Peter had 4 bags which had equal number of mangoes.He sold 8 mangoes and remained with 24 mangoes.How many mangoes were in each bag?​

A. The characteristic equation for the associated homogeneous equation is:

r² - 4r + 4 = 0

B. The characteristic equation has a repeated root of 2, so the fundamental solutions for the associated homogeneous equation are:

[tex]y1(t) = e^(2t)[/tex]

[tex]y2(t) = te^(2t)[/tex]

The Wronskian of these solutions is:

[tex]W(y1, y2) = det([y1 y2; y1' y2']) = det([e^(2t) te^(2t); 2e^(2t) (2t+1)e^(2t)]) = 4e^(4t)[/tex]

So,[tex]W(y1, y2) = 4e^(4t)[/tex]

C. We need to compute the following integrals:

[tex]W(t)dt = ∫(2e^(2t))(te^(2t))dt = ∫(2t)e^(4t)dt = (1/4)te^(4t) - (1/8)e^(4t) + C1[/tex]

[tex]W(dt) = ∫(4e^(4t))dt = (1/4)e^(4t) + C2[/tex]

D. The general solution is:

[tex]y(t) = c1 y1(t) + c2 y2(t) + yp(t)[/tex]

To find a particular solution, we assume yp(t) takes the form:

[tex]yp(t) = A e^(2t)[/tex]

where A is a constant to be determined. We substitute this into the nonhomogeneous equation and solve for A:

[tex]y'' - 4y' + 4y = -6e^(2t)[/tex]

[tex](4A - 4A) e^(2t) = -6e^(2t)[/tex]

[tex]0 = -6e^(2t)[/tex]

This equation has no solution, so we need to modify our assumption for yp(t) by multiplying by t:

[tex]yp(t) = A t e^(2t)[/tex]

We substitute this into the nonhomogeneous equation and solve for A:

[tex]y'' - 4y' + 4y = -6e^(2t)[/tex]

[tex](8A - 8A + 4A) te^(2t) = -6e^(2t)[/tex]

[tex]4A = -6[/tex]

[tex]A = \frac{-3}{2}[/tex]

So, a particular solution is:

[tex]yp(t) = (-3/2) t e^(2t)[/tex]

Therefore, the general solution to the nonhomogeneous equation is:

[tex]y(t) = c1 e^(2t) + c2 t e^(2t) - (3/2) t e^(2t)[/tex]

or

[tex]y(t) = (c1 - (3/2) t) e^(2t) + c2 t e^(2t)[/tex]

where c1 and c2 are constants determined by initial conditions.

A non-homogeneous equation is a type of mathematical equation that involves both homogeneous and nonhomogeneous terms. In general, a homogeneous equation is one in which all the terms have the same degree, whereas a nonhomogeneous equation contains terms of different degrees.

In the context of linear algebra, a nonhomogeneous equation is typical of the form Ax = b, where A is a matrix, x is a vector, and b is a non-zero vector. The term "nonhomogeneous" refers to the fact that b is not the zero vector. In differential equations, a nonhomogeneous equation is one that includes a forcing function or input that is not equal to zero. The solution to such an equation can be found by adding the particular solution to the general solution of the corresponding homogeneous equation.

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Answer:

The answer is letter D.

Step-by-step explanation:

Ye

Answer:

The answer is C

x -10 < -20

x < -20 + 10

x< -10

The sign won't change to the other side because the variable we were asked to find is in the positive form.

Answer:

To find the point that partitions the line segment AB in a ratio of 1:3, we can use the following formula:

P = (3B + 1A) / 4

where P is the point that partitions the line segment in a ratio of 1:3, A and B are the endpoints of the line segment, and the coefficients 3 and 1 represent the ratio of the segment we are dividing.

Substituting the values, we get:

P = (3*(-1, -5) + 1*(-5, 3)) / 4

P = (-3, -7)

Therefore, the point that partitions the line segment AB in a ratio of 1:3 is (-3, -7).

