100 points.

My teacher asked for me to specify which two theorems I used. And I don't know. Here is my work can someone help please.


Isosceles Right Triangle Reflection to prove ASA Congruence


1. Answer the following questions:
A. What line of reflection did you choose for your transformation?
- I used the y-axis as my line of reflection.
B. How are you sure that each point was reflected across this line?
- I am sure because the sides are all opposite, but the numbers stayed the same.
C. What reflection rule did you apply to your triangle?
- (x, y) ➟ (-x, y)

2. What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.
- I learned that if two sides of my triangle are congruent then the angles opposite of them are congruent as well. The third angle is 90 degrees.

3. Did your triangle undergo rigid motion? Explain why.
- Yes, it did. It did because the distance and position stayed the same while the points and the plane moved.

The CO emission of a gasoline engine equipped with a three-way catalytic converter is influenced by several factors, including the in-cylinder gas temperature, the exhaust gas temperature, and the equivalence ratio of the air-fuel mixture. Understanding the relationship between these factors and CO emission is essential for controlling and reducing CO emissions in gasoline engines.

The CO emission of a gasoline engine equipped with a three-way catalytic converter is affected by the in-cylinder gas temperature, the exhaust gas temperature, and the equivalence ratio of the air-fuel mixture.

Firstly, the in-cylinder gas temperature plays a crucial role in CO formation. Higher in-cylinder temperatures promote the oxidation of CO to carbon dioxide (CO2) within the combustion chamber.

Thus, when the in-cylinder gas temperature is high, more CO is converted to CO2, resulting in lower CO emissions. On the other hand, lower in-cylinder temperatures can inhibit the oxidation of CO, leading to higher CO emissions.

Secondly, the exhaust gas temperature also influences CO emissions. A higher exhaust gas temperature provides more energy for the catalytic converter to facilitate the oxidation of CO.

As the exhaust gas passes through the catalytic converter, the elevated temperature enhances the chemical reactions that convert CO to CO2. Therefore, higher exhaust gas temperatures generally result in lower CO emissions.

Lastly, the equivalence ratio of the air-fuel mixture affects CO emissions. The equivalence ratio is the ratio of the actual air-fuel ratio to the stoichiometric air-fuel ratio. In a three-way catalytic converter, the stoichiometric air-fuel ratio is crucial for the efficient conversion of pollutants.

Deviations from the stoichiometric ratio can lead to incomplete combustion and increased CO emissions. Lean air-fuel mixtures (excess air) with equivalence ratios greater than 1 result in lower CO emissions, as excess oxygen promotes the oxidation of CO to CO2.

Conversely, rich air-fuel mixtures (excess fuel) with equivalence ratios less than 1 can result in incomplete combustion, leading to higher CO emissions.

In conclusion, the in-cylinder gas temperature, exhaust gas temperature, and equivalence ratio of the air-fuel mixture all play significant roles in determining the CO emission levels in a gasoline engine equipped with a three-way catalytic converter.

By controlling and optimizing these factors, it is possible to reduce CO emissions and improve the environmental performance of gasoline engines.

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Answer:

6x - 3 + 4x = 13

10x - 3 = 13

10x = 16

x = 1.6

Any equation whose solution is    x=1.6   has the same solution as this one has.

Step-by-step explanation:

Their hourly wage in 9 more years is $23.60 per hour.

To find the hourly wage in 9 more years, we can use the formula for exponential growth:

A = \(P * (1 + r)^t\)

Where:

To find the annual growth rate, we can use the formula:

r = \((A/P)^(^1^/^t^)\) - 1

Substituting the given values, we get:

r = \((\$16.09 / \$6.90)^(^1^/^1^1^)\) - 1

r = 0.0883 or 8.83%

Now we can use this growth rate to find the hourly wage in 9 more years:

A = $6.90 * \((1 + 0.0883)^9\)

A = $23.60 (rounded to the nearest cent)

Therefore, the hourly wage of the automobile plant workers in 9 more years, if their wages continue to grow exponentially at the same rate, would be $23.60 per hour.

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Answer:

10

Step-by-step explanation:

Align the data from smallest to largest

3,8,9, 11, 14,  15*

The median is the middle number

3,8,9,     11, 14,  15*

It would be between the 9 and 11 since there is an even number of numbers

(9+11)/2 = 20/2 = 10

The median is 10

Solution:

Arranging the data in ascending order:

3,8,9,11,14,15

N(total number of items)=6

Median=(N+1/2) th item

=(6+1/2)th item

=(7/2)th item

=3.5th item.

