Is there an AAA similarity?

Answers

Answer 1

The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that "If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or percentage) and consequently the two triangles are similar".

A triangle is a closed two-dimensional shape or polygon with the fewest sides in mathematics. A triangle is made up of three sides and three angles. The most significant attribute of a triangle is that the sum of its internal angles equals 180°.

Conditions for Triangle Similarity

If the corresponding angles of two triangles are identical, they are said to be comparable triangles.

If their respective sides have the same proportion/ratio.

For more questions on Similarity of triangles

https://brainly.com/question/21874653

#SPJ4

Is There An AAA Similarity?

Related Questions

write the ratio of 14 and 18 in its lowest terms

Answers

Answer:

the correct answer is 7 and 9

Answer:

7 and 9

Step-by-step explanation:

14 ÷ 2 and 18÷ 2

= 7 and 9

Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)| 0
2
4
6
10
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]

Answers

0*.5+2*.2+4*.15+6*.1+10*.05= 2.1

The expected value of the winnings from a game is 2.1.

What is expected value?

Expected value is used when we want to calculate the mean of a probability distribution. The weighted average of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value.

For the given situation,

Payouts, x = 0, 2, 4, 6, 10

Probabilities, P(x) = 0.5, 0.2, 0.15, 0.1, 0.05

The formula of expected value is [tex]E ( X ) = \mu = \sum [xP( x )][/tex]

⇒ [tex]E(X)=(0)(0.5)+(2)(0.2)+(4)(0.15)+(6)(0.1)+(10)(0.05)[/tex]

⇒ [tex]E(X)=0+0.4+0.6+0.6+0.5[/tex]

⇒ [tex]E(X)=2.1[/tex]

Hence we can conclude that the expected value of the winnings from a game is 2.1.

Learn more about expected value here

https://brainly.com/question/24321198

#SPJ2

is the relationship between the variables in the table an inverse variation or a direct variation? write an equation to model it.

x= 2 6 7 14
y= 21 7 6 3

Answers

The relationship between the variables in the table is an inverse variation The equation to model is y = 42/x.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 8 is an equation.

We have,

x:  2  6  7  14

y: 21  7  6  3

Now,

When x = 2, y = 21

This can be written as,

y = kx

21 = 2k

k = 21/2

The equation is y = (21/2)x _____(1)

or

y = k/x

21 = k/2

k = 42

The equation is y = 42/x _____(2)

Now,

We will check which equation fits the table.

From (1)

y = (21/2)x

When x = 6,

y = (21/2) x 6 = 21 x 3 = 63

From (2),

When x = 6,

y = 42/6 = 7

When x = 7,

y = 42/7 = 6

When x = 14,

y = 42/14 = 3

This equation satisfies the table.

Thus,

The relationship is an inverse variation.

The equation is y = 42/x.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Find the domain and range of the graph

A. D: X ≤ 5
R: y ≤ 7


B. D: X ≤ 7
R: y ≤ 5

C. D : X < 5
R: y < 7

D. D: X < 7
R: y < 5

Answers

General Formulas and ConceptsAlgebra I

Domain

The set of x-values that can be inputted into function f(x)

Range

The set of y-values that are outputted by function f(x)

Interval Notation

ApplicationStep 1: Define

Let's organize what is given to us from the problem.

We are given a graph of a function.

Step 2: Solve

We need to analyze the graph to determine the domain and range of the graph.

If we take a look at our x values, we see that our graph starts at x = 3 and continues infinitely.

∴ we can write the graph's x-values as [3, ∞), or x ≥ 3.

⇒ The domain of the graph is equal to x ≥ 3.

If we take a look at our y values, we see that our graph begins at y = 1 and also continues infinitely.

∴ we can write the graph's y-values as [1, ∞), or y ≥ 1.

⇒ The range of the graph is equal to y ≥ 1.

