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The parallelogram ABCD's congruency can be proven using Side-Angle-Side (SAS) congruence theorem.

Prove that ΔABC ≅ ΔDCB using the Side-Angle-Side (SAS) congruence theorem.

Given that ABCD is a parallelogram, AB || CD and BC || AD. Therefore, ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DCA because they are corresponding angles.

AB ≅ CD and BC ≅ AD because opposite sides of a parallelogram are congruent.

Lastly, AC ≅ AC because it is a shared side between the two triangles.

Therefore, the following congruent parts:

∠ABC ≅ ∠DCB (by corresponding angles)

AB ≅ CD (by opposite sides)

BC ≅ AD (by opposite sides)

AC ≅ AC (shared side)

The SAS congruence theorem concludes that ΔABC ≅ ΔDCB.

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Image transcribed:

Prove ΔABC ≅ ΔDCB

Answer:

Step-by-step explanation:

104.4 divided by 4 = 26.1

Answer:

183.3

Step-by-step explanation:

Since there were 1 angle and 2 sides, I used law of cosines

Answer: It snowed 3.5 inches on Monday and Tuesday combined.

Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow

Hope this helped!

Answer$81

Step-by-step explanation:

The rate of change of the area outside the circle but inside the square is 1 m² per minute.

Area is the measure of the size of a two-dimensional (2D) shape or planar region. It is expressed in terms of square units, such as square metres (m2) and square feet (ft2). The area of a shape is the total space contained within its boundaries.

To answer this question, we need to find out the area outside the circle but inside the square. This can be done by subtracting the area of the circle from the area of the square.

The area of the circle is equal to πr², where r is the radius of the circle. In this case, the radius is 3 meters, so the area of the circle is π×32 = 28.27 m².

The rate of change of the area outside the circle but inside the square is 1 m²per minute.

The area of the square is equal to side², where side is the length of one side of the square. In this case, the side is 16 meters, so the area of the square is 162 = 256 m².

Subtracting the area of the circle from the area of the square gives us the area outside the circle but inside the square. This is 256 - 28.27 = 227.73 m².

Now, we know the area outside the circle but inside the square, and we know that the radius of the circle is increasing at a rate of 1 meter per minute and the sides of the square are increasing at a rate of 2 meters per minute. This means that the area outside the circle but inside the square is increasing at a rate of (2 - 1) = 1 m²per minute.

Therefore, the rate of change of the area outside the circle but inside the square is 1 m² per minute.

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Answer:

Step-by-step explanation:

The chain rule is used when a function is composed of two or more functions, where one function is applied to the output of the other. In other words, it is used when a function is "nested" inside another function. Thus, option A is correct.

We can solve this problem by applying the chain rule and the product rule of differentiation. Let's begin by simplifying the expression inside the parentheses:

[tex]y = ex (e^-2x + 7)[/tex]

Now, let's apply the product rule:

[tex]dy/dx = (ex)'(e^-2x + 7) + ex(e^-2x + 7)'[/tex]

Using the chain rule, we can find (ex)':

[tex](ex)' = ex[/tex]

And using the chain rule again, we can find [tex](e^-2x + 7)':[/tex]

[tex](e^-2x + 7)' = (-2e^-2x)[/tex]

Substituting these values back into the original equation, we get:

[tex]dy/dx = ex(e^-2x + 7) + ex(-2e^-2x)[/tex]

Simplifying, we get:

[tex]dy/dx = ex(e^-2x + 7 - 2e^-2x)[/tex]

[tex]dy/dx = ex(e^-2x - e^-2x + 7)[/tex]

[tex]dy/dx = ex(7)[/tex]

Therefore, the answer is A) 7.

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Answer:

3.7

Step-by-step explanation:

1.5, 2.2, 2.8, 3.4, 5, 5.6, 6.8, 7

Q1 = 2.2+2.8 = 5.0 divided 2 = 2.5

Q3 = 5.6+6.8 = 12.40 divided 2 = 6.2

IQR = 6.2 - 2.5 = 3.7

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Answer:

Step-by-step explanation:

We need to convert the 1 terabyte into bits, which is:

1 terabyte = 1,000 gigabytes (GB) x 1,000 megabytes (MB) x 1,000 kilobytes (KB) x 1,000 bytes (B) x 8 bits (b)

1 terabyte = 1,000,000,000,000 bytes x 8 bits

1 terabyte = 8,000,000,000,000 bits

Let's assume the total storage of all the family's phones, tablets, and cloud storage is x bits. Then, the number of more bits of storage Theresa's computer has is:

8,000,000,000,000 bits - x bits

We are not given the value of x, so we cannot calculate the exact difference.

However, we can still express the answer in scientific notation by noting that:

8,000,000,000,000 = 8 x 10^12

So, the difference in bits of storage can be written as:

(8 x 10^12) - x bits

The volume of the cylinder in terms of π is  128π centimetres³.

