C is the circumcenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent?
It is given that triangle ABD is an isosceles triangle, so segments AB and DB are congruent by the definition of isosceles triangle.
It is given that C is the circumcenter of triangle ABD, making segment BE a median.
By the definition of perpendicular, angles AEB and DEB are 90°, so triangles ABE and DEB are right triangles.
Triangles ABE and DEB share side BE making it congruent to itself by the reflexive property.
Triangles ABE and DBE are congruent by HL.


Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD, segment BC is extended past C with dashed lines so that it intersects with side AD at point E.
There is an error in line 1; segments AB and BD are given to be congruent.
There is an error in line 2; segment BE should be a perpendicular bisector.
There is an error in line 4; segment BE is not a shared side.
The proof is correct.

The pH of the solution is 12.81.

1) [OH⁻] = 0.065 M

2) [H₃O⁺] = 1.54 x 10⁻¹³ M.

3)  pH = 12.81.

HCl is completely dissociated into its ions in solution:

KOH + H₂O  → H₃O⁺ + K⁺ + OH⁻,

1) [OH⁻] = 0.065 M.

2) [H₃O⁺]:

∵ [H₃O⁺][OH⁻] = 10⁻¹⁴.

∴ [H₃O⁺] = [tex]\frac{10^{-14}}{OH^-}[/tex] = [tex]\frac{10^{-14}}{0.065}[/tex] = 1.54 x 10⁻¹³ M.

3) pH:

Typically, a pH meter is used to measure pH, which converts the difference in electromotive force (electrical potential or voltage) between appropriate electrodes put in the solution under test into pH measurements. A pH meter's basic components are a voltmeter connected to an electrode that responds to pH and an electrode that is constant. The reference electrode is typically a mercury-mercurous chloride (calomel) electrode, however a silver-silver chloride electrode is occasionally used. The pH-responsive electrode is often made of glass.

For strong acids like HCl:

pH = - log[H₃O⁺] = - log[1.54 x 10⁻¹³ M] = 12.81

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Answer:

The slope of the line that travels through the points (4, 4) and (5, 3) is -1.

Step-by-step explanation:

The slope formula is:

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

where m is the slope of the line, (x1, y1) and (x2, y2) are the given points. Plugging in the values for (4, 4) and (5, 3):

m = (3 - 4) / (5 - 4)

m = -1 / 1

m = -1

The slope of the line that travels through the points (4, 4) and (5, 3) is -1.

Answer:

11x-11x+9 it's the answer the number having same value in top add then or sub them ok bro

The required, maximum number of people Yoseph can have at the party is 13 people.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

As mentioned in the question, Joseph wants to surprise his wife with a birthday party at her favorite restaurant .it will cost birr 56.50 per person for dinner, including tips and taxes. his budget for the party is birr 735.

So, the ratio of the budget to the cost per person defines the maximum number of people Yoseph can have at the party,
= 735 / 56
= 13 people

Thus, the required, maximum number of people Yoseph can have at the party is 13 people.

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in the knitting pattern, since the m<2 is the exterior angle, the measure of the exterior angle is 132°

Exterior angles of a right-angled triangle are calculated by the sum of the opposite interior angles. It can also be calculated by using the sum of angles in a triangle, followed by using the sum of angles on a straight line to determine the exterior angles.

Here, m < 1 = 42°, and the other angle is 90°

Thus, if the sum of the two opposite interior angles equals the exterior angles, then:

m< 2 = 42° + 90°

m< 2 = 132

Therefore, in the knitting pattern, since the m<2 is the exterior angle, the measure of the exterior angle is 132°

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Therefore, the inverse of the function y = x^2 + 2 is: y = ±√(x - 2)

To find the inverse of the function y = x^2 + 2, we need to switch the roles of x and y, and then solve for y.

Step 1: Write the function with x and y swapped:

x = y^2 + 2

Step 2: Solve for y. To do this, we'll need to isolate the y variable on one side of the equation. We can start by subtracting 2 from both sides:

x - 2 = y^2

Step 3: Take the square root of both sides. When we do this, we'll need to include both the positive and negative square root, since a square can have two possible roots:

±√(x - 2) = y

Step 4: Simplify the answer by using the ± symbol to show that there are two possible inverses:

y = ±√(x - 2)

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The total area of the rectangular openings which should be painted is 1.3 sq meters.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

Given that, the total area covered by 6 rectangular openings is 1.3 square meters, we need to calculate the total amount of area of rectangular openings which should be painted,

Since, it is already given that the area of the rectangular opening is 1.3 m²

Therefore, the area which need to be painted is 1.3 m²

Hence, the total area of the rectangular openings which should be painted is 1.3 sq meters.

