In Exercises 11 and 12, write a rule for the translation of LMN to L'M'N'

The incenter Theorem states that the angle bisectors of a triangle intersect at a point equidistant from the sides.

using the Angle Bisector Theorem and the congruence of triangles.

Incenter theorem can use the properties of angle bisectors and the concept of congruent triangles.

Triangle ABC

The angle bisectors of triangle ABC intersect at a point equidistant from the sides.

Draw the triangle ABC.

Let the angle bisectors of angles A, B, and C meet the opposite sides at points D, E, and F, respectively.

Prove that the distances from the incenter denoted as I to the sides of the triangle are equal.

Consider angle A.

Since AD is the angle bisector of angle A, it divides angle A into two congruent angles.

Let's denote them as ∠DAB and ∠DAC.

By the Angle Bisector Theorem, we have,

(AB/BD) = (AC/CD) ___(1)

Similarly, considering angle B and angle C,

(CB/CE) = (BA/AE) ___(2)

(CA/FA) = (CB/BF) ____(3)

Rearranging equations (1), (2), and (3), we get,

AB/BD = AC/CD

CB/CE = BA/AE

CA/FA = CB/BF

Rearranging equation (1), we get,

AB/BD = AC/CD

AB × CD = AC × BD

Similarly, rearranging equations (2) and (3), we get,

CB × AE = BA × CE

CA × BF = CB × FA

Now, consider triangles ABD and ACD.

According to the Side-Angle-Side (SAS) congruence ,

AB × CD = AC× BD

Angle DAB = Angle DAC (common angle)

Therefore, triangles ABD and ACD are congruent.

By congruence, corresponding parts are congruent.

AD = AD (common side)

Angle DAB = Angle DAC (corresponding congruent angles)

Similarly, prove that triangles ECB and ACB are congruent,

BC ×AE = BA × CE

Angle CBE = Angle CBA

Therefore, triangles BCE and ACB are congruent.

By congruence, corresponding parts are congruent.

BE = BE (common side)

Angle EBC = Angle EBA (corresponding congruent angles)

prove that triangles CAF and BAC are congruent:

CA × BF = CB ×FA

Angle ACF = Angle ACB

Therefore, triangles CAF and BAC are congruent.

By congruence, corresponding parts are congruent.

FA = FA (common side)

Angle FCA = Angle FCB (corresponding congruent angles)

Points D, E, and F are equidistant from the sides of triangle ABC.

The angle bisectors of triangle ABC intersect at a point I, called the incenter, which is equidistant from the sides.

Hence, the incenter theorem is proven.

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The vector ū = as a linear combination is ū = [7 3] + J[-2 1]

To find the coefficients for the linear combination of x and y, we need to solve the system of equations: a[6 -1] + b[-5 4] = [u1 u2]

where a and b are the coefficients we want to find. Writing out the system of equations explicitly, we have:

6a - 5b = u1

a + 4b = u2

Solving this system gives:

a = (u1 + 2u2)/17

b = (3u1 - u2)/17

Substituting these coefficients into the linear combination, we get:

ū = [(u1 + 2u2)/17][6 -1] + [(3u1 - u2)/17][-5 4]

= [(6u1 + 3u2 - 2u1 + u2)/17][6 -1] + [(-5u1 + 4u2 + 15u1 - 3u2)/17][-5 4]

= [(4u1 + 4u2)/17][6 -1] + [(10u1 + u2)/17][-5 4]

= [7u1/17 + 2u2/17][6 -1] + [-2u1/17 + u2/17][-5 4]

= [7 3] + J[-2 1]

Therefore, the vector ū can be expressed as ū = [7 3] + J[-2 1].


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The claim that two situations are similar, despite major differences being ignored and only minor similarities being emphasized, is a fallacy known as false analogy.

False analogy is a logical fallacy that occurs when two situations are compared based on minor similarities while ignoring significant differences. It involves drawing an invalid or weak comparison between two unrelated or dissimilar things. In this fallacy, the person making the claim assumes that because two situations share some superficial similarities, they must be similar in all aspects. However, this overlooks the fundamental differences that make the situations distinct.

For example, if someone argues that banning the use of plastic bags in a city is similar to banning the use of cars, based solely on the fact that both involve restricting a common item, they would be committing a false analogy. While there may be minor similarities between the two situations, such as the concept of imposing restrictions, there are major differences in terms of environmental impact, necessity, and alternatives. Ignoring these significant differences leads to an invalid comparison and can result in flawed reasoning.

In conclusion, false analogy occurs when two situations are deemed similar based on minor similarities while disregarding major differences. It is essential to carefully evaluate the relevant factors and understand the nuances of each situation before drawing comparisons to ensure logical and valid arguments.

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Answer:

ok what is this a study guide a test or something else?

Step-by-step explanation:

Answer:

A,C,D are triangles, B is not.

Step-by-step explanation:

Let 3 sides of a triangle be a,b,c.

