for f(x)=3x-2 and g(x)=x^2+1 find (f+g)(x)

a) The given symbolic logic statement can be translated into English as follows:

"Not exists x such that (P(x) and Q(x)), and for all y, if R(y) then P(y)."

b) Potential ambiguities in the translated statement:

The scope of the negation symbol "¬" is not explicitly defined. It can be interpreted as applying only to the first part of the statement or to the entire statement.

The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which parts of the statement they apply to.

c) To eliminate ambiguities while maintaining the original meaning, the statement can be rewritten as follows:

"(∀x)(¬(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y))"

In the revised statement: The negation symbol "¬" applies to the entire first part of the statement, indicating that there does not exist any x for which both P(x) and Q(x) are true.

The quantifiers (∀x) and (∀y) explicitly indicate that the following predicates apply universally to all values of x and y.

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The integer number that represents the situation running up 24 steps is given as follows:

+24.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For altitudes, the signs are given as follows:

In this problem, we have an increase of altitude of 24 steps, hence the integer number is given as follows:

+24.

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The percentage of people borrowing from financial institutions generally exceeds borrowing from friends or family due to formality, legal protection, larger loan amounts, privacy, expertise, and long-term implications.

The percentage of people who would borrow from a financial institution compared to the percentage of people who would borrow from friends or family can vary depending on various factors such as cultural norms, economic conditions, individual preferences, and access to financial services. However, in general, borrowing from financial institutions is often more common and prevalent than borrowing from friends or family for several reasons.

Formality and Legal Protection: Borrowing from financial institutions offers a more formal and legally protected process. When individuals borrow from a financial institution, they enter into a contractual agreement that outlines the terms and conditions of the loan. This agreement provides a legal framework that protects both the borrower and the lender. In contrast, borrowing from friends or family often lacks the same level of formality and legal protection, which can lead to ambiguity and strain personal relationships.

Access to Larger Loan Amounts: Financial institutions typically have more capital and resources to lend larger amounts of money compared to friends or family members. If someone requires a substantial loan, such as for purchasing a home or starting a business, they are more likely to turn to a financial institution. These institutions have processes in place to evaluate creditworthiness, collateral, and other factors, allowing them to provide loans that meet the borrower's specific needs.

Privacy and Independence: Borrowing from a financial institution offers a level of privacy and independence that may be preferred by individuals. Some people might feel uncomfortable disclosing personal financial details or discussing their financial challenges with friends or family. Financial institutions provide a professional environment where individuals can maintain privacy and retain control over their financial matters.

Expertise and Financial Advice: Financial institutions employ professionals with expertise in lending and financial management. When borrowing from a financial institution, borrowers can benefit from the advice and guidance of these professionals. They can help borrowers understand the terms of the loan, explore different options, and make informed financial decisions. Friends and family members may not possess the same level of financial knowledge or experience, limiting their ability to provide comprehensive advice.

Long-Term Implications: Borrowing from friends or family can have long-term implications for personal relationships. Financial transactions have the potential to create tension, conflicts, or misunderstandings among individuals, especially if there are difficulties in repaying the borrowed amount. Relying on financial institutions can help maintain healthy personal relationships, as the borrowing and lending processes are conducted on a professional level, minimizing the emotional and relational strain that can arise from borrowing from loved ones.

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Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.

Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.

In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.

The number of pages Li Wei can read in a week = 90

The number of pages Collen can read in a week = 126

Li Wei's reading rate per hour = 30 pages

Collen's reading rate per hour = 24 pages

Let the hours that Li Wei and Colleen can be on the same page= x

The total number of pages Li Wei can read = 90 + 30x

The total number of pages Colleen can read = 126 + 24x

For Li Wei and Colleen to be on the same, the two expressions are equated.

90 + 30x = 126 + 24x

6x =  36

x = 6

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Answer:

To find Salina Grant's gross pay, we need to calculate the pay for each range and add them together.