Answer

∴ the answer to the question is equal to:

A. D: x ≥ 3

    R: y ≥ 1

___

Learn more about functions: https://brainly.com/question/30200855

Learn more about Algebra I: https://brainly.com/question/16898384

___

Topic: Algebra I

Unit: Functions

solve for x and graph the solution on the number line below 7+x<16

Answers

Step-by-step explanation:

x<16-7x<11

.....................

Emily invested $2,000 in an account at a 3.5% interest rate. She kept the money in her account for four years. Determine, to the nearest dollar, the balance in the account after four years.

Answers

Answer:

$280

Step-by-step explanation:

$2000 * 3.5% * 4 = $8000 * 0.035 = $280

2000 x .035 = 70, 4 years= 4 times so 70 x 4
=280
Now Emily has invested 2000 so she started with 2000 plus the interest rates her account made
Final answer = 2280

Add the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of a. Add: 3a 3 8a - 6 and 4a 2 - 9a 11

Answers

Adding the polynomial 3a³ + 8a - 6 and 4a² - 9a + 11 gets 3a³ + 4a² - a + 5.

The answer in descending powers of a is 3a³ + 4a² - a + 5.

A polynomial is a mathematical expression consisting of a sum of powers in one or more variables (indeterminates) with non-negative integer exponents.

Adding the polynomial 3a³ + 8a - 6 and 4a² - 9a + 11                                        

(3a³ + 8a - 6) + (4a² - 9a + 11) = 3a³ + 4a² - a + 5

The coefficients of  a³, a², a and 1 is 3, 4, -1 and 5 respectively.                      

Descending powers of a in the polynomial is a³, a², a. So the answer in descending powers of a is 3a³ + 4a² - a + 5.

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

"Add the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of a.

Add: 3a³ + 8a - 6 and 4a² - 9a + 11"

To know more on polynomial

https://brainly.com/question/22236183

#SPJ4

a stadium is filled to 80% capacity. If 2,560 people are in the stadium, how many people would fill the stadium to its full capacity?

Answers

2048 people would fill the stadium to its full capacity

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given that a stadium is filled to 80% capacity

There are  2,560 people are in the stadium

We need to find how many people would fill the stadium to its full capacity.

We have to convert 80% to decimal by dividing 2560 with 100

80/100

0.8

Now multiply 0.8 with 2560

0.8×2560

2048

Hence, 2048 people would fill the stadium to its full capacity

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

You have an ant farm with 22 ants . The population of ants in your farm will double every 3 months

Answers

The number of ants in 6 months will be 88 ants.

How to calculate the value?

The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this situation, in an ant farm with 22 ants and the population of ants in your farm will double every 3 months.

The number of ants in 6 months will be:

= 22 × (6/3)²

= 22 × 2²

= 88 ants

Learn more about word problem on:

brainly.com/question/21405634

#SPJ1

Complete question

You have an ant farm with 22 ants . The population of ants in your farm will double every 3 months. What is the number of ants in 6 months.

Making connections between arithmetic sequences and linear function


Use the graph or the formula to write the equation of the line in a slope intercept form

Answers

On solving the provided question, we can say that -  here in graph we have on solving equation [tex]x^2+ 3y^2 \\[/tex]  =  [tex]4+3 = 7[/tex]

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here-

from graph, x= 2

y = 1

[tex]x^2+ 3y^2 \\[/tex]

[tex]4+3 = 7[/tex]

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes

Answers

Call the radius of the cylinder and sphere, r And the height  of the cylinder  = 2r

How to Calculate Volume in Cubic Centimeters?Calculating volume is just another way of saying that you're measuring the amount of space inside a three-dimensional object. You can use standardized formulas for calculating the volume of shapes like cubes, cylinders and spheres, as long as you know their basic measurements.So60  =  pi * r^2 * 2r30 =  pi * r^330/pi  =  r^3[30/pi]^1/3  =  rSo...the volume of the sphere is(4/3)pi [ (30/pi)^1/3 ]^3  =(4/3) pi * 30/pi  =40 cm^3A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of one millilitre.How to Work out Volume with Cubic Centimetres. If a container was filled with water and it had a length of 20 cm, a height of 5 cm and a depth of 4 cm to work out the volume of water you would need to multiply all 3 numbers together. 20 cm x 5 cm x 4 cm = 400 cm³

To learn more about Volume in Cubic Centimeters refers to:

brainly.com/question/463363

#SPJ4

If $x$ is a positive multiple of 8 and $x^2>100$, but $x<20$, what is $x$?