Median=3rd item+4th item/2

=9+11/2

= 20/2

=10

Median =10

Hope it helps...

Answer:

Area of sector of circle = 7.6302 inches (Approx.)

Step-by-step explanation:

Given:

Angle of section = 35°

Radius of circle = 5 inch

Find:

Area of shaded section

Computation:

Area of shaded section  = Area of sector of circle

Area of sector of circle = [θ/360][πr²]

Area of sector of circle = [35/360][(22/7)(5)²]

Area of sector of circle = [0.0972][(3.14)(25)]

Area of sector of circle = [0.0972][78.5]

Area of sector of circle = 7.6302 inches (Approx.)

Step-by-step explanation:

\((7 \: + \: \sqrt{6} ) ^{2} \)

\((7 + \sqrt{6)} (7 + \sqrt{6} )\)

\(49 + 14 \sqrt{6} + 6\)

\(55 + 14 \sqrt{6} \)

The expanded and simplified answer is 55 + 14√6.

The simplified form can be found by carrying out mathematical operations that are pending in the expression. Like the addition, subtraction, multiplication, or division of any number in the expression.

Given: (7 + √6)^(2)

First, we have to square the expression and expand it.

(a + b)^2 = a^2 +2ab b^2

Similarly we can open the brackets of the given expression:

(7 + √6)^(2) = 49 + 2*7*√6 + 6

= 55 + 14√6

This is similar to the format b+c√6. Here b would be 55 and c would be 14. The given expression was expanded and written in the form of b+c√6.

Therefore, we have expanded and simplified the given expression as 55 + 14√6.

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The width of a rectangular room is 3 m shorter than its length. If its perimeter must not exceed 42 m, calculate the greatest length that the room can have.

Option b . The slope of line CD is 4/3 is the correct answer.  The lines AB and CD are hypotenuse of a similar triangle there slopes are equal. Other features of a similar triangle applies too.

Triangles are said to be similar when there corresponding angles and sides are congruent. Typically, the proportions of the corresponding sides are equal sides are equal.

Hence similar triangles has equal slope since the slope is a proportion of corresponding sides. The angles are also equal.

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complete question

These triangles are similar. The equation for line AB is given. What is the slope of line CD?

A. The slope of line CD is 5.

B. The slope of line CD is 4/3.

C. There is not enough information to find the slope of line CD.

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

55.00

Step-by-step explanation:

basically I subtracted 84.25 from 75.49 and I got 8.76. So I too kthat answer and subtracted 8.76 from 63.76. So the answer is 55.00

The exact value of the expression tan 15 + tan 30 / (1 - tan 150 tan 30) is 2/3.

The expression tan 15 + tan 30 / (1 - tan 150 tan 30) can be simplified by expressing each term in terms of sine and cosine functions.

First, let's express tan 15 in terms of sine and cosine. We can use the formula for the tangent of the sum of two angles:

tan(A + B) = (tan A + tan B) / (1 - tan A tan B)

In this case, A = 15 and B = 30. Plugging in these values, we have:

tan(15 + 30) = (tan 15 + tan 30) / (1 - tan 15 tan 30)

Simplifying the right side, we get:

tan(45) = (tan 15 + tan 30) / (1 - tan 15 tan 30)

Since tan 45 equals 1, we have:

1 = (tan 15 + tan 30) / (1 - tan 15 tan 30)

Next, let's express tan 30 in terms of sine and cosine. We know that tan 30 equals sin 30 / cos 30. Since sin 30 equals 1/2 and cos 30 equals √3/2, we have:

tan 30 = (1/2) / (√3/2) = 1 / √3

Now, let's express tan 150 in terms of sine and cosine. We know that tan 150 equals sin 150 / cos 150.

Since sin 150 equals 1/2 and cos 150 equals -√3/2, we have:

tan 150 = (1/2) / (-√3/2) = -1 / √3

Now, we can substitute these values back into the expression:

1 = (tan 15 + 1 / √3) / (1 - (-1 / √3) * (1 / √3))

Simplifying further:

1 = (tan 15 + 1 / √3) / (1 + 1 / 3)

Multiplying both sides by 3 to eliminate the fraction:

3 = 3(tan 15 + 1 / √3)

3 = 3tan 15 + 1

Subtracting 1 from both sides:

2 = 3tan 15

Finally, dividing both sides by 3:

2/3 = tan 15

So, the exact value of the expression tan 15 + tan 30 / (1 - tan 150 tan 30) is 2/3.