Step-by-step explanation:

The value of X is 42.5 and Y is 90.98.

How to solve equations?

To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:

Simplify both sides of the equation by combining like terms and following the order of operations.

Add or subtract the same value from both sides of the equation to isolate the variable term.

Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.

Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.

Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:

[tex]10x/10 = 425/10[/tex]

Simplifying the left side of the equation gives:

[tex]x = 42.5[/tex]

Therefore, X is 42.5.

To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:

[tex]81729 = 898.12 \times Y[/tex]

Simplifying the right side of the equation gives:

[tex]Y = 81729 / 898.12[/tex]

[tex]Y = 90.98[/tex]

Therefore, Y is 90.98.

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The percentiles for the standard normal distribution

a. 0.93

b. -0.88

c. 0.67

d. -0.65

e. -1.28

To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.

The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.

Step 1: Write down the given percentiles as a decimal and round to two decimal places.

For example, for the 81st percentile, 0.81 will be used.

Step 2: Use the standard normal distribution table to find the corresponding z-score.

Step 3: Round off the obtained answer to two decimal places.

a) 81st percentile:

The area to the left of the z-score is 0.81.

The corresponding z-score is 0.93.

Hence, the 81st percentile for the standard normal distribution is 0.93.

b) 19th percentile:

The area to the left of the z-score is 0.19.

The corresponding z-score is -0.88.

Hence, the 19th percentile for the standard normal distribution is -0.88.

c) 76th percentile:

The area to the left of the z-score is 0.76.

The corresponding z-score is 0.67.

Hence, the 76th percentile for the standard normal distribution is 0.67.

d) 24th percentile:

The area to the left of the z-score is 0.24.

The corresponding z-score is -0.65.

Hence, the 24th percentile for the standard normal distribution is -0.65.

e) 10th percentile:

The area to the left of the z-score is 0.10.

The corresponding z-score is -1.28.

Hence, the 10th percentile for the standard normal distribution is -1.28.

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Answer:

Step-by-step explanation:\Write an expression for the sequence of operations describe below Add C and the quotient of 2 and D do not simplify any part of the expression

Answer:

The midpoint of the diameter is (4, 1)

This is the center of the circle

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

Explanation:

Add up the x coordinates and divide in half

(-1+9)/2 = 8/2 = 4

The x coordinate of the midpoint is x = 4

Repeat for the y coordinates

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

The y coordinate of the midpoint is y = 1

The midpoint is located at (x,y) = (4,1)

The midpoint of any diameter is the center of the circle. This is because all diameters go through the center.

The distance from the center to either endpoint represents the radius of the circle (aka half the diameter).

[tex]3[/tex] days [tex]0[/tex] hours. The answer is three because the function [tex]W[/tex] that solves the differential equation gives the number of weeds in a large garden.

A number is calculated and represented using a decimal, which is an algebra quantity. In handwriting, numerical symbols like "3" are used to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.

Vets Day and Memorial Day are commonly celebrated on November 11 in the United States and overseas, respectively. The history, mythology, and mathematical importance of this particular time and date are all explained here.

[tex]\frac{dw}{dt}=\frac{1}{12}(-318+24W)[/tex]

[tex]\frac{d^{2}W }{dt^{2} }=\frac{d}{dt}[\frac{1}{12} (-318+24W)][/tex]

When [tex]W=14, \frac{dW}{dt}[/tex]

[tex]=\frac{1}{12}(-318+24*14)[/tex]

[tex]=\frac{18}{12}=1.5[/tex]

[tex]=2\frac{dW}{dt}=2*1.5[/tex]

[tex]=3[/tex]

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The beam is 7.8 feet far away from the base of the house

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

It involves the use of trigonometric functions such as sine, cosine and tangent.

Using the attached image:

Let b represent the distance from the base of the house to the beam. We can say:

cos 71° = b/24 (adjacent/hypotenuse)

b = 24 * cos 71°

b = 7.8 feet  

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The price after discount is $33 and option 1 is the correct answer.

A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.