For the first 25 chairs, Salina will be paid $10 for each chair, so her pay for this range is:

25 chairs x $10 per chair = $250

For the next 15 chairs (26-40), Salina will be paid $13 for each chair, so her pay for this range is:

15 chairs x $13 per chair = $195

For the remaining 7 chairs (over 40), Salina will be paid $17.50 for each chair, so her pay for this range is:

7 chairs x $17.50 per chair = $122.50

Adding up all three ranges, Salina's gross pay is:

$250 + $195 + $122.50 = $567.50

Therefore, Salina Grant's gross pay for assembling 47 chairs in one week is $567.50.

Step-by-step explanation:

The approximation of [tex]\sqrt{44}[/tex], to the hundredths place, is given as follows:

[tex]\sqrt{44} = 6.63[/tex]

The estimate of a non-exact square root of x is done finding two numbers, as follows:

For this problem, we want to estimate the root to the hundredth's place, hence the number that we must compare is:

44 x 10^4 = 440000.

(as each 10² is equivalent to the square root of a decimal digit).

Then the numbers are:

Hence the square root is approximated as follows:

663/100 = 6.63.

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The simple interest owed on a $340 loan at 6.6% interest for 9 years is $201.96.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given that:

Principal P = $340

Interest Rate r = 6.6%

Time t = 9 years

First convert the interest rate from percent to decimal:

Rate = r/100

Rate = 6.6/100

Rate = 0.066

Now, plug the values into the above formula and solve for interest.

I = P × r × t

I = $340 × 0.066 × 9

I = $201.96

Therefore, the simple interest is $201.96.

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Answer:

b

Step-by-step explanation:

Answer:

The correct statement is: The temperature of the object is decreasing exponentially by 0.007% each minute.

Step-by-step explanation:

The exponential term in the function, [tex]e^{0.007 h}[/tex], is greater than 1. This means that the temperature is increasing over time.

However, the exponent is very small, so the increase in temperature is very slow. In fact, the temperature is increasing by only -0.007% each minute.

We can use the following formula to calculate the percent change in temperature each minute.

[tex]\boxed{\bold{Percent\: change = \frac{(new \:value - \:old \: value) }{ old\:value }* 100\%}}[/tex]

In this case, the new value is the temperature after one minute, and the old value is the temperature at the start of the minute.

So, the percent change in temperature is:

[tex]= \frac{10 + 160e^{-0.007 * 1} - 10) }{ 10} * 100\%[/tex]

≈ -0.007%

Therefore, the temperature of the object is decreasing exponentially by 0.007% each minute.

i) The monthly basic salary of the married COAS General is Rs 79,200.

ii. Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480

iii. The total income tax paid by him is Rs 24.8.

His taxable income can be calculated as follows:

Total Monthly Income = Rs 79,200 + Rs 2,000 + Rs 79,200 = Rs 1,60,400

EPF Contribution = 10% of Basic Salary = 10% of Rs 79,200 = Rs 7,920

Life Insurance Premium = Rs 50,000

Total Deductions = EPF Contribution + Life Insurance Premium = Rs 7,920 + Rs 50,000 = Rs 57,920

Taxable Income = Total Monthly Income - Total Deductions

Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480

For income up to Rs 6,00,000: No income tax

For income between Rs 6,00,001 and Rs 8,00,000: 1% of the amount exceeding Rs 6,00,000

Taxable Income in this slab = Rs 2,480 (Rs 1,02,480 - Rs 6,00,000)

Income tax for this slab = 1% of Rs 2,480 = Rs 24.8

Therefore, the total income tax paid by him is Rs 24.8.

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Answer:

x+1

Step-by-step explanation:

you have to rewrite the equestion, factor the expression, and than reduce it

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Dana had to pay her friend $900, 3 months ago, and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month. $1499.45, single payment would settle both payments today.

Given:

Simple interest = Principal × Rate × Time

Simple interest = $900 × 0.015 × 3

Simple interest = $40.50

Present Value = Future Value / (1 + Rate x Time)

Present Value = $580 / (1 + 0.015 × 3)

Present Value = $580 / 1.045

Present Value = $558.95

Total amount $580 loan is $558.95.

Total amount owed = $940.50 + $558.95

Total amount owed = $1499.45

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The five number summary of the data set for the box plot would be :

First, order the numbers in ascending order:

2, 8, 9, 11, 14, 15, 17, 19, 20

The minimum is the smallest number which is 2. The maximum is the largest number which is 20.