A triangle have the sum of 3 angles = 180 degree

and

a-b<c<a+b (similar for a and b)

a. three sides measuring 6 cm, 8 cm, and 10 cm

Satisfied the a-b<c<a+b property -> triangle

b. three angles measuring 40 degrees, 70 degrees, and 65 degrees

Total of 3 angles = 40+70+65 = 175 > 180

-> not triangle

c. three angles measuring 10 degrees, 25 degrees, and 145 degrees

Total of 3 angles = 10+25+145 = 180

-> triangle

d. three sides measuring 9 m, 15 m, and 9 m

Satisfied the a-b<c<a+b property -> triangle

Answer:

C

All triangle must equal 180, 40 + 70 + 65 = 175

Answer:

6x - 9

Step-by-step explanation:

We can use the distributive property to solve.

3(2x - 3)

(3 * 2x) + (3 * -3)

6x - 9

Best of Luck!

3(2x-3)

Multiplying each term in the parentheses by 3

3×2x-3x-3

calculate the product

6x-3×3

multiply the number

6x-9

\(\dfrac{z}{10} =5\)

Multiply both sides by 10:

\((\dfrac{z}{10} )\times10=(5)\times10\)

\(\fbox{z = 50}\)

z/10 = 5

Multiply both sides by 10:

z/10 * 10 = 5 * 10

z = 50

Answer:

\(\rm y = -\dfrac{5}{6} x-\dfrac{1}{3}\)

Step-by-step explanation:

The slope intercept form of a line equation is

y = mx + b where m is the slope and b the y-intercept

Slope is given as \(- \dfrac{5}{6}\)

So equation of line is
\(\rm y = -\dfrac{5}{6}x + b\\\\We\;can\;find\;bby\;substituting\;the\;x,\;y\;values\;for\;point\;(2,\;-2)\;into\;the\;equation\\\rm y = -\dfrac{5}{6}x + b\\\\\\\rm We\;can\;find\;by\;substituting\;the\;x,\;y\;values\;for\;point\;(2,\;-2)\;into\;the\;equation\\\\-2 = -\dfrac{5}{6}\times2 + b\\\\-2 = -\dfrac{10}{6} + b\\\\-2 = -\dfrac{5}{3} + b\\\\\)

\(\rm Adding\;\dfrac{5}{3} \;to\;both\;sides\;:\\\dfrac{5}{3} - 2 = b\\\\\dfrac{5-6}{3} = b\\\\b = -\dfrac{1}{3}\)

So equation of line is
\(\rm y = -\dfrac{5}{6} x-\dfrac{1}{3}\)

Answer:

\(\huge\boxed{y=-\frac{5}{6}x-\frac{1}{3}}\)

Useful Information:

The equation of a straight line: \(y=mx+c\)

Step-by-step explanation:

To work this out you would first need to substitute the gradient into the equation, this gives you\(y=-\frac{5}{6}x+c\).

The next step is to substitute the x and y coordinates from the point (2,-2) into the equation, this gives you \(-2=-\frac{5}{6}(2)+c\)

In order to work out the value of c, you would have to bring the value of \(-\frac{5}{6}(2)\) over to the other side, this can be done by adding \(\frac{5}{6}(2)\) or \(-\frac{5}{3}\) to -2, which gives you \(-\frac{1}{3}\).

The final step is to substitute the m value of  \(-\frac{5}{6}\) and the c value of  \(-\frac{1}{3}\) into the equation, this gives you \(y=-\frac{5}{6}x-\frac{1}{3}\)

1) Substitute the gradient.

\(y=-\frac{5}{6}x+c\)

2) Substitute the x and y coordinates.

\(-2=-\frac{5}{6}(2)+c\)

3) Bring \(-\frac{5}{6}(2)\) over to the other side.

\(c=-2+\frac{5}{6}(2)\)

4) Simplify to find the value of c.

\(c=-\frac{1}{3}\)

5) Substitute the m and c values.

\(y=-\frac{5}{6}x-\frac{1}{3}\)

The truth values of the statement are

a) Q(Denver, Colorado) is true

b) Q(Detroit, Michigan) is false

c) Q(Massachusetts, Boston) is true

d) Q(New York, New York) is false

In this case, we are considering statements of the form "x is the capital of y," where x and y are specific places. These statements can have different truth values, depending on whether they are true or false. Let's explore the truth values of some specific examples.

a) Q(Denver, Colorado)

This statement asserts that Denver is the capital of Colorado. Is this true or false? Well, the capital of Colorado is actually Denver, so this statement is true. Therefore, the truth value of Q(Denver, Colorado) is true.

b) Q(Detroit, Michigan)

This statement asserts that Detroit is the capital of Michigan. Is this true or false? Actually, Lansing is the capital of Michigan, not Detroit. Therefore, this statement is false. The truth value of Q(Detroit, Michigan) is false.

c) Q(Massachusetts, Boston)

This statement asserts that Boston is the capital of Massachusetts. Is this true or false? Yes, Boston is indeed the capital of Massachusetts, so this statement is true. The truth value of Q(Massachusetts, Boston) is true.

d) Q(New York, New York)

This statement asserts that New York is the capital of New York. Is this true or false? Actually, Albany is the capital of New York, not New York City. Therefore, this statement is false. The truth value of Q(New York, New York) is false.