Given that, one-day discount rate of 45% is applied.

Thus,

Discount = 60.20 * 0.45 = 27.09

Price after discount = 60.20 - 27.09 = 33.11

Hence, the price after discount is $33 and option 1 is the correct answer.

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Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.y has a mean of 203 and a variance of 85.

A function, in mathematics, is a reIationship between a set of possibIe inputs and an equaIIy IikeIy set of outputs, where each input is associated to exactIy one outcome. Functions are commonIy represented as equations or graphs, and they are used to modeI many reaI-worId processes in domains such as physics, engineering, and economics.

Function types incIude Iinear, quadratic, trigonometric, and exponentiaI functions, among others. CaIcuIus, a fieId of mathematics that investigates how quantities change over time or space, heaviIy reIies on functions.

given

The foIIowing is the MacIaurin series for the function g(x) = (1+x)e(-x):

g(x) = ∑[n=0 to ∞] ((-1)ⁿ*xⁿ) / n!

We may simpIify and pIug in the first few vaIues of n to determine the first four nonzero terms of this series:

n = 0: ((-1)⁰*x⁰) / 0! = 1

n = 1: ((-1)¹*x¹) / 1! = -x

n = 2: ((-1)²*x²) / 2! = x²/2

n = 3: ((-1)³*x³) / 3! = -x³/6

The MacIaurin series for g(x) therefore has the foIIowing first four nonzero terms:

1 - x + x²/2 - x³/6

Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.  y has a mean of 203 and a variance of 85.

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The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

Answer:

x=0 & x=2

Step-by-step explanation:

To find when f(x)=g(x), then look for a value that is the same for both functions in the table. 0 occurs twice for the same x value. 0 also appear twice for the x value 2. This is when they are equal. The solution is x=0 and x=2

Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).

The volume of any cylinder can be calculated using the formula,

V = πr²h

(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)

As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:

Volume of oil = (1/5) x Total Volume

Substituting the given values, we have:

Total Volume =  π(80cm)²(200cm) = 4,031,240 cm³

Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³

Converting cm³ to litres, we have:

1 litre = 1000 cm³

Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres

Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.

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The value of the angle m<CED is 100 degrees

Corresponding angles are simply described as those angles that are formed by same corners or corresponding corners with a transversal when two parallel lines are joined by any other line.

Also, corresponding angles are created when two parallel lines are intersected by a transversal.

The different types of corresponding angles are;

Note that corresponding angles are equal.

From the information given, we have that;

m < BHG = m<CED

If m< BHG = 100 degrees

Then, m< CED = 100 degrees

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1. The most difficult decision I had to make during the process was whether or not to pursue a higher degree. It was difficult because I had to weigh the financial and time commitment.

2. If I could improve something about my business, it would improve the customer service and communication.

3. What I learned in this experience I can also apply in many other areas of my life such as problem solving, communication, and time management.

1. Throughout the process, choosing whether or not to go for a graduate degree was the hardest choice I had to make. It was challenging since I had to compare the costs and time required to finish the degree against any potential advantages it might have for my job. Ultimately, I decided to pursue a higher degree since I felt that the benefits of doing so would outweigh the costs.

2. I would invest in better tools for customer support, implement a customer feedback system, and create more opportunities for customers to share their feedback and ideas. I would also invest in better training for customer service staff to ensure they are equipped with the necessary skills to handle customer inquiries and complaints effectively.

3. These skills can be used in my work life, personal relationships, and even my studies. By learning how to better manage my time and communicate effectively, I can become more productive and efficient in any task I take on. Additionally, problem solving is a skill that is applicable to many aspects of life, such as finding creative solutions to difficult issues or troubleshooting technical problems.

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The complete question is:

1. The most difficult decision I had to make during the process was …………… It was difficult because ……………. .

2. If I could improve something about my business, it would improve …… .

3. What I learned in this experience I can also apply in …………….

Answer:

The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:

(10a-6) + (7a+4) + (7a+4) + (10a-6)

Simplifying the expression:

= 34a - 4

Therefore, the perimeter of the quadrilateral is 34a - 4.

a

=

334

a

73

Write the problem as a mathematical expression.

a

=

334

a

73

Subtract

334

a

73

from both sides of the equation.

a

−

334

a

73

=

0

Factor

a

out of

a

−

334

a

73

.