The median is the number in the middle which is 19. The Q1 is the number in the middle of the first half of the numbers which is 9. The Q3 is the number in the middle of the second half which is 19.

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Answer:

min=2

1st quartile= 8.5

median=14

3rd quartile=18

max=20

Step-by-step explanation:

To achieve a mean of 78 with four scores, the fourth score must be 90.

We need to consider the current mean, the number of tests, and the desired mean in order to find the fourth score needed to achieve a mean of 78

Let's assume the three test scores are x1, x2, and x3.

We know that the mean of these three scores is 74. So we can assume that

The sum of these numbers is 74 or

(x1 + x2 + x3)/3 = 74

Let's denote it as x4 ,to find the fourth score we will use the formula to calculate the mean:

(x1 + x2 + x3 + x4)/4 = 78

To solve for x4, we can rewrite it as:

x1 + x2 + x3 + x4 = 78 * 4

Now, we can substitute the value of the mean of the first three scores into the equation:

(x1 + x2 + x3) + x4 = 312

we know that,

(x1 + x2 + x3) = 3 * 74

or,

3 * 74 + x4 = 312

Simplifying this, we get:

222 + x4 = 312

Subtracting 222 from both sides:

x4 = 312 - 222

x4 = 90

Therefore, to achieve a mean of 78 with four scores, the fourth score must be 90.

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The side lengths for the triangle are given as follows:

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Then the length AC is given as follows:

[tex]AC = \sqrt{(5 - (-7))^2 + (0 - 3)^2}[/tex]

AC = 12.4.

The length AB is given as follows:

[tex]AB = \sqrt{(-3 - (-7))^2 + (6 - 3)^2}[/tex]

AB = 5.

The length BC is given as follows:

[tex]BC = \sqrt{(5 - (-3))^2 + (6 - 0)^2}[/tex]

BC = 10.

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Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called unit conversion fractions

Unit conversion fractions are used to convert between different units of measurement within the same quantity.

The fraction 12 in/1 ft represents the conversion factor from inches to feet, where 12 inches is equivalent to 1 foot.

This fraction allows us to convert a certain length measured in inches to an equivalent length in feet.

Similarly, the fraction 1 yd/3 ft represents the conversion factor from yards to feet, where 1 yard is equivalent to 3 feet.

This fraction allows us to convert a certain length measured in yards to an equivalent length in feet.

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Fill in each blank so that the resulting statement is true

Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called _________fractions

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =[tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

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Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

(a) Probability of getting a flush is 0.000546.

(b) Probability of getting three of a kind is 0.00451.

(c) Probability of getting two pairs is 0.0150.

We have,

(a)

To calculate the probability of getting a flush, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of balls = 11 (red) + 11 (yellow) + 11 (green) + 11 (black) = 44 balls

The number of ways to choose 4 balls (without replacement)

= 44C4 = 44! / (4! x (44 - 4)!) = 44! / (4! x 40!)

= 44 x 43 x 42 x 41 / (4 x 3 x 2 x 1)

= 7315

The number of favorable outcomes:

There are 4 different colors of balls, so we have 4 possible flushes (all red, all yellow, all green, all black).

Probability of getting a flush = Number of favorable outcomes / Total number of outcomes = 4 / 7315 ≈ 0.000546

(b)

To calculate the probability of getting three of a kind, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).

Number of ways to choose 3 balls of the same denomination: We have 11 denominations, so we can choose 3 balls of the same denomination in 11C1 = 11 ways.

Number of ways to choose the fourth ball of a different denomination: After choosing 3 balls of the same denomination, we have 3 denominations left from which we can choose the fourth ball. So, the number of ways to choose the fourth ball = 3.

Number of favorable outcomes = Number of ways to choose 3 balls of the same denomination x Number of ways to choose the fourth ball of a different denomination

= 11 x 3

= 33

Probability of getting three of a kind = Number of favorable outcomes / Total number of outcomes = 33 / 7315 ≈ 0.00451

(c)

To calculate the probability of getting two pairs, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).