Answers

Answer:

16

Step-by-step explanation:

16 is a positive multiple of 8, in which 16²=256>100 and 16<20 are true statements.

Answer:

[tex]$x=\boxed{16}$[/tex]

Step-by-step explanation:

Since $x$ is a positive multiple of 8, it must be at least 8. Since $x^2>100$ and $x$ is at least 8, the only solution is $x=16$.

To verify this, note that $x=8$ does not satisfy the inequality $x^2>100$, but $x=16$ does, so $x=16$ is the only solution that works.

Therefore, $x=\boxed{16}$.

Please help me on this

Answers

Answer:

1. a

2. d

3. none of the above - correct answer is root 133. there has to be a typo I think. if they force you to choose do C.

Step-by-step explanation:

A,B,C1,2,3

BRAINLIST??

In Mohammad’s class, 80% of the students are boys. There are 24 boys in the class. What is the total number of students in Mohammad’s class?

Answers

Answer:

30 students

Step-by-step explanation:

80%  of  N   =   24            where N  is  the total number of students

So

.80 N   =  24

N =  24 /  .80     =      30

sorry this was a late response

Are the following statements true or false? Justify your answers. Complete parts (a) through (c) below. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) (a) In statistics, results are always reported with 100 % certainty. Choose the correct answer below A. False. In statistics, results are always reported with 100 % certainty only when discrete variables are measured. Results cannot be reported with 100 % certainty when continuous variables are measured. B. True. Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. Since it is a science, results are always reported with 100 % certainty. C. True. Statistics would not be useful if they were not presented with 100 % certainty . Statistics is a form of mathematics, which means that as long as correct procedures are used, all results must be correct. D. False. In statistics, results are not reported with 100% certainty. Because statistical studies draw on samples, and because there is variation within groups, results cannot be reported with 100 % certainty.

Answers

The correct option that tests the given claim on statistics is; D. False. In statistics, results are not reported with 100% certainty. Because statistical studies draw on samples, and because there is variation within groups, results cannot be reported with 100 % certainty.

How to interpret the conclusion of a statistics research?

Statistical research is defined as the rigorous development of improved or new statistical methods grounded in probability and statistical theory.

Statistical data analysis is basically a procedure that is used to perform various statistical operations.

Now, from the question, the claim is that In statistics, results are always reported with 100 % certainty.

Now, this claim needs to be examined because there is no perfect human being and as such since statistics is drawn from a lot of samples and groups, there is guaranteed to be some form of variability in responses or results as the case may be.

Therefore, we can say that is option D.

Read more about statistics research at; https://brainly.com/question/15703255

#SPJ1

A population has a standard deviation x=18.4. How large a sample must be drawn so that a 98% confidence interval will have a margin of error equal to 4.1?

Answers

Answer:

"109" will be the appropriate response.

Step-by-step explanation:

The given values are:

Standard deviation,

[tex]\sigma=18.4[/tex]

Margin of error,

[tex]E = 4.1[/tex]

Using the table,

[tex]Z_{(\frac{0.02}{2} )}=2.326[/tex]

Now,

The sample size will be:

⇒  [tex]n=(\frac{Z_{(\frac{0.02}{2})\times \sigma}}{E} )^2[/tex]

On substituting the values, we get

⇒      [tex]=(\frac{2.326\times 18.4}{4.1} )^2[/tex]

⇒      [tex]=(\frac{42.7984}{4.1} )^2[/tex]

⇒      [tex]=(10.4386341)^2[/tex]

⇒      [tex]=109[/tex]

Which expression is the factored form of 2x^2 7x 3?