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Answer:

3,076.5 rounded

Step-by-step explanation:

58 divided by 2.8 = 25.2173913043 for the unit rate. Then multiply by 122 = 3,076.5217391246.

Answer:

2/5, 8/25, 3/20, 37/100, 24/25

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If we know that percentages are fractions of 100, we can convert these percentages:

Simplifying these fractions:

Therefore, the percentages as simplified fractions are listed above.

The values of x and y after solving the simultaneous equations are; x = 37/11 and y = 17⁸/₁₁

The two simultaneous equations given are;

-2x + y = 12   -------(1)

y = -26 - 9x   ------(2)

Let us make y the subject in eq 1 to get;

y = 2x + 12   -----(3)

Subtract eq 2 from eq 3 to get;

0 = 2x + 12 + 26 + 9x

11x + 37 = 0

11x = 37

x = 37/11

Similarly;

y = 2(37/11) + 12

y = 74/11 + 12

y = 6⁸/₁₁ + 12

y = 18⁸/₁₁

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Answer:

In 2005, there were 1,200 students at the school.

Step-by-step explanation:

In 2005, there were 1,200 students at the school. This can be calculated by taking 85% of 1020 (the number of students in 2006) and multiplying it by 100. 85% of 1020 is 861. Multiplying this by 100 gives us 86,100. Dividing this by 85 gives us 1,200. Therefore, in 2005 there were 1,200 students at the school.

The function, f(x), that models the number of tenrecs after x years is f(x) = 698(2)^x

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

Initial value, a = 698

Rate, b = 2 i.e. doubles

Using the above as a guide, we have the following:

f(x) = ab^x

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

f(x) = 698(2)^x

Hence, the function is f(x) = 698(2)^x

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The value(s) of c guaranteed by the mean value theorem for integrals for the function over the given interval is proved.

The mean value theorem for integrals states that if a continuous function f is defined on a closed interval [a, b], then there exists a number c in the interval (a, b) such that the average value of the function over the interval is equal to the value of the function at c.

Mathematically, this can be expressed as:

[tex]\frac{1}{b-a} \int_{a}^{b} f(x) dx = f(c)[/tex]

where c is a number in the interval (a, b) and the integral sign represents the area under the function from a to b.

The mean value theorem for integrals tells us that there is always a point in the interval where the average value of the function is equal to the function's value at that point. However, it does not tell us the value of c. To find the value of c, we need to solve for it in the equation above.

In conclusion, the mean value theorem for integrals is a useful tool for understanding the average value of a function over an interval and finding the value of c where the average value is equal to the function's value at that point.

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The solution is, if the expression x^3 + 10x + 25 is factorable then, the value of b is, 10 = b.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Begin by expanding (x + 5)^2

(x + 5)(x + 5)

First: x*x = x^2

Outside: x *  5 (the last term which is a 5)

Inside: 5+ x

Last:  5*5 = 25

x^2 + 5x + 5x + 25

x^3 + 10x + 25

Hence, The solution is, the value is, 10 = b.

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The cost of the rentals be equal after 2 days

A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.

Let d represent the he number of days for which the car is rented

The cost for Hertz can be represented will be

= 115 + 210d,

The cost for Avis will be

= 255 + 190d.

We can set the two costs equal to each other and solve for d:

115 + 210d = 255 + 190d

95 = 45d

d = 95 / 45

d = 2

Hence, the cost of the rentals will be equal after 2 days.

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Answer:36

Step-by-step explanation: 2x6x3=36

Nakeisha has 36 different outfits to choose from.

It is a theorem that states that if there are n things, each with [tex]n_1[/tex] ,[tex]n_2[/tex] , [tex]n_3[/tex], ..... [tex]n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

N=  [tex]n_1[/tex] x [tex]n_2[/tex] x [tex]n_3[/tex] x.....x [tex]n_n[/tex]

Given:

We have 2 pairs of pants, 6 t-shirts, and 3 pairs of shoes.

For the pants we have [tex]n_1[/tex] = 2

For the t-shirts we have [tex]n_2[/tex] = 6

For the shoes we have [tex]n_3[/tex] = 3

Thus, the total number of outfits is given by:

= 2 x 6 x 3

= 36

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If one could fund the entire federal budget by working a single 8-hour work day, approximately 3,085.35 seconds of that working day would be devoted to paying the amount earmarked for public broadcasting.

Scientific notation is a method of writing extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, it is written in scientific notation.

Here,
To put the amount earmarked for public broadcasting into perspective, we can compare it to the total annual federal budget and calculate how much time would be spent working to pay for it.

First, let's convert both amounts to the same unit of measurement, such as dollars per second. If we assume an 8-hour work day,
8 * 60 * 60 = 28,800 seconds,

Then the federal budget can be funded at a rate of,
= 4.75 × 10¹²/ 28,800 seconds
= 165,278.47 dollars per second.

