From the top of an 18-meter lighthouse, the angle of depression to sight a boat is 4°. What is the distance between the boat and the base of the lighthouse, to the nearest tenth?


ASAP TIMED

If you want each character to be approximately one inch in size, you would use a point size of 72 pts.

Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.

Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.

Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.

Therefore the correct answer is option b.) 72 pts.

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The student's original statement has an issue in the way the "not" operator is used. The "not" operator (!) is negating the entire expression, including the variable 'x', rather than just the inequality. This leads to incorrect evaluation.

To correctly determine if x is not greater than 20, you should use the "less than or equal to" (<=) operator instead. Here is the corrected statement:

if (x <= 20)

This statement will be true if x is less than or equal to 20, which is the intended condition.

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Answer:

Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.

Step-by-step explanation:

please

give brianliest

Answer: Area = 0

Step-by-step explanation:

((2*2)*3.14)-(4*3.14) = 0

Answer:

8;-2

Step-by-step explanation:

8 is the x axis and -2 is the y axis

Answer:

Step-by-step explanation:

The given equation is 7(x+4) = -21 . Therefore, the value of x is 7

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation is made up of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Many times the right side of the equation is assumed to be zero. Assuming this does not reduce generality, this can be achieved by subtracting the right side from both sides.

According to the Question:

The given equation is:

   7(x+4)= -21

⇒ 7x + 28 = -21

⇒ 7x = -49

⇒ x = 7

Complete Question:

Solve the Equation : 7(x+4)= -21

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The bottom of the ladder is moving at a rate of 4/3 ft per second.

To solve the problem, we can use the Pythagorean Theorem:[tex]$x^2 + y^2 = 64$[/tex], where x is the distance from the wall to the bottom of the ladder and y is the length of the ladder. We differentiate this equation with respect to time t and use the chain rule to get [tex]$\frac{d}{dt} (x^2 + y^2) = \frac{d}{dt} 64$[/tex]

Simplifying, we get

[tex]$2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$[/tex]

When the bottom of the ladder is 4 feet from the wall, we have x = 4 and y = 8, so we can substitute these values into our equation and solve for [tex]$\frac{dx}{dt}$[/tex]:

[tex]$2(4)\frac{dx}{dt} + 2(8)(-2) = 0$[/tex]

[tex]$\frac{dx}{dt} = \frac{16}{8} = \frac{4}{3}$[/tex]

Therefore, the bottom of the ladder is moving at a rate of [tex]$\frac{4}{3}$[/tex] ft/s.

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The perimeter of the updated blueprint will be 24 times the sum of the original length and width.

If Ezra wants to multiply the dimensions of the stage by a certain percentage to make the image 12 times larger than the original, he needs to find out what percentage that is.

To do this, he can divide the desired size of the new stage by the original size of the stage, and then multiply by 100 to get the percentage increase. So, if the original blueprint dimensions are x by y, and he wants to make the image 12 times larger, the new dimensions will be 12x by 12y.

To find the percentage increase, he can use the following formula:

Percentage increase = [(new size - original size) / original size] x 100

In this case, the new size is 12 times the original size, so the formula becomes:

Percentage increase = [(12x * 12y - x * y) / (x * y)] x 100

Simplifying this expression gives:

Percentage increase = [(144xy - x * y) / (x * y)] x 100 = 14300%

Therefore, Ezra needs to multiply the dimensions of the stage by 14300% to make the image 12 times larger than the original blueprint.

To find the perimeter of the updated blueprint, he can use the formula for the perimeter of a rectangle, which is: Perimeter = 2(length + width)

In this case, the length and width have been multiplied by 12, so the new perimeter becomes:

Perimeter = 2(12x + 12y) = 24(x + y)

Therefore, the perimeter of the updated blueprint will be 24 times the sum of the original length and width.

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The twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.

A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is the simplest pοlygοn, which is a flat shape cοnsisting οf straight lines.

We can use the Law οf Cοsines tο find the length οf side QR:

[tex]c^2 = a^2 + b^2 - 2ab[/tex] cοs(C)

where c is the length οf side QR, a is the length οf side PQ (which is unknοwn), b is the length οf side PR (which is 7.8 cm), and C is the angle οppοsite side c (which is 30°). Substituting the given values, we get:

[tex]QR^2 = PQ^2 + 7.8^2 - 2(PQ)(7.8)cos(30^\circ )[/tex]

[tex]QR^2 = PQ^2 + 60.84 - 7.8PQ[/tex]

Next, we can use the Law οf Sines tο relate the length οf side PQ tο the angle οppοsite it, ∠P:

PQ/sin(30°) = QR/sin(P)

PQ = QR(sin(30°)/sin(P))

Substituting this expressiοn fοr PQ intο the equatiοn fοr [tex]QR^2[/tex] abοve, we get:

[tex]QR^2 = [QR(sin(30^\circ)/sin(P))]^2 + 60.84 - 7.8[QR(sin(30^\circ)/sin(P))][/tex]

Simplifying and rearranging, we get a quadratic equatiοn in terms οf QR:

[tex]QR^2 - 3.9QR + 28.99 = 0[/tex]

Using the quadratic fοrmula, we find that:

QR ≈ 7.466 cm οr QR ≈ 3.866 cm

Since we knοw that QR < PQ + PR = 6 + 7.8 = 13.8, the οnly valid sοlutiοn is QR ≈ 7.466 cm. Therefοre, we have:

[tex]cos(R) = (PQ^2 + QR^2 - PR^2)/(2PQQR)[/tex]

[tex]cos(R) = (PQ^2 + 7.466^2 - 7.8^2)/(2PQ(7.466))[/tex]

[tex]cos(R) = (PQ^2 - 4.928)/[2PQ(7.466)][/tex]

Since cοs(R) ≤ 1, we have:

[tex]PQ^2 - 4.928 ≤ 2PQ(7.466)[/tex]

Sοlving fοr PQ using the quadratic fοrmula, we get:

PQ ≤ 5.474 cm οr PQ ≥ 20.032 cm

Since PQ < PR, the οnly valid sοlutiοn is:

PQ ≈ 5.474 cm

Nοw we can use the Law οf Cοsines again tο find ∠R:

[tex]cos(R) = (PQ^2 + PR^2 - QR^2)/(2PQPR)[/tex]

[tex]cos(R) = (5.474^2 + 7.8^2 - 7.466^2)/(2(5.474)(7.8))[/tex]

cοs(R) ≈ 0.828

R ≈ 33.6° οr R ≈ 326.4°

Therefοre, the twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.

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The probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.

We need to make some assumptions about the population proportion of persons with a retirement account and the standard deviation of the sampling distribution of sample proportions. Let's assume that the population proportion is p = 0.5 (i.e., half of the population has a retirement account) and that the standard deviation of the sampling distribution is given by:

σ = sqrt((p*(1-p))/n)

where n is the sample size.

Substituting the values given in the question, we have:

σ = sqrt((0.5*(1-0.5))/555) = 0.0258

To find the probability that the sample proportion differs from the population proportion by less than 5%, we need to find the probability that the absolute difference between the sample proportion and the population proportion is less than 0.05. This can be written as:

P(|p_hat - p| < 0.05)

where p_hat is the sample proportion.

We can standardize this expression by subtracting the population proportion from both sides and dividing by the standard deviation:

P(|p_hat - p|/σ < 0.05/σ)

P(-0.97 < Z < 0.97)

where Z is a standard normal variable. We can find this probability using a standard normal table or a calculator:

P(-0.97 < Z < 0.97) = 0.8327

Rounding to four decimal places, we have:

P(|p_hat - p| < 0.05) = 0.8327

Therefore, the probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.

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Answer:

£164.50

Step-by-step explanation:

If the discount is 6%, then the discounted price is 94% of the original price.

95% of £175 = 0.94 × £175 = £164.50

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

1) We know that there is a total of 24 hours in a day.

therefore, 7/8 hours of Wednesday =

number of hours in a day = 24

number of hours every Wednesday = 7/8

= 7/8 x 24 hours

= 7 x 3 hours

= 21 hours

7/8 hours every Wednesday means 21 hours every Wednesday.  

2) We know that there are a total of 24 hours in a day;

therefore, 3/8 hours of Friday =

number of hours in a day = 24

number of hours every Friday = 3/8

= 3/8 x 24 hours

= 3 x 3 hours

= 9 hours

3/8 hours every Friday means 9 hours every Friday.

therefore, the total number of hours = 21 + 9 = 30

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

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Answer:

i don't know i haven't done integers in a long time

Step-by-step explanation:

Alexis has 12 quarters and 8 dimes.

Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.

We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:

10d + 25q = 380

To make things easier, let's divide both sides of the equation by 5:

2d + 5q = 76

Now we can use the first equation to solve for d in terms of q:

d + q = 20

d = 20 - q

Substituting this into the second equation gives:

2(20 - q) + 5q = 76

Expanding the parentheses and simplifying, we get:

40 - 2q + 5q = 76

3q = 36

q = 12

Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:

d + q = 20

d + 12 = 20

d = 8

The total value of 12 quarters and 8 dimes is:

12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80


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Answer:

The answer should be 20,365.714 but I am not sure

Step-by-step explanation:

Answer:

I attached your answer along with an explanation

Step-by-step explanation:

Please Like me follow me and Give me Crown for more help. :)

The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.