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The future value of $900 saved each year for 10 years at 8 percent is approximately $12,585.90.

To calculate the future value, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r,

where:

FV is the future value,

P is the annual payment or deposit ($900 in this case),

r is the interest rate per compounding period (8% or 0.08),

and n is the number of compounding periods (10 years).

Substituting the given values into the formula:

FV = 900 * ((1 + 0.08)^10 - 1) / 0.08,

FV ≈ $12,585.90.

Therefore, the future value of saving $900 each year for 10 years at an 8% interest rate is approximately $12,585.90.

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Answer:

x<-10

Step-by-step explanation:

4x-12-5x>-2

-1x-12>-2

    +12 +12

-1x>10

-1x/-1>10/-1

x<-10

u switch the inequality when the number is divided by a negative number btw:) hope this helped:D

Answer:

393.7 feet per hr

Step-by-step explanation:

200cm per min

12000cm per hr

cm to feet. divide by 30.48

393.7 ft per hr

Answer:

The value of "X" would be 2.

To solve for x, you'd have to get it by itself. To do so, you'd simplify both sides by solv8ng the exonents of each side (2^2 = 4) and (2^3 = 8). This leaves you with 4x = 8, which you'd then divide both sides by 4. Thus getting 2 as a final answer.

I hope this helps!

(can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

183661939573002745832863730

Answer:

GK=JK

Step-by-step explanation:

SSS congruency  is side-side-side congruency. We are given that GH=JH and KH=KH, which are both sides.

For SSS, we need 3 pairs of congruent sides. We already have 2 pairs.

The options are:

<G=<J

<H=<H

GK=JK

the first two options, <G=<J and <H=<H are talking about congruent angles. We don't need to know about congruent angles for SSS

GK=JK is talking about a pair of congurent sides. Then, we would have 3 pairs of congruent sides, satisfying the criteria needed for SSS. Therefore, we must know that GK=JK.

Hope this helps!

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Welk is most likely to be classified as a luxury good. A luxury good is a good for which demand increases more than proportionally with income.

This means that as people's incomes increase, they are more likely to spend a larger proportion of their income on luxury goods.

The income elasticity of demand for a good is a measure of how responsive demand is to changes in income. A positive income elasticity of demand indicates that demand increases as income increases, while a negative income elasticity of demand indicates that demand decreases as income increases.

The income elasticity of demand for Welk is 4.667, which is much higher than the income elasticities of demand for Kang (-3) and Lafgar (1.667). This indicates that demand for Welk is much more responsive to changes in income than demand for Kang or Lafgar.

Therefore, Welk is most likely to be classified as a luxury good.

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Answer:

option D is pretty close but not parallel obviously

Answer:thxx

Step-by-step explanation:

Answer:

p = s + dgh

p - s = dgh

(p - s) / dg = h

Answer = h= p-s/dg

The formula that represents the height "h" in terms of p, s, d, and g is expressed as  (p - s)/dg

Given the formula for determining the pressure, p, exerted  on an object at a depth, h, below the surface of a  liquid expressed as p = s + dgh where:

s is the atmospheric  pressure,

d is the density of the liquid, and;

g is the  acceleration due to gravity

We are to make h the subject of the formula;

p = s + dgh

Subtract s from both sides

p - s = dgh

dgh = p - s

Divide both sides by dg

dgh/dg = (p - s)/dg

h =  (p - s)/dg

Hence the formula that represents the height "h" in terms of p, s, d, and g is expressed as (p - s)/dg

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Answer:

0.025

Step-by-step explanation:

Answer: 0.025

Step-by-step explanation:

Accounting is a profession that has been in existence for thousands of years. Its roots can be traced back to ancient civilizations, such as the Babylonians, who kept records of their financial transactions on clay tablets. Over time, the practice of accounting has evolved, and today, it plays a vital role in society.

The modern accounting profession can be traced back to the early 19th century when the Industrial Revolution spurred the need for accurate record-keeping and financial reporting. As the business landscape grew more complex, the demand for accounting services increased, leading to the creation of professional accounting organizations and the establishment of accounting standards.

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Answer:

the slope or gradient is 8/2=4