Tap for more steps...

a

(

1

−

334

a

72

)

=

0

If any individual factor on the left side of the equation is equal to

0

, the entire expression will be equal to

0

.

a

=

0

1

−

334

a

72

=

0

Set

a

equal to

0

.

a

=

0

Set

1

−

334

a

72

equal to

0

and solve for

a

.

Tap for more steps...

a

=

1

72

√

334

,

−

1

72

√

334

The final solution is all the values that make

a

(

1

−

334

a

72

)

=

0

true.

a

=

0

,

1

72

√

334

,

−

1

72

√

334

The result can be shown in multiple forms.

Exact Form:

a

=

0

,

1

72

√

334

,

−

1

72

√

334

Answer: 6

Step-by-step explanation:

Average rate of change is the same as slope.

To find the average rate of change between two points, use the formula y2 - y1 / x2 - x1

Plug in the (0, 7) and (6, 43) coordinates.

43 - 7 / 6 - 0 = 6

To find the point on the given plane that is closest to the given point (5,6,2), we can use Lagrange multipliers.

Let f be the function that represents the plane x-y+z=3 and let g be the function that represents the point (5,6,2). Then, the point on the plane closest to (5,6,2) is the point that minimizes g=x2+y2+z2. We can use the method of Lagrange multipliers to solve this problem.

Let lambda be the Lagrange multiplier. Then, we need to solve the system of equations given by:
x2+y2+z2-2x-2y-2z=0x-y+z-3=0

By solving this system of equations, we obtain the point 13/14x=7/7y=11/7z=5/7, which is the closest point on the plane to the given point (5,6,2).

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Answer:

Y=x^2+7x-3

complete the square to re-write the quadratic function in vertex form.

pls help

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.

y = x^2 + 7x - 3

y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)

y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)

y = (x + 7/2)^2 - 49/4 - 3

y = (x + 7/2)^2 - 61/4

So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).

The angles of △ABC can be determined by dividing 360 degrees by the number of congruent triangles. Therefore, each angle of △ABC measures 90 degrees as all the sides are congruent.

Since triangle ABC is isosceles, we know that angle BAC is equal to angle BCA. By drawing the perpendicular bisector of AC from point D, we can see that it intersects AC at its midpoint M. Therefore, we have AD = MC, and angle AMD is equal to angle CMD. Similarly, by drawing the perpendicular bisector of AC from point F, we have FC = CE, and angle CFE is equal to angle ECF. Since AD = DE and BF = EF, we have angle ADE = angle DEF and angle BEF = angle BFE. Therefore, we have four congruent triangles: △AMD, △BME, △ECF, and △FBC. Each of these triangles has angles that add up to 180 degrees, so we can find the measures of the angles of △ABC by dividing 360 degrees by the number of congruent triangles. Thus, each angle of △ABC measures 90 degrees.

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Answer: The total surface area of the cylinder is 850π m².

Step-by-step explanation:

The cylinder has a curved surface area of 408π m², which is the area of the lateral surface of the cylinder. The lateral surface of a cylinder is the curved surface that connects the top and bottom bases of the cylinder.

The formula for the lateral surface area of a cylinder is given by: Lateral Surface Area = 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder.

We are given that the length of the cylinder is 17 m. Since the length of a cylinder is the same as its height, we can substitute h = 17 m into the formula for the lateral surface area to get:

408π m² = 2πr(17 m)

Simplifying this equation, we get:

r = 12 m

Now that we know the radius of the cylinder, we can find the total surface area of the cylinder. The formula for the total surface area of a cylinder is given by:

Total Surface Area = 2πr(r + h)

Substituting r = 12 m and h = 17 m into this formula, we get:

Total Surface Area = 2π(12 m)(12 m + 17 m) = 850π m²

Therefore, the total surface area of the cylinder is 850π m².