We can use the formula for calculating probabilities of combinations:

P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players

Total number of ways to choose 2 DVD players out of 6 is:

C(6,2) = 6! / ([2!] [4!]) = 15

Number of ways to choose 2 non-defective DVD players out of 4 is:

C(4,2) = 4! / ([2!] [2!]) = 6

Therefore, the probability that Cecil chooses 2 non-defective DVD players is:

P(not defective) = 6/15 = 2/5

So the value of P(not defective) is 2/5.

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The probability that a randomly selected adult weighs between 120 and 165 lbs is approximately 0.8186.

Since the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs, we can use the standard normal distribution to calculate the probability.

We first need to standardize the values using the formula: z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation.

For x = 120 lbs, z = (120 - 140) / 25 = -0.8, and for x = 165 lbs, z = (165 - 140) / 25 = 1.0. We can then use a calculator to find the probability between -0.8 and 1.0, which is approximately 0.8186.

Thus, the chance of picking an adult at random who weighs between 120 and 165 lbs is roughly 0.8186.

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The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.

We can use the formula for the volume of a cone, which is:

Volume = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:

13.4 = (1/3)π(3.2)²h

Multiplying both sides by 3 and dividing by π(3.2)², we get:

h = 3 × 13.4 / π(3.2)²

h ≈ 2.5 m

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There are 5²⁵ possible ways to select 25 cans of soda from 5 types, while there are [5¹⁸] (25 choose 7) possible ways to select 25 cans with at least 7 Dr. Peppers, and only [3²²] (25 choose 3) possible ways to select 25 cans with only 3 Dr. Peppers available.

(a) Since there are five types of soda and we are selecting 25 cans, we can choose any type of soda for each can. Therefore, the number of ways to select 25 cans of soda is 5²⁵.

(b) If we must include at least seven Dr. Peppers, then we can choose the remaining 18 cans from any of the five types of soda (including Dr. Pepper). We can choose 7 Dr. Peppers in (25 choose 7) ways. Therefore, the number of ways to select 25 cans of soda with at least seven Dr. Peppers is (25 choose 7) [5¹⁸].

(c) If there are only three Dr. Peppers available, then we must choose all three Dr. Peppers and select the remaining 22 cans from the four types of soda (excluding Dr. Pepper). We can choose the remaining 22 cans in 4²² ways. Therefore, the number of ways to select 25 cans of soda with only three Dr. Peppers available is 3 [4²²].

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Complete question:

From an unlimited selection of five types of soda, one of which is Dr. Pepper, you are putting 25 cans on a table.

(a) Determine the number of ways you can select 25 cans of soda.

(b) Determine the number of ways you can select 25 cans of soda if you must include at least seven Dr. Peppers.

(c) Determine the number of ways you can select 25 cans of soda if it turns out there are only three Dr. Peppers available.

The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.

A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]

The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.

The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.

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Answer: No

Step-by-step explanation:

Because the length of the box is shorter than the length of the club

20in<26in

The width of the box is also shorter than the width of the club

13in<16in

The height of the box is also shorter than the height of the club

11in<16in

But what about putting it at an angle?

So we know  [tex]a^{2} +b^{2} =c^{2}[/tex]

so let's try [tex]20^{2} +13^{2} =x^{2}[/tex]

                               [tex]x^{2}[/tex]=569

                               [tex]x=\sqrt{159}[/tex]

x is near 23.85 in, but 23.85<26. So no.

Answer: 6

Step-by-step explanation:

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

The factors of 78 are: 1, 2, 3, 6, 13, 26, 39, 78

Then the greatest common factor is 6.

Heres something you need to learn about the greatest common factor (gcf)

What is the Greatest Common Factor?

The largest number, which is the factor of two or more numbers is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors that are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

Let us consider the example given below:

Greatest Common Factor (GCF)

For example – The GCF of 18, 21 is 3. Because the factors of the number 18 and 21 are:

Factors of 18 = 2×9 =2×3×3

Factors of 21 = 3×7

Here, the number 3 is common in both the factors of numbers. Hence, the greatest common factor of 18 and 21 is 3.

Similarly, the GCF of 10, 15 and 25 is 5.

How to Find the Greatest Common Factor?

If we have to find out the GCF of two numbers, we will first list the prime factors of each number. The multiple of common factors of both the numbers results in GCF. If there are no common prime factors, the greatest common factor is 1.

Finding the GCF of a given number set can be easy. However, there are several steps need to be followed to get the correct GCF. In order to find the greatest common factor of two given numbers, you need to find all the factors of both the numbers and then identify the common factors.

Find out the GCF of 18 and 24

Prime factors of 18 – 2×3×3

Prime factors of 24 –2×2×2×3

They have factors 2 and 3 in common so, thus G.C.F of 18 and 24 is 2×3 = 6

Also, try: GCF calculator

GCF and LCM

Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.

Least Common Multiple of two or more numbers is the smallest number (non-zero) that is a multiple of all the numbers.