The cylinder below has a height of 8 centimetres and a diameter of 8 centimetres. Therefore, the volume of the cylinder can be found as follows:

volume of the cylinder = πr²h

where

Therefore,

r = 8 / 2 = 4 centimetres

h = 8 centimetres

volume of the cylinder = π × 4² × 8

volume of the cylinder = 128π centimetres³

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Each interior angles of the rectangle QUAD is equal to 90°, and the angles ∠2 and ∠5 are complementary, so the value of x = 4.

The angles ∠2 and ∠5 form one of the interior angles of a rectangle, hence they are complementary as they add up to 90°.

we shall solve for x as follows:

x + 30 + 2x - 48 = 90

3x + 78 = 90

3x = 90 - 78 {subtract 78 from both sides}

3x = 12

x = 12/3 {divide through by 3}

x = 4

In conclusion, each interior angles of the rectangle QUAD is equal to 90°, and the angles ∠2 and ∠5 are complementary, so the value of x = 4.

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Answer:

Step-by-step explanation:

5/9 + (-4/9) - (-2)

5/9 - 4/9 + 2

[tex]5-4+18/9[/tex]

19/9 or 2.1, 2 1/9

Answer:

i have solved it step by step

Answer:

To find the number of bags of rice in 2850kg, we need to divide the total weight of rice by the weight of each bag. In this case, each bag weighs 50kg, so:

Number of bags = 2850 kg / 50 kg per bag

Simplifying this expression, we get:

Number of bags = 57 bags

Therefore, there are 57 bags of rice in 2850kg.

To find the value, we need to know the price per bag of rice. If we know this price, we can simply multiply the number of bags by the price per bag to get the total value. Without knowing the price, we cannot determine the value.

Answer:

57

Step-by-step explanation:

The length of the segment PD obtained using the relationship between similar right triangles is; PD = 7.5 units

A right triangle is a triangle that has an interior angle of 90° (a right angle) and the side opposite the right angle (90°) interior angle is known as the hypotenuse side, while the other two sides of the triangle are the legs of the right triangle.

The possible drawing in the question, obtained from a similar online question, created with MS Word is attached.

The equation of the line that passes through the points A and D, y = -2·x + 6, indicates;

The coordinates of the y-intercept of the line of the equation, is; (0, 6)

The y-intercept indicates that OD = 6 units

The x-intercept coordinates of the graph of the equation, can therefore be obtained as follows; 0 = -2·x + 6

2·x = 6

x = 6/2 = 3

x = 3

The x-intercept is; (0, 3)

The x-intercept indicates that OA = 3 units

The length of the side of the square, s, is therefore;

s = √(s²) = √(6² + 3²) = 3·√5

OA = The length of the x-intercept of ; y = -2·x + 6

The ∠DAO ≅ ∠OPA, and m∠DOA = m∠POA = 90°

Therefore;

∠DOA  ≅ ∠POA

ΔOPA is similar to ΔOAD, by Angle-Angle similarity postulate

The ratio of corresponding sides of similar triangles indicates;

OP/OA = OA/OD

Therefore;

OP/OA = OA/OD

OP/3 = 3/6

OP = 3 × 3/6 = 1.5

PD = OP + OD (Segment addition postulate)

PD = 1.5 + 6 = 7.5

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Answer:

Numbers between 100 and 200 which are also equal to a square number multiplied by a prime number are:

Step-by-step explanation:

A square number is a number that has been multiplied by itself.

For example, 25 is a square number as 5 × 5 = 25.

The square numbers between zero and 200 are:

A prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).

Since the smallest square number is 4, and our final number needs to be between 100 and 200, we only need to list the primes numbers that are less than 50 as 4 × 50 = 200.

Begin with the smallest prime number, 2. If we divide 100 and 200 by this prime number, we get 50 and 100. Therefore, to find a number between 100 and 200 that is equal to a square number multiplied by a prime number, the square number should be more than 50 and less than 100.  Therefore:

The next smallest prime number is 3. If we divide 100 and 200 by 3 we get 33.33.. and 66.66...  Therefore, the prime number 3 should be multiplied by a square number that is more than 33 and less than 67:

The next prime number is 5. If we divide 100 and 200 by 5 we get 20 and 40.  Therefore, the prime number 5 should be multiplied by a square number that is more than 20 and less than 40:

Continuing this way, all the numbers that are between 100 and 200, which are also equal to a square number multiplied by a prime number are:

Number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In simpler terms, a prime number is a number that can only be evenly divided by 1 and itself.

To find this number, I first looked for square numbers between 100 and 200. The square numbers within this range are 121 (11 squared) and 169 (13 squared).

I then checked if either of these square numbers could be multiplied by a prime number to equal a number between 100 and 200. After some calculation, I found that 169 cannot be multiplied by a prime number to give a number between 100 and 200. However, 121 can be multiplied by 2 to give 242, which is greater than 200.

Finally, I checked if there were any other square numbers I missed. I found that 7 squared is equal to 49, which when multiplied by 3 (a prime number) gives 147, a number between 100 and 200 that satisfies the problem.

Therefore, the number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

I hope this helps!

