficient of 0.74, but its likely that this isn't causal.

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Answer:

ss

Step-by-step explanation:

sas

The radius of the circle who center is at ( 5 , 2 ) and the point on the circle is ( -3 , 4 ) is given by r = 2√17 units

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r

Let the center of the circle be A ( 5 , 2 )

Let the point on the circle be P ( -3 , 4 )

Now , standard form of a circle is

( x - h )² + ( y - k )² = r²

So , r² = ( 5 - ( -3 ) )² + ( 2 - 4 )²

On simplifying the equation , we get

r² = ( 8 )² + ( 2 )²

r² = 64 + 4

r² = 68

Taking square roots on both sides , we get

r = √68

r = 2√17

Hence , the radius of the circle is 2√17 units

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The average annual depreciation of the car over the 5 years span is $2500/year.

It is given that Hank paid $16,780 for a used car 5 years ago. Because he did not properly maintain the car, he sold it for $4,280.

We can write the average annual depreciation as -

Annual depreciation = (4280 - 16780)/5

Annual depreciation = (4280 - 16780)/5

Annual depreciation = - 2500

Therefore, the average annual depreciation of the car over the 5 years span is $2500/year.

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The letter used to represent Pearson's product-moment correlation coefficient is "r".

This coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no linear correlation.

To calculate Pearson's correlation coefficient, we first standardize the variables by subtracting their means and dividing by their standard deviations. Then, we calculate the product of the standardized values for each pair of corresponding data points. The sum of these products is divided by the product of the standard deviations of the two variables. The resulting value is the correlation coefficient "r".

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Let r be a partial order on set S, and let t be a subset of S. If a and a' are both elements of t, where a is the greatest element and a' is a maximal element, then it can be proven that a = a'.

To prove that a = a', we consider the definitions of greatest and maximal elements. The greatest element in a set is an element that is greater than or equal to all other elements in that set. A maximal element, on the other hand, is an element that is not smaller than any other element in the set, but there may exist other elements that are incomparable to it.

Given that a is the greatest element in t and a' is a maximal element in t, we can conclude that a' is not smaller than any other element in t. Since a is the greatest element, it is greater than or equal to all elements in t, including a'. Therefore, a is not smaller than a'.

Now, to prove that a' is not greater than a, suppose by contradiction that a' is greater than a. Since a' is not smaller than any other element in t, this would imply that a is smaller than a'. However, since a is the greatest element in t, it cannot be smaller than any other element, including a'. This contradicts our assumption that a' is greater than a.

Hence, we have shown that a is not smaller than a' and a' is not greater than a, which implies that a = a'. Therefore, if a is the greatest element and a' is a maximal element in t, then a = a'.

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Answer:

b

Step-by-step explanation:

got it right on edge 2022

From the sample that we have here the conditions for constructing the t confidence is not met because:  the 10% condition is not met.

For the confidence interval to be constructed, the assumptions and conditions that must first be fulfilled are:

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Answer:

You need to know that pairs of two angles are congruent and the pair of sides adjacent to one of the given angles are congruent

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:

3:4:7

Step-by-step explanation:

14-(3+4)

=14-7

=7

red:white:blue

3:4:7

Answer:

Step-by-step explanation:

3 + 4 + 7 = 14 which is the total

The blue balloons number 7 because 14 - (3 + 4) = 14 - 7 = 7

So the ratio is 7 blue / 14 (which is the total)

7/14 = 1/2 or 1 to 2

Answer:

4/3 also can be written 4:3

Step-by-step explanation:

Compare numbers in the order that the question asks for them. Order matters.

walkers/cyclers

= 80/60

Simplify.

= 8/6

= 4/3

The ratio of walkers to cyclers is 4/3 (also can be written 4:3)

The attack rate among the unvaccinated children is 9.68%.

The attack rate is a measure of the proportion of individuals who develop a disease within a specific population or group. In this case, we want to calculate the attack rate among the unvaccinated children who developed measles.

Total number of unvaccinated children: 4,810

Number of unvaccinated children who developed measles: 466

Attack rate = (Number of unvaccinated children who developed measles / Total number of unvaccinated children) * 100

Attack rate = (466 / 4,810) * 100

= 0.0968 * 100

= 9.68%

The attack rate among the unvaccinated children in the given measles outbreak is 9.68%. This means that approximately 9.68% of the unvaccinated children contracted measles during the outbreak.

This highlights the importance of vaccination in preventing the spread of measles and protecting individuals from the disease.

Vaccination not only reduces the risk of infection in vaccinated individuals but also contributes to herd immunity, which helps protect those who cannot be vaccinated, such as infants or individuals with compromised immune systems.

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Answer: x=7

Step-by-step explanation: 6x-15=27

6x=42

x=7