Factoring Greatest Common Factor

Factor method is used to list out all the prime factors, and you can easily find out the LCM and GCF. Factors are usually the numbers that we multiply together to get another number.

Example- Factors of 12 are 1,2,3,4,6 and 12 because 2×6 =12, 4×3 = 12 or 1×12 = 12. After finding out the factors of two numbers, we need to circle all the numbers that appear in both the list.

Greatest Common Factor Examples

Example 1:

Find the greatest common factor of 18 and 24.

Solution:

First list all the factors of the given numbers.

Factors of 18 = 1, 2, 3, 6, 9 and 18

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24

The largest common factor of 18 and 24 is 6.

Thus G.C.F. is 6.

Example 2:

Find the GCF of 8, 18, 28 and 48.

Solution:

Factors are as follows-

Factors of 8 = 1, 2, 4, 8

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 28 = 1, 2, 4, 7, 14, 28

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest common factor of 8, 18, 28, 48 is 2. Because the factors 1 and 2 are found all the factors of numbers. Among these two numbers, the number 2 is the largest numbers. Hence, the GCF of these numbers is 2.

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The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.

If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.

The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)

It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.

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Coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. The side chains of the tetraalkylammonium are modified with the ethylene glycol ether, which is a highly polar solvent, allowing for better solubility in nonaqueous electrolyte solutions. Additionally, the ethylene glycol ether has the ability to modify the stability of the ionic species, preventing aggregation and ensuring the longevity of the battery. This increases the redox capacity and enhances the performance of the flow battery.

The ethylene glycol ether-tetraalkylammonium coupling has been proven to be an effective method for improving the solubility and stability of anthraquinone-based ionic species. For example, it has been observed that the coupling of ethylene glycol ether to anthraquinone-based ionic species enhanced the current density of the battery by more than 3 times. Furthermore, the coupling process has also been found to improve the energy efficiency and storage capacity of the nonaqueous redox flow battery.

Overall, coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method for enabling highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. This process has been proven to improve the performance of the battery, including current density, energy efficiency, and storage capacity.

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The option that would result in the smallest margin of error in estimating the mean salt content, u, is 95% confidence, n = 50. The correct answer is Option D.

The margin of error is the amount by which a statistic is expected to differ from the true value of the population parameter. The interval estimate is calculated with the help of a margin of error. The margin of error and the interval estimate are inversely related to each other. If we want a small margin of error, we must increase the sample size.

The confidence level is the likelihood that a population parameter will fall within a specified range of values. The confidence level is determined by the sample size and margin of error. The sample size and margin of error are directly related to each other. When the sample size is smaller, the margin of error is larger. When the sample size is larger, the margin of error is smaller.

The margin of error is the highest at a confidence level of 50%. In general, as the confidence level increases, the margin of error decreases, and vice versa. As the sample size increases, the margin of error decreases. It follows that a 95% confidence level, n = 50 would yield the smallest margin of error in estimating the mean salt content, u. Hence, option D) 95% confidence, n = 50 would result in the smallest margin of error in estimating the mean salt content, u.

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The measure of angle R in ΔSRT which is drawn inside the circle is 77.5°.

Circle is a two-dimensional shape that is defined as the set of all points that are equidistant from a central point. It is often represented as a round shape with a curved boundary.

Since SR is a diameter of the circle, it follows that angle STR is a right angle (90°). Therefore, we can find the measure of angle SRT using the following equation:

∠SRT + ∠STR = 180°

(2x-23°) + 90° = 180°

2x + 67° = 180°

2x = 180° - 67°

2x = 113°

x = 56.5°

∠TRS = 5x-97°

∠TRS = 5(56.5°)-97°

∠TRS = 192.5°

Finally, we can find the measure of angle SRT:

∠SRT = 180° - ∠STR - ∠TRS

∠SRT = 180° - 90° - 192.5°

∠SRT = -102.5°

Therefore, to find the measure of angle R, we need to add 180° to angle SRT:

∠R = ∠SRT + 180°

∠R = -102.5° + 180°

∠R = 77.5°

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The best type of inspection to use depends on the nature of the purchase. Each type of inspection has its own advantages and disadvantages, and should be chosen based on the requirements of the product and the level of risk associated with the inspection.

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BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Triangle congruence: Two triangles are said to be congruent if their three corresponding sides and their three corresponding angles are of identical size.

You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another.

Two triangles are congruent if they satisfy all five conditions for congruence.

They include the right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and angle-side-angle (SSS) (RHS).

So, in the given △DAB and △DCB:

AC = AC = Common

∠DAC = ∠BAC = AC is the angle bisector

∠DCA = ∠BCA = AC is the angle bisector

Then, △DAB ≅ △DCB under the ASA congruency rule,

Then, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Therefore, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

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