Next, we can divide the amount earmarked for public broadcasting by the rate of funding to find the number of seconds devoted to paying for it,

= 510 × 10⁶ / 165,278.47 dollars per second
= 3,085.35 seconds

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Answer: $7,291.14

Step-by-step explanation: To calculate the value of the car in 2020, you can use the formula y = 20,000(0.85)^10.

Here, y represents the value of the car in 2020, 20,000 is the initial value of the car, and 0.85 is the depreciation rate. The exponent 10 represents the number of years that have passed, so the formula calculates the value of the car after 10 years by multiplying the initial value by the depreciation rate raised to the power of 10.

To perform this calculation, you can calculate 0.85^10 first, and then multiply that result by 20,000:

0.85^10 = (0.85)(0.85)(0.85)...(0.85) (10 times)

      = 0.364569708

y = 20,000 * 0.364569708

 = 7,291. 139416

So the value of the car in 2020 would be approximately $7,291.14.

The system of equations are solved graphically and the value of x and y are -1 and -1 respectively

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the first equation be be P

y = 3x + 2   be equation (1)

Let the second equation be Q

y = -x - 2   be equation (2)

Now , the slope of the line P is m₁ = 3

The slope of the line Q is m₂ = -1

On simplifying the equations , we get

3x + 2 = -x - 2

Adding x on both sides , we get

4x + 2 = -2

Subtracting 2 on both sides , we get

4x = -4

Divide by 4 on both sides , we get

x = -1

Substitute the value of x in equation (1) , we get

y = -3 + 2

y = -1

Hence , the equations are plotted on the graph value of x and y are ( -1 , -1 )

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The option A is correct because the value of the statement is 6+3/n-8.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

According to the statement

we have given that the statement and we have to write the statement in the numerical form.

So, For this purpose

we know that the given statement is

"Six more than the quotient of three and a number, decreased by eight".

In this statement "Six more than" indicates the sum between the quotient and 6.

And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.

"Decreased by eight" indicates a subtraction between the quotient an 8 units".

If we unit all parts of the statements, we would have

6+3/n-8

So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.

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The inequality equation is 0 < y ≤ 56/17

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( -56 / y ) - 11 ≤ -28   be equation (1)

On simplifying the equation , we get

Adding 11 on both sides of the equation , we get

-56 / y ≤ -17

On further simplification , we get

( -56 + 17y ) / y ≤ 0

Therefore , the inequality equation is 0 < y ≤ 56/17

Hence , the inequality is 0 < y ≤ 56/17

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This implies that the QS of good Y increases at the same price and as such, the S curve of good Y will experience a rightward shift.

The quantity provided (QS) of the good Y at different prices would be determined by the supply (S) curve of the good Y. (P). The fact that resource X is utilized in the supply of good Y suggests that resource X is an input employed in the creation of good Y. When a result, as the P of resource X declines, the cost of producing good Y increases, and in response, the producers of good Y raise the QS of good Y. This suggests that the QS of good Y grows at the same rate, leading to a rightward shift in the good Y S curve

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Answer: G24

Step-by-step explanation:

ITS REALLY EASY I DID THIS ONCE BUT I GOT 100% so

Answer:

Step-by-step explanation:

All answers are mentioned below.

A function is a mathematical concept that assigns to each input value (or "argument") exactly one output value (or "image"). In other words, a function is a rule that assigns a unique output for each input value. . A function can be represented graphically as a curve, or analytically as a formula. Functions play a central role in many areas of mathematics, science, and engineering.

1. True. The function f(x) = 2x^3 + 8 has no restrictions on x, so the domain of the function is all real numbers.

2. False. The range of the function f(x) = 2x^3 + 8 is (8, ∞), not (0, ∞). The value of the function f(x) will always be greater than or equal to 8 for all values of x.

3. False. The y-intercept of the function f(x) = 2x^3 + 8 is (0, 8), not (0, 0). When x = 0, the value of the function f(x) is 8.

4.True. The function f(x) = 2x^3 + 8 is an odd function, which means that it has a center of symmetry at x = 0. The center of symmetry of an odd function is the point at which the function is symmetric about the y-axis. The value of the function at the center of symmetry is equal to the y-intercept, which in this case is 8. Therefore, the center of symmetry of the function f(x) = 2x^3 + 8 is (0, 8).

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The range of the function f(x) = [tex]2x^{3}[/tex] + 8 is (8, ∞), not (0, ∞). The center of symmetry of an odd function is the point at which the function is symmetric about the y-axis.

A function is a mathematical concept that assigns to each input value (or "argument") exactly one output value (or "image"). In other words, a function is a rule that assigns a unique output for each input value. . A function can be represented graphically as a curve, or analytically as a formula. Functions play a central role in many areas of mathematics, science, and engineering.