Answers

The factored form of quadratic equation 2x² + 7x + 3 is 2(x + 1/2) (x + 3)

A quadratic equation can be expressed in:

- Standard form: y = ax² + bx + c

- factored form: y = a(x - x₁) (x - x₂)

Here, x₁ and x₂ are the roots of the given function.

Suppose we are given a quadratic equation:

y = ax² + bx + c

To find the factored form, use the following properties:

x₁ . x₂ = c/a

x₁ + x₂ = - b/a

In this case, the quadratic function is:

y = 2x² + 7x + 3

We have to find x₁ and x₂ such that:

x₁ . x₂ = 3/2

x₁ + x₂ = - 7/2

Hence,

x₁ = - 1/2

x₂ = - 3

Therefore the factored form is:

y = 2(x + 1/2) (x + 3)

Your question is incomplete, but most probably your question was:

Which expression is the factored form of 2x² + 7x + 3?

Learn more about quadratic equation here:

https://brainly.com/question/29280392

#SPJ4

subtract x2+2x+1-(x-3)

Answers

Answer:

(x to the second power)+x+4

Step-by-step explanation:

Ur welcome

Pls help will give brainlest if it’s right

Answers

The answer is Public Service

Natalia paid $38.95 for three medium-sized pizzas and a salad. If Natalia paid $11.98 for the salad, how much did each pizza cost? Enter your answer in the box.

Answers

Answer:

$8.99

Step-by-step explanation:

I have no idea what to do can someone help

Answers

Answer:

k = 20

can i have brainliest

Step-by-step explanation:

K=20 would be the answer

Please help!!!! I'LL GIVE 5 STAR RATING AND A THANKS

Answers

Answer:

9.1

Step-by-step explanation:

For the first one, I just multiplied 4.55 and 0.5 by 2 somthey are proportional. Or divide distance by time!

Solve for x. Round your answer to the nearest tenth if necessary. NO SCAMS OR LINKS PLEASE!!!!!! ANSWER IS NOT 14.1 ​

Answers

Answer:

[tex]\boxed {\boxed {\sf x\approx 7.3}}[/tex]

Step-by-step explanation:

The triangle has a small square in the corner representing a 90 degree angle. This is a right triangle so we can use the Pythagorean Theorem to solve for the sides.

[tex]a^2+b^2=c^2[/tex]

In this equation, a and b are the legs and c is the hypotenuse.

x and 8.5 are the legs because they make up the right angle. 11.2 is the hypotenuse because it is opposite the right angle.

a= xb=8.5 c=11.2

Substitute the values into the formula.

[tex]x^2+(8.5)^2=(11.2)^2[/tex]

Solve the exponents.

(8.5)²= 8.5*8.5= 72.25 (11.2)²= 11.2*11.2= 125.44

[tex]x^2+72.25 =125.44[/tex]

Solve for x by isolating the variable. 72.25 is being added, so we subtract 72.25 from both sides because subtraction is the inverse operation of addition.

[tex]x^2+72.25-72.25 = 125.44-72.25[/tex]

[tex]x^2=125.44-72.25[/tex]

[tex]x^2=53.19[/tex]

x is being squared, so we take the square root of both sides.

[tex]\sqrt{x^2}=\sqrt {53.19}[/tex]

[tex]x=\sqrt{53.19[/tex]

[tex]x=7.29314746869[/tex]

Round to the nearest tenth. The 9 in the hundredth place tells us to round the 2 up to a 3.

[tex]x \approx 7.3[/tex]

The unknown side, x, is approximately 7.3

What is the domain of the function y=5√6−2x​

Answers

The domain is all values of x that makes the expression defined.

