Select the correct answer.
In the given diagram, line segment BD bisects angle ABC. Segment BD is extended to E, where line segment EC is parallel to
line segment AB. Write a two-column proof to show that AB = BC

Answer:

[tex]a=7[/tex]

Step-by-step explanation:

The legs of an isosceles right triangle are congruent.

The Pythagorean Theorem may be used to calculate the length of side a: [tex]a^{2}[/tex] = 72 + [tex]b^{2}[/tex] = 49 + [tex]b^{2}[/tex]. When we solve for a, we obtain a = (49 + [tex]b^{2}[/tex]). As a result, the length of side an equals the square root of 49 multiplied by the square of side b.

The Pythagorean Theorem is a mathematical equation that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the other two sides. The Pythagorean Theorem is stated in equation form as [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex], where a and b are the lengths of the triangle's legs (the two sides that meet at a right angle) and c is the length of the hypotenuse.

In the given question,

a = 7 * sin(45°)

  = 7 * 0.707

  = 4.949

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6  is the length of segment AC in right-angled triangle .

What is a right-angle triangle, exactly?

A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees.

               Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

  let length of AC is x

   BC + CD = AC + DE

  4 + 8 = X + 6

     12 = X + 6

       X = 6

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The length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.

What is a triangle ?

Triangle can be defined in which it contains 3 sides and 3 angles and the sum of three angles is 180 degrees .

Given

Triangle GHC is similar to triangle JKC

JK = 15

KC = 20

JC = 18

GH = 6

SO,

△GHC ~ △JKC

we know that

(GH/GC) = (JK/JC)

(6/GC) = (15/18)

GC= 6 * 18 / 15

GC = 36 / 5

GC = 7.2

Hence , the length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.

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By using the recursive formula for the sequence, we will see that the second term is:

f(2) = -4

We know that the sequence is defined by the recursive formula:

f(1) = 3

f(n + 1) = -3*f(n) + 2

(notice that the formula is written incorrectly in the question, as it not completely defines a sequence).

We want to find the second term of the sequence, which is f(2).

Using the second part of the formula, we will get:

f(2) = -3*f(1) + 2

And we know that f(1) = 3

Then:

f(2)= -3*3 + 2

f(2) = -6 + 2 = -4

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Answer:

0.10 and 0.90 are the correct answers.

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} & \sf Jazz&\sf Blues & \sf Ragtime & \sf Total\\\cline{1-5} \sf Adult & 14& 15&11 & 40\\\cline{1-5} \sf Children &36 &6& 18& 60\\\cline{1-5} \sf Total &50 &21 &29 & 100\\\cline{1-5}\end{array}[/tex]

From observation of the table:

To find the percent of the children surveyed that preferred ragtime music, divide the number of children that preferred ragtime music by the total number of children:

[tex]\begin{aligned}\implies \sf Percent&=\dfrac{\sf Children\;who\;preferred\;ragtime}{\sf Total\;children}\\\\&=\dfrac{18}{60}\\\\&=\dfrac{18 \div6}{60\div 6}\\\\&=\dfrac{3}{10}\\\\&=\dfrac{3 \times 10}{10 \times 10}\\\\&=\dfrac{30}{100}\\\\&=30\%\end{aligned}[/tex]

1100 Absolute is a 30.55% increment relative percent

To find an Increment percentage in population we need the Number of increases in population.

4700- 3600 = 1100

That is absolutely increased number.

For relative increment, we need to find the Percentage -

so the population in 2007 was 3600

so  percentage = 1100/3600*100

=> 30.55%

SO Relative increase =  30.55%

Here we can see that percent is the way to analyze the change, Increment/decrease in terms of 100 as it multiple the fractional changes in quantity by 100 to make it out of 100. So percentage simply means out of 100.

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The algebraic expression that she can use to represent the scenario would be = $x-25/2

Algebraic expression is defined as the expression that can be used to represent a constant algebraic number, variables, and the algebraic operations.

The amount of money Tamika and her friend sold their old toys= X dollars

The amount of money that Tamika had to pay back to her parents = $25

Therefore the remaining amount = X - 25

The amount of money that she divided between her friend and her = $ x-25/2

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Answer:

Step-by-step explanation

since they are complementary their angles should add up to 90.

18+(8x-28)=90

you solve from there

add common values

8x-10+90

add 10 to both sides

8x=100

divide by 8

x=12.5

The answer is:

Work/explanation:

Since we're given both angles, we can set up an equation and find x.

The sum of two complementary angles is 90°.

Now, set up the equation:

[tex]\sf{8x-28+18=90}[/tex]

[tex]\sf{8x-10=90}[/tex]

Add 10 on each side

[tex]\sf{8x=100}[/tex]

Divide each side by 8

[tex]\sf{x=12.5}[/tex]

The values of trigonometric functions are sinα = -10 and cotα =  -10/24.