Answer:

i did this in 8th grade. (I'm homeschooled)

Step-by-step explanation:

Heres the best i got

Therefore , the solution of the given problem of function comes out to be the function's behavior on that range because it is not specified for negative values of x.

The midterm exam will include questions on design, geometry, numbers, each division, as well as actual and hypothetical geographic places. A piece of work describes the connections between variable elements that cooperate to produce the same outcome. A utility is a structure made up of numerous unique parts that work together to create unique outcomes for each input.

Here,

Given that the function in the graph you supplied is undefinable for negative values of x, its domain is (0, infinity).

Therefore, referring to the function as declining on the interval is illogical. (0, -infinity).

As we travel from right to left on the interval, we can observe that the function's values are indeed decreasing. (0, infinity).

We refer to this interval as the function's declining one because of this.

On the interval, we could state that the function is decreasing.

(-infinity, 0). However, in this specific instance, we are unable to discuss the function's behavior on that range because it is not specified for negative values of x.

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The solution of the equation is x = 2. If we had multiplied both sides by a different number, such as 3 or -4.

What is solution of the equation ?

The solution of an equation is the value(s) of the variable(s) that make the equation a true statement. In other words, it is the value(s) that satisfy the equation.

For example, consider the equation 3x + 4 = 13. To find the solution, we need to determine the value of x that makes the equation true. the solution of the equation 3x + 4 = 13 is x = 3.

According to the question:
The first statement, "Both sides of an equation can be multiplied by the same number without changing the solution of the equation" is always true.

Example: Consider the equation 3x = 6. If we multiply both sides of this equation by 2, we get:

2 * 3x = 2 * 6

6x = 12

The solution of the equation is x = 2. If we had multiplied both sides by a different number, such as 3 or -4, we would still get the same solution.

The second statement, "A number can be added to both sides of an equation changing the solution of the equation" is sometimes true.

Example: Consider the equation 2x = 4. If we add 3 to both sides of the equation, we get:

2x + 3 = 4 + 3

2x + 3 = 7

The solution of the equation is x = 2.5. Adding 3 to both sides did not change the solution.

However, if we add a number that is equal to or related to the variable, the solution will change. For example, if we add x to both sides of the equation 2x = 4, we get:

2x + x = 4 + x

3x = 4 + x

The solution of the equation is x = 4/2 = 2, which is different from the previous solution of x = 2. Therefore, the statement "A number can be added to both sides of an equation changing the solution of the equation" is sometimes true, depending on the number being added.

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Answer:

C) Pi

Step-by-step explanation:

Pi is an irrational number, it cannot be written down as non-infinite decimal, basically meaning that in order for it to be a rational number you need an approximate value for Pi.

Answer:

Horizontal Compress of 1/4.

Vertical compress of 1/4 as well.

Step-by-step explanation:

Looking at the graph the big Parallelogram HIJK gets becomes smaller parallelogram H'I'J'K'

I have counted the vertical and horizontal of the graph.

So the dilation is

Horizontal Compress of 1/4.

Vertical compress of 1/4.

Answer: a )The answer is 196.126.

b )

Step-by-step explanation:

a) Multiply 33.1 and 18.2= 602.62

Divide the result by 5.8:

602.62 / 5.8 = 196.126

Therefore, 33.1x18.2 / 5.8 = 196.126.

The linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450.

What is a linear equation?

A linear equation is a mathematical equation in which the highest power of the variable(s) is one.

ax + b = 0

or

y = mx + b

where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.

Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:

450 - 10x

The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.

The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450

where y is the amount of money Todd has in his savings after x weeks.

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35/84

It can be simplified to 5/12 by dividing by 7.

So the probability that Angela gets to go to the meeting is 2/5.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.

Here,

There are a total of 5 people in the club, so there are 10 possible pairs of people that could be chosen to go to the meeting. Since each pair is equally likely to be chosen, the probability of any particular pair being chosen is 1/10.

To determine the probability that Angela gets to go to the meeting, we need to count the number of pairs that include Angela. There are 4 other people in the club, so there are 4 possible pairs that include Angela. Therefore, the probability that Angela gets to go to the meeting is:

P(Angela) = number of pairs that include Angela / total number of pairs

= 4 / 10

= 2 / 5

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Answer:

To find the real and imaginary parts of the complex number 26 = a + bi, we can use the fact that:

a + bi = 26

Taking the complex conjugate of both sides, we get:

a - bi = 26

Adding the two equations, we get:

2a = 52

Solving for a, we get:

a = 26

Substituting this value into one of the equations, we get:

26 + bi = 26

Therefore, b = 0.

Therefore, the real part of 26 is a = 26, and the imaginary part is b = 0.

Answer:

64, 69, 88, 88, 91, 92, 93, 95, 97, 97, 100

Median= 92

Mode= 88, 97

Mean= 88.55

Range= 36

Quartile 1= 88

Quartile 2= 92

Quartile 3= 97

Interquartile range= 9

Minimum= 64

Maximum= 100

Not sure if this helped but I hope it did