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

What is the domain of the given function?

Given the function in the question;

y = 5√(6−2x)​

To find the domain, set the radicand greater than or equal zero and solve for x.

6 - 2x ≥ 0

Subtract 6 from both sides

6 - 6- 2x ≥ 0 - 6

-2x ≥ -6

Divide both sides by -2

-2x/-2 ≤ -6/-2

x ≤ -6/-2

x ≤ 3

Therefore, the domain is;

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

Learn more about domain here: https://brainly.com/question/28135761

#SPJ1

Multiple Choice

2. Match the graph to the table of values.
The first quadrant of a coordinate plane is shown with four plotted points.The x-axis is titled 'Time in seconds,' and the y-axis is titled 'Height in meters.' The four points resemble a layout similar to a checkmark with the first point located slightly higher than the second point. The second, third, and fourth points follow a linear pattern with a positive slope.
A.
Time (s) Height (m)
1

5

2

10

3

15

4

20

B.
Time (s) Height (m)
1

2

2

3

3

5

4

9

C.
Time (s) Height (m)
1

4

2

3

3

5

4

7
Multiple Choice

Match the graph to the table of values.
The first quadrant of a coordinate plane is shown with four plotted points. The x-axis is titled 'Time in seconds,' and the y-axis is titled 'Height in meters.' The four points start in the lower left corner of the first quadrant and follow a linear pattern with a positive slope.

A.
Time (s) Height (m)
1

5

2

10

3

15

4

20

B.
Time (s) Height (m)
1

2

2

3

3

5

4

9

C.
Time (s) Height (m)
1

4

2

3

3

5

4

7

100 POINTS FOR ANSWERS AND EXPLANATION! PLS I NEED HELP ASAP! Thanks!

Answers

Answer:

Step-by-step explanation:

Choice A: t=1, h=5; t=2, h=10

Choice B: t=1, h=2; t=2, h=3

Choice C: t=1, h=4; t=2, h=3

ans is C as it fits the descriptions

Choice A: t=1, h=5; t=2, h=10; t=3, h=15

Choice B: t=1, h=2; t=2, h=3; t=3, h=5  <== non-linear

Choice C: t=1, h=4; t=2, h=3; t=3, h=5 <== non-linear

ans is A as it fits the descriptions

Triangle GHI is similar to triangle JKL. Find the measure of side JK. Round your answer to the nearest tenth!

Answers

Given: Two triangle AGHI AJKL.

To find: measure of side JK and round the answer nearest tenth.

Solution: from figure

IH=5, GH=8,LK=16 from similarity rule

IH/LK=GH/JK

5/16 = 8/x

⇒5x=16x8

x=16×8/5

⇒x=25.6 or

x= 26 (nearest tenth), this is side JK

Definition of Triangle

A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides. This is one of the important parts of geometry.

Some major concepts, such as Pythagoras theorem and trigonometry, are dependent on triangle properties. A triangle has different types based on its angles and sides.

Shape of Triangle

Triangle is a closed two-dimensional shape. It is a three-sided polygon. All sides are made of straight lines. The point where two straight lines join is the vertex. Hence, the triangle has three vertices. Each vertex forms an angle.

Learn more about triangle at https://brainly.com/question/2773823.

#SPJ4

3. At the grocery store, three flavors of Cheerios are sold.

Flavor A is 20 ounces and costs $4.49. The unit rate is ------------- per ounce.

For Flavor B, the equation y = 0.20x represents the cost (y) per ounce (x) in each box. The unit rate is------------------------ per ounce.
For Flavor C, the table below shows the amount paid per ounce. The unit rate is ---------------------- per ounce
Ray is making bouquets of balloons. In each bouquet 2 out of every 5 balloons are red. Write an equation to help Ray determine how many red balloons are needed compared to the the total number of balloons used.