What is the trigonometric functions?

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[) are real functions that relate an angle of a right-angled triangle to ratios of two side lengths.

They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.

We have given,

tanα = -(24/10)  and π α < 2π

To Find: sinα =? & cotα = ?

 [tex]{\displaystyle \tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}}\tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}[/tex]

cotα =   -10/24

sinα = -10

Therefore, the values of trigonometric functions are sinα = -10 and  cotα =   -10/24.

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To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.

What is integral definition ?

The integral definition of the Laplace transform is a mathematical method used to find the Laplace transform of a function. It is defined as,

F(s) = L{f(t)} = ∫ f(t) e^(-st) dt , Where F(s) is the Laplace transform of the function f(t), s is a complex variable known as the frequency domain variable, and t is the time domain variable.

Given the functions f(t) provided ,

f(t) = e^(-8t)sin(5t)

F(s) = L{e^(-8t)sin(5t)} = ∫ e^(-8t)sin(5t) e^(-st) dt = (5/(s+8+5i))(e^(-8-s)) - (5/(s+8-5i))(e^(-8-s))

f(t) = e^(-st)sinh(7t)

F(s) = L{e^(-st)sinh(7t)} = ∫ e^(-st)sinh(7t) e^(-st) dt = (7/(s^2+49))(e^(-s-7i)) - (7/(s^2+49))(e^(-s+7i))

f(t) = -7t cosh(5t)

F(s) = L{-7t cosh(5t)} = ∫ -7t cosh(5t) e^(-st) dt = (-7/s^2)(e^(-s-5)) - (7/s^2)(e^(-s+5))

f(t) = 9t sin(ut)

F(s) = L{9t sin(ut)} = ∫ 9t sin(ut) e^(-st) dt = (9/(s^2 + u^2))(e^(-su)) - (9/(s^2 + u^2))(e^(su))

Note that in all cases, we should check if the integral converges, and that the limits of integration are appropriate.

To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.

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Answer:

Equilateral Triangle

Step-by-step explanation:

Answer:

Equilateral

Step-by-step explanation:

The Answer to this given question is a Equilateral

Reason : The sides of an equilateral triangle are congruent, which means that all sides are of equal length.

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The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).

Probability theory is the study of how likely it is that an event will occur or that a statement is true. A number between 0 and 1, roughly 0 signifying how unlikely an event is to occur and 1, signifying certainty, is the probability of an event occurring. The likelihood or likelihood that a particular event will occur is expressed numerically as a probability. It is also possible to express probabilities as percentages between 0% and 100% or as percentages between 0 and 1. the percentage of all possible outcomes divided by the total number of events in a complete collection of equally likely alternatives that result in a specific occurrence.

given

It may take the following forms:

(4,6),(5,5),(5,6),(6,5),(6,6)

the likelihood that the total exceeds 9 is 1/36+1/36+1/36+1/36.

=5/36.

B) The following are some possible scenarios:

(1,4),(4,1),(3,3),(3,2),(4,2),(5,1),(1,5),(6,4),(4,6)

The likelihood that the number will be divisible by five, six, or both is

1/36 plus eight times

=9/36

Therefore, The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).

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As rain drop and sink through the rock, it often solvates some of the iron. It conveys that iron along with it as it continues to seep through the rock and soil.

When the rainwater becomes groundwater or dart into freshwater sources like lakes and rivers, it may become the part of the local water supply.

Municipal water systems that get their water from these sources can end up with high levels of iron in their water, and the riddle they have set up to remove bacteria and other harmful contaminants may not always riddle it out.

Wells that portray water from aquifers with high iron content may contain high iron concentrations as well.

Iron in water generally takes two types of ferrous iron, which is soluble in water, and next one is ferric iron, which is insoluble.

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Answer:

Domain: [0, ∞)

Range: [√5, ∞)



Step-by-step explanation:

Find the domain by finding where the piecewise is defined. The piecewise range is the set of values that correspond with the domain.

Domain: [0, ∞)

Range: [√5, ∞)

hope that helps...

Answer:

he earns $500 from the lessons from both groups of students.

Step-by-step explanation:

To summarize:

There are 14 students in set R (piano students)

There are 10 students in set R (piano students) who are not in set S (saxophone students)

There are 11 students in set S (saxophone students)

There are 14 + 11 = 25 total students in both sets R and S

There are 4 students who are common to both R and S, that are taking saxophone for free

The music teacher will get $280 for the piano students

The music teacher will get $220 for the saxophone students.

So the total he earns is $280 + $220 = $500 from the lessons from both groups of students.