A skater has a mean score of 7. 25 points. An equation to determine the skaters total scores received from eight judges is equals to the x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

Mean is called the average of the values and is calculated by dividing the addition of values by the total number of values. It is denoted by [tex]\bar X[/tex]. That is bar above X represents mean of x number of values. Mathematically, Mean = (Sum of all the values/Total number of values).We have in a skating compotion where each skater receives score from eight judges. Now, Mean or average of score points obtained by a skater = 7.25 points. Let the skater's received score from eight judges be equals to x₁,x₂,x₃,x₄,x₅,x₆,x₇, x₈. Total score received by skater = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ and we have to write the equation to determine the skaters total scores. Now, in this case mean of scores means the sum of scores received by skaters from eight judges divided by eight (judges).

=> 7.25 = (x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈)/8

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 8× 7.25

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 58

which is equation of 8 variables for total score. Therefore, the required equation is x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

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Given that the graph is falling downward, it can be seen that the graph is negative.

Before the tank's water level starts to drop, there are 120 gallons there.

Finding the slope of the graph will give us the amount of water that was lost every minute.

Slope is equal to a climb or a run.

increase = water in gallons

run equals time in minutes.

Slope equals y2 - y1 / x2 - x1

Two points will be chosen from the graph.

( 30, 80) and (60, 40) (60, 40)

Let x1=30, y1=80, x2=60, and y2=40.

Slope = 40 - 80 / 60 - 30

Slope = -40 / 30

Slope = -4/3

The result in the negative represents a loss in gallons of water per minute.

According to the line of best fit, a gallon of water was lost every minute or so.

The graph indicates that the tank will be empty in around 60 minutes.

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Ann has 60 $1 bills, 5 $10 bills, and 20 $20 bills.

Let's assume Ann has $1x, $10y, and $20z bills.

From the given information, we can write two equations based on the relationships between the numbers of bills:

z = 4y (Ann has four times as many $20 bills as $10 bills)

x = 3z (Ann has three times as many $1 bills as $20 bills)

We know that the total amount of money Ann has is $204, so we can write a third equation:

x + 10y + 20z = 204

Now we can use substitution method here, substitute equation 2 into equation 1 to get:

z = 4y

x = 3z

x = 3(4y) = 12y

Substituting these equations into equation 3, we get:

12y + 10y + 20(4y) = 204

42y = 204

y = 4.86

Since y must be a whole number (representing the number of $10 bills), we can round up to y = 5.

Using equation 1, we can find that z = 4y = 20 (representing the number of $20 bills).

Using equation 2, we can find that x = 3z = 60 (representing the number of $1 bills).

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The given question is incomplete, the complete question is:

Ann has $ 1, $10, and $20 bills. She has 4 times as many $20 bills as $10 bills. She has 3 times as many $1 bills as $20 bills. She has a total of $204 .What is the number of $1, $10, and $ 20 bills she has

The measure of the angle DAB for the right angled triangle ABD is found as   45°.

A right-angled triangle has two acute angles that add up to 90°. The smallest angle is the one that is opposite the smallest side, and the greatest angle is the one that is against the largest side.

In a triangle, the two angles that face the two equivalent sides are also equal. There can only be one right angle and one obtuse angle in a triangle.

For the question-

Triangle ABC is right angled at B.

D point makes:  AC = CD

And , AB = BC

Since ∠ABD = 90, given C is mid point.

Then, It is altitude on AD and it bisects the angle ABD into 2 equal halves as: ∠ABC = ∠CBD = 45.

Now, For triangle ABC

∠ABC = 45

∠BCA = 90

Then,

∠BAC + ∠ABC + ∠BCA = 180

∠BAC + 45 + 90 = 180

∠BAC = 180 - 135

∠BAC = 45°

Thus, the measure of the angle DAB for the right angled triangle ABD is found as  45°.

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