7. Let x represent the number of balloons used compared to y which is the number of red balloons.
10.
Review the keywords below. Find at least 2 words commonly used for "Rate of Change". Drag and Drop them to the box for "Rate of Change" to earn full credit.

Answers

The unit rate of flavor A is; $0.2245 per ounce

The unit rate of flavor B is; $0.20 per ounce

An equation to help Ray determine how many red balloons are needed compared to the the total number of balloons used is; y = ²/₅x

How to find the unit rate?

A unit rate is also called unit ratio and it describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

We are given that Flavor A is 20 ounces and costs $4.49. Thus;

Unit rate of flavour A = $4.49/20 = $0.2245 per ounce

For Flavor B, the equation y = 0.20x represents the cost (y) per ounce (x) in each box. Thus, the unit rate is $0.20 per ounce

Since ray is making bouquets of balloons. In each bouquet 2 out of every 5 balloons are red.

If x is the number of ounces, then the unit rate is 2/5 . Thus, the equation is; y = ²/₅x

Read more about Unit rate at; https://brainly.com/question/19493296

#SPJ1

what a quadrilateral with two sets of parallel lines that are Opposite sides are parallel.

Answers

There are many special types of quadrilateral. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel .

Hope this helps!

If you thanks my answers I will give brainliest and thanks back

Answers

Answer:

deal

Step-by-step explanation:

Answer: for real. I give you a thanks in your answer I will give you more please give me a Brainliest I really needed it :D

Step-by-step explanation:

Use point-slope form to find the equation of the line with a slope of -3 that passes through the point (-1,0)? Express your answer in slope-intercept form.​

Answers

Answer:

y = -3x - 3

Step-by-step explanation:

y = -3x + b

0 = -3(-1) + b

0 = 3 + b

-3 = b

y = -3x - 3

Other Questions
Can you help me plz with this work plz What is the Sudetenland and why was it important? Which ordered pair is not graphed below? Choose 1 answer PLEASE HELPWhich statements about gravity are true?Select all that apply.A The moon's gravity has no effect on the tides.B A 180-pound person on Earth weighs 30 pounds on the moon.C A space ship has the same mass on Earth as it has on the moon. 2x^(2)+12x+8using completing square TOLL ROAD Mr. Espinoza randomly chooses one of five toll booths whenentering a toll road when driving to work. What is the probability he willselect the middle toll booth on Monday and Tuesday? Julian went shopping for a new pair of sneakers. Sales tax where he lives is 5.75%. If the price of the pair of sneakers is pp dollars and cents, which expression represents the total price plus tax? Phenylephrine is a nasal decongestant and is the active ingredient in Sudafed, which contains phenylephrine hydrochloride (PEHCl).a. Trueb. False i need help with this plseeee please help me Ill mark u as brainliest Where do monarchs usually obtain their power ? What are the 4 main types of irony? 34. You deposit $2,000 in an account that earns simple interest at a rate of 3% per year. How much interest will youhave earned after 3 years? Does the policy define plagiarism giving the reader a clear understanding of what the institution considers plagiarism? If so, how is it defined? What does Michael Pollan say will win over the logic of capitalism, efficiency, or human designs? A circle has a circumference of 8. It has an arc of length 32/5.What is the central angle of the arc, in degrees? Dalton's Law: John puts 1250 PSI of Oxygen, 780 PSI of Nitrogen and 550 PSI of Helium in a SCUBA tank. What is the total pressure? What does Kigo mean in poetry? Which of the following best describes the culture of science and how scientists work?A. Scientists commonly repeat other scientists' experiments to verify their work.B. Scientists attempt to prove their hypotheses.C. Scientists commonly make subjective conclusions in their work.D. Scientists develop hypotheses based solely on their own observations. In an orthogonal cutting operation, the tool has a rake angle = 0. The chip thickness before the cut= 0.30 mm and the cut yields a deformed chip thickness = 0.65 mm. Calculate (a) the shear plane angle and (b) the shear strain for the operation.