There are only three correct equations for the area of the right triangle which are:

The area of a triangle is calculated by dividing the product of the base and height of the triangle.

base of the triangle = x

height of the triangle = x + 2

area of the triangle = 1/2(x)(x + 2)

so

1/2(x)(x + 2) = 24...(1)

1/2 is also 0.5, so the equation 0.5(x)(x + 2) = 24 is correct.

by cross multiplication, equation (1) becomes;

x(x + 2) = 48

x² + 2x = 48 {expand the left hand side}

x² + 2x - 48 = 0 {subtract 48 from both sides}

so the equation x² + 2x - 48 = 0 is correct.

Considering the last equation, x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x = 100 - 4 {collect like terms}

2x² + 4x = 96 {divide through by 2}

x² + 2x = 48

x² + 2x - 48 = 0

so the equation x² + (x + 2)² = 100 is equivalent to the equation (1) and so is also correct.

Therefore, the equations 0.5(x)(x + 2) = 24, x² + 2x - 48 = 0, and x² + (x + 2)² = 100 are correct and can be used to find the length of sides for the right triangle.

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Answer:

5509 yes votes

Step-by-step explanation:

We will start by adding together our ratio, so we know how many voters there were in a total ratio, so we can divide our total number of people by it, and then multiply it by the number of people who said yes (7 people).

Our ratio was 7:4, so adding those two numbers together gives us 11. Then, dividing 8657 by 11 gives us:

8657 / 11 = 787

Now, we will multiply 787 by 7, since that was the number of people who said yes:

787 * 7 = 5509

So, there were 5509 yes votes.

Hope this helped!

O a² + 10² 5² =25 + 100 =2a ,2a=125 , a=\sqrt{125} , a=11.18 m

Therefore, the missing side (a) is 11.18 m.

We are trying to find the missing side (a) of the triangle shown in the diagram.

To do this, we will use the Pythagorean Theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side.

The two shorter sides of the triangle are 5 m and 10 m.

We will use the Pythagorean Theorem to calculate the missing side (a).

First, we need to square the lengths of the two shorter sides:

5² = 25

10² = 100

Next, we add the squares of the two shorter sides together:

25 + 100 = 125

Finally, we take the square root of the sum to find the length of the missing side:

√125 = 11.18 m

Therefore, the missing side (a) is 11.18 m.

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Price divided by size is the formula for calculating the price per square foot (in square feet). For instance, if a 2,000-square-foot property is being sold for $300,000, the price per square foot would be $150 if you took the overall price and divided it by the size.

What do you mean by rectangular area?

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Answer:

-35/24

Step-by-step explanation:

5/8 - (3 - 1/4) + 2/3 =

Distribute the negative sign to 3 and -1/4. When a negative sign is distributed to a negative number, that number becomes positive:

- (3 - 1/4)  ==> -3 + 1/4

5/8 - 3 + 1/4 + 2/3 =

Now multiply the equation by 24/24 = 1. Multiplying anything by 1 results in the same equation. For example, 8 * 1 = 8.

Also multiply the equation by 24/24 because 24 is the LCM (Least Common Multiple) of the denominators 8, 4, and 3: 8*3=24. 6*4=24.

(5/8 - 3 + 1/4 + 2/3) * 24/24 =

(5*24/8 - 3*24 + 1*24/4 + 2*24/3) / 24 = ==> multiply each term by 24 and

                                                                    divide the entire expression by 24

(120/8 - 72 + 24/4 + 48/3) / 24 = ==> simplify

(15 - 72 + 6 + 16) / 24 =

(-57 + 22) / 24 = -35/24                                      

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The value of the numerical expression 5/8 - (3 - 1/4) + 2/3 is -35/24.

When used to represent a quantity or a mathematical relationship, symbols and numbers are combined to form an expression in mathematics. It may contain exponents, brackets, variables, constants, and mathematical operations like addition, subtraction, multiplication, and division.

To simplify the expression 5/8 - (3 - 1/4) + 2/3, we need to follow the order of operations (also known as PEMDAS):

First, we need to simplify the expression inside the parentheses (3 - 1/4):

3 - 1/4 = 12/4 - 1/4 = 11/4

Next, we need to subtract 11/4 from 5/8:

5/8 - 11/4 = 5/8 - 22/8 = -17/8

Finally, we need to add 2/3 to the result:

-17/8 + 2/3

To add these two fractions, we need to find a common denominator. The least common multiple of 8 and 3 is 24, so we can rewrite the fractions with a denominator of 24:

-17/8 + 2/3 = (-51/24) + (16/24) = -35/24

Therefore, the value of the numerical expression 5/8 - (3 - 1/4) + 2/3 is -35/24.

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Researchers frequently select a level of significance of 0.05. The reason for this is that if we chose a lower threshold of significance, we will have less room to reject the null hypothesis and so a higher likelihood of making a type 2 error.