1. True. The function f(x) = [tex]2x^{3}[/tex] + 8 has no restrictions on x, so the domain of the function is all real numbers.

2. False. The range of the function f(x) = [tex]2x^{3}[/tex] + 8 is (8, ∞), not (0, ∞). The value of the function f(x) will always be greater than or equal to 8 for all values of x.

3. False. The y-intercept of the function f(x) = [tex]2x^{3}[/tex] + 8 is (0, 8), not (0, 0). When x = 0, the value of the function f(x) is 8.

4.True. The function f(x) = [tex]2x^{3}[/tex] + 8 is an odd function, which means that it has a center of symmetry at x = 0. The center of symmetry of an odd function is the point at which the function is symmetric about the y-axis. The value of the function at the center of symmetry is equal to the y-intercept, which in this case is 8. Therefore, the center of symmetry of the function f(x) = [tex]2x^{3}[/tex] + 8 is (0, 8).

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Answer:

Step-by-step explanation:

To increase a number by a certain percentage, we can multiply the number by (1 + the percentage as a decimal).

To find 25% of 28, we can convert 25% to a decimal by dividing by 100:

25% = 25/100 = 0.25

Now, to find what 28 is increased by 25%, we can multiply 28 by (1 + 0.25):

28 * (1 + 0.25) = 28 * 1.25 = 35

So, the result when 28 is increased by 25% is 35.

Answer: 35

Step-by-step explanation:

we know 28 / 4 = 7

so, 7 is 25% of 28, therefore, we can add 7 to 28 and the answer is 35.

(a)The probability that the selected individual owns shares in the balanced fund is 8%, that is 0.08.

(b)The probability that the selected individual owns shares in a bond fund is 26%.

(c)The probability that the selected individual does not own shares in a stock fund is 57%.

(a) A probability is a number that indicates how likely an event is to occur. In this case, the event is the selected individual owning shares in the balanced fund. The percentage of customers who own shares in the balanced fund is given as 8%. This means that if 100 customers own shares in just one fund, 8 of them would own shares in the balanced fund.

(b) To find the probability that the individual owns shares in a bond fund, we need to add up the percentages of customers who own shares in each of the bond funds:

Short bond: 14%

Intermediate bond: 7%

Long bond: 5%

Total bond funds: 14% + 7% + 5% = 26%

So, the probability that the selected individual owns shares in a bond fund is 26%.

(c) To find the probability that the selected individual does not own shares in a stock fund, we need to find the complement of the probability that the individual owns shares in a stock fund. The probability that the individual owns shares in a stock fund is the sum of the percentages of customers who own shares in each of the stock funds:

Moderate-risk stock: 25%

High-risk stock: 18%

Total stock funds: 25% + 18% = 43%

So, the probability that the selected individual does not own shares in a stock fund is 1 - 43% = 57%.

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--The question is incomplete, answering to the question below--

"A mutual fund company offers its customers a variety of funds: a money-market fund, three different bond funds (short, intermediate, and long-term), two stock funds (moderate and high-risk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows.

Money-market 23%

High-risk stock 18%

Short bond 14%

Moderate-risk stock 25%

Intermediate bond    7%

Balanced 8%

Long bond 5%  

A customer who owns shares in just one fund is randomly selected.

(a)What is the probability that the selected individual owns shares in the balanced fund?

(b) What is the probability that the individual owns shares in a bond fund?

(c) What is the probability that the selected individual does not own shares in a stock fund?"

The solution of the equations -4x-2y= -12 and 4x+8y= -24 is {6, -6).

The question above has 2 equation.

Equation I = -4x-2y= -12

Equation II=4x+8y= -24.

Equation I = -4x-2y= -12, replace to 4x= -2y+12

then substituted 4x= -2y+12 into the second equation, namely 4x+8y= -24.

4x+8y= -24

=(-2y+12) +8y= -24

6y+12= -24

6y = -24-12

6y= -36

y = -6

found the value of y is -6.

The next, substitute the value y= -6 into the equation II

4x+8y= -24

4x+8(-6) =-24

4x-48=-24

4x=-24+48

4x=24

x=24/4

x=6

found the value of x is 6.

Therefore the x and y values of those equation in question are 6 and -6.

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The speed of 3 miles per minute expressed in feet per minute will be 15,840 feet per minute.

Unit transformation is the technique of restoring the dimensions of a provided piece between miscellaneous units.

The speed is given below.

Speed = 3 miles per minute

We know that in one mile, there are 5,280 feet. Then convert the speed from miles per minute to feet per minute. Then we have

Speed = 3 x 5,280 feet per minute

Speed = 15,840 feet per minute

The speed of 3 miles per minute expressed in feet per minute will be 15,840 feet per minute.

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