So, as we can see, the truth values of these statements depend on the specific relationships between x and y. When x is indeed the capital of y, the statement Q(x, y) is true, and when x is not the capital of y, the statement is false.

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Answer:

8. y=2x+6

9. y=1/2x-5

Step-by-step explanation:

Use point slope form to figure out the y intercept. Because it needs to be parallel, the same slope will be used to solve for point slope form.

Answer:

  a. The proof is in your picture

  b. Yes

  c. All four triangles are congruent by the HL theorem

Step-by-step explanation:

Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.

Your picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.

Sides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.

The same HL theorem reasoning applies to all of the triangles.

__

Additional comment

The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.

Answer:

971

Step-by-step explanation:

40782/42=971

Answer: 971 marbles per class

Step-by-step explanation:

40,782 marbles divided by 42 classes =

971 marbles per class

Check

971 x 42= 40782

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

Answer:

look at the screenshot

Step-by-step explanation:

Here are three different equations that relate C and B:

1. B = (2/7) * C

2. B/C = 2/5

3. 5C = 2B

1. B = (2/7) * C

Since the ratio of cocoa to cocoa butter is 5:2, we can write 5 + 2 = 7, which represents the total number of parts. Dividing 2 by 7, we get 2/7, which represents the fraction of cocoa butter in the mixture. To find the number of grams of cocoa butter needed for C grams of cocoa, we multiply C by 2/7.

2. B/C = 2/5

Dividing the number of grams of cocoa butter (B) by the number of grams of cocoa (C), we get the ratio of cocoa butter to cocoa, which is 2/5.

3. 5C = 2B

Since the ratio of cocoa to cocoa butter is 5:2, we can write the equation 5 * C = 2 * B, which represents the number of parts of cocoa to the number of parts of cocoa butter. Solving for B in terms of C, we get B = (2/5) * C.

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In an experiment on a damped spring oscillator with spring constant n/m, student c obtains the displacement vs time curves as in fig. 2(a), and records the maximum displacement data points as below is y = - 3.7148.

Here we have to find the displacement for the graphs of y and t that is maximum and We can find that by y = mc where m, = slope, c= intercept.

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Answer:

the answer is  21600000

Step-by-step explanation:

Starch and protein levels are checked for In order to present the idea of chemical compound variety, it is necessary to test for the presence of starches and protein macromolecules.

Hypothesis: It is a negative result if the biuret reagent remains blue after a test for protein since the reagent itself is blue. The test for protein is positive if a solution is pinkish purple or purple. The starch test solution is a yellowish brown color. We utilized iodine to test for starch in some solutions if any ingredient produced a mixture that was yellowish brown in color. Polysaccharides, monosaccharides, and disaccharides are separated from starch by iodine. Iodine interacts with molecules, changing the color of the molecules, while starch is a coiled polymer of glucose.

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Answer:

7

Step-by-step explanation:

To evaluate, substitute x = 2 into f(x), that is

f(2)= 2(2)² - 1 = 2(4) - 1 = 8 - 1 = 7

Using the dilation rule, the length of P'R' is: C. 12 units.

Given that the scale factor of dilation is 4, and PR is 3.

Therefore:

P'R' = 4(PR)

P'R' = 4(3)

P'R' = 12 units.

Therefore, using the dilation rule, the length of P'R' is: C. 12 units.

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Answer:

Its c (12)

Step-by-step explanation:

Edge

The upper control limit of the three-sigma process is approximately 3.807 defective units per sample.

To calculate the upper control limit (UCL) of the three-sigma (z) process, we first need to find the average number of defective units per sample and the standard deviation.
1. Calculate the average number of defective units per sample (p-bar):

Divide the total number of defective units (150) by the number of samples (40).
p-bar = 150 / 40 = 3.75 defective units per sample
2. Calculate the proportion of defective units (p) in each sample:

Divide the average number of defective units (3.75) by the sample size (100).
p = 3.75 / 100 = 0.0375
3. Calculate the standard deviation (σ) of the process using the formula:

σ = √(p * (1 - p) / n),

where n is the sample size.
σ = √(0.0375 * (1 - 0.0375) / 100)

= √(0.03609375 / 100) ≈ 0.0190
4. Calculate the three-sigma upper control limit (UCL) using the formula:

UCL = p-bar + 3 * σ
UCL = 3.75 + 3 * 0.0190 ≈ 3.75 + 0.057 ≈ 3.807.

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Answer:

Your answer is 15

Step-by-step explanation:

2+5= 7

7+5= 12

12+5=17

17-2= 15

The length of line segment is the horizontal distance between two points

Suppose

a line has endpoints

The length of the line is

Answer:

v=24

Step-by-step explanation:

V= 3\(\sqrt{10^{2} - 6^{2} }\)

V= 3\(\sqrt{100-36}\)

V= 3\(\sqrt{64}\)

V= 3×8

V= 24