On the other hand, if the degree of significance is higher, more type 1 errors are made, leading us to reject the hypothesis even though it is correct. Therefore, 0.05 is a balanced level that is neither significantly greater nor significantly smaller. The health care and nutrition-related industries are mostly included in some of the studies where we require a lower level of importance. This type of industry has a higher error rate, which causes more fatalities and negative side effects.

We can use a higher level of relevance in a variety of circumstances, such as the entertainment and marketing-related industries. The reason for this is that even if there are more potential for error, it won't harm the person; instead, it just affects the information, which we can assess using common sense.

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Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true include the following: A, it cannot be proportional because the straight line through the points does not go through the origin.

In Mathematics, the graph of any proportional relationship between two (2) variables is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

By critically observing the graph which shows a relationship between the x-values and y-values, we can logically deduce that it does not start from the origin (0, 0) and as such, it does not represent a proportional relationship.

In this context, we can reasonably infer and logically conclude that cost is not proportional to area in the situation represented by this graph.

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Answer: If Pedro starts reading at page 20 and reads at an average rate of 25 pages per hour, and Bella starts reading at the same time but starts at page 60 and reads at an average rate of 18 pages per hour,

We can use the formula: distance = rate x time

To find out when they will meet we need to find out when they are on the same page.

let's say t be the time in hours, Pedro will be reading t25 pages, and Bella will be reading t18 pages.

So we can write the equation: 20+t25 = 60+t18

Solving this equation we get t = 2

So, they will meet after 2 hours.

Pedro will be on page 20+225 = 70, and Bella will be on page 60+218 = 96

So they will meet at page 70 when Pedro reaches that page after 2 hours of reading, which means Bella will have read 26 pages more than Pedro on that point.

Step-by-step explanation:

Answer: it will be improper

Step-by-step explanation:11/4

Answer:11/4

Step-by-step explanation:it is improper.

As long as they are not all on the same line, three points can define a plane in a three-dimensional space.

Intersecting Space with Planes A plane just divides space into two distinct regions. Space is divided into a maximum of four sections by two planes. Space can only be divided into eight sections by three planes.

One line has the ability to split a plane into two regions; two non-parallel lines have the ability to divide a plane into four regions; three non-parallel lines have the ability to divide a plane into seven regions; and so on.

Four unique, nonintersecting zones can be created by selecting three separate points on a circle and connecting each pair of them with a chord.

Three points can define a plane in a three-dimensional space as long as they are not all on the same line.

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One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions.

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The order for the process of Statistcal Method will be Identify the research objective, Collect the data needed to Answer the Research question, Describe the data, and Perform Inference.

For any statistics method, we first must have an objective as to why are we conducting that research. Hence the first process has to be Identifying the research objective.

For any statistical method, samples need to be drawn to conduct statistic tests. This essentially requires data to work with. Hence, Collecting the data needed to Answer the Research question must be the next step.

After data is collected, numerous tests are possible to be performed on any set of data but to select the most appropriate statistic, we need to first understand the nature, range, and limitations of the data. Hence, the net step should be to describe the data.

The last step out of the available step would be to perform the inference since this is the only other step possible from the ones mentioned.

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Answer:

4/7 = 12/g cannot be true, as the numbers on the right side of the equation are not related to the numbers on the left side of the equation and cannot be used to solve for the variable "g".

The correct way to solve for the variable in an equation like this is by cross-multiplying and simplifying the equation.

4/7 = 12/g

multiply both sides by 7g

4*g = 12

Divide both sides by 4

g = 3

So in this case the value of g is 3, but the given numbers 21 15 24 3 are not related to this equation.

Step-by-step explanation:

Answer:12/21

Step-by-step explanation:

cross-multiply 4/7 = 12/g so 4g = 84 . 4 x3 =12 7x3=21 So the answer is 12/21.

The function is  A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is  $175.64.

What is compound interest?

The interest that is calculated using both the principal and the  interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the principal = $120

Rate of interest = 6.4%  = 6.4/100 = 0.064C. Then,

Now using compound interest formula then,

Amount A = P[tex](1+\frac{r}{n} )^{nt}[/tex]

Here n=4 compound quarterly

A = 120[tex](1+\frac{0.064}{4} )^{4t}[/tex]

=> A= 120[tex](1+0.016)^{4t}[/tex]

=> A = 120[tex](1.016)^{4t}[/tex]

The function is A = 120[tex](1.016)^{4t}[/tex]. Now years t = 6 then

=> A = A = 120[tex](1.016)^{4*6}[/tex] = 120[tex](1.016)^{24}[/tex]

=> A =  $175.64

Hence the function is  A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is  $175.64 .

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