Number of ways to choose the first pair: We have 11 denominations, so we can choose the first pair in 11C1 = 11 ways.

Number of ways to choose the second pair: After choosing the first pair, we have 10 denominations left from which we can choose the second pair. So, the number of ways to choose the second pair = 10.

Number of favorable outcomes

= Number of ways to choose the first pair x Number of ways to choose the second pair

= 11 x 10

= 110

Probability of getting two pairs = Number of favorable outcomes / Total number of outcomes = 110 / 7315 ≈ 0.0150

Thus,

(a) Probability of getting a flush = 4/7315 ≈ 0.000546

(b) Probability of getting three of a kind = 33/7315 ≈ 0.00451

(c) Probability of getting two pairs = 110/7315 ≈ 0.0150

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The solution is :  (5-b ) is the expression that shows the number of books Hazel checked out.

Here, we have,

given that,

Bill checked out 5 books from the library.

Hazel checked out b fewer books than Bill.

now, we have to find the expression that shows the number of books Hazel checked out.

let,

that shows the number of books Hazel checked out = x

so, we have,

that shows the number of books Hazel checked out =  b fewer books than Bill.

as, Bill checked out 5 books from the library.

so, we get,

the number of books Hazel checked out = 5 - b

so, we have,

x = 5-b

Hence, The solution is :  (5-b ) is the expression that shows the number of books Hazel checked out.

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Answer:

5)  17.62 units² (2 d.p.)

6)  338.29 units² (2 d.p.)

7)  246.20 units² (2 d.p.)

Step-by-step explanation:

To find the area of a triangle given two sides and the included angle, use the Sine Rule (Area of a Triangle) formula:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Rule (Area of a triangle)}\\\\$A=\dfrac{1}{2}ab \sin C$\\\\\\where: \\ \phantom{ww}$\bullet$ $a$ and $b$ are adjacent sides. \\ \phantom{ww}$\bullet$ $C$ is the includ\:\!ed angle.\\\end{minipage}}[/tex]

[tex]\hrulefill[/tex]

Given values:

The two sides of the triangle are 'a' and 'c', and the included angle is 'B'.

Substitute the given values into the formula and solve for area:

[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ac \sin B\\\\&=\dfrac{1}{2} \cdot 7 \cdot 8 \cdot \sin 141^{\circ}\\\\&= 28 \sin 141^{\circ}\\\\& = 17.6209709...\\\\&= 17.62\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Given values:

The two sides of the triangle are 'a' and 'b', and the included angle is 'C'.

Substitute the given values into the formula and solve for area:

[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ab \sin C\\\\&=\dfrac{1}{2} \cdot 30\cdot 24 \cdot \sin 70^{\circ}\\\\&= 360\sin 70^{\circ}\\\\&= 338.289343...\\\\& = 338.29\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Given values:

The two sides of the triangle are 'b' and 'c', and the included angle is 'A'.

Substitute the given values into the formula and solve for area:

[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} bc \sin A\\\\&=\dfrac{1}{2} \cdot 20 \cdot 25 \cdot \sin 100^{\circ}\\\\&= 250 \sin 100^{\circ}\\\\&= 246.201938...\\\\& = 246.20\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week [tex]\sf = 19 \times 40 = \$760[/tex]

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, [tex]\sf \dfrac{8x}{100}=760[/tex]

Or, [tex]\sf 8x= 76000[/tex]

Or, [tex]\sf x= \dfrac{76000}{8}=9500[/tex]

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

Kenya needs to initially put in the amount of $2,208.2in the account to have at least $7,000 after 15 years.

We can use the formula for compound interest:

A = P(1 + r/n)ⁿ

where A is the amount of money in the account after t years, P is the initial principal, r is the annual interest rate (as a decimal), and n is the number of times per year the interest is compounded.

Here, we want to find P, so we can rearrange the formula as:

P = A / (1 + r/n)ⁿ

We are given that r = 0.08 (8% interest) and n = 1 (interest is compounded annually).

We also know that A = $7,000 and t = 15 years.

So we can plug in these values and solve for P:

P = 7000 / (1 + 0.08/1)¹⁵

P = 7000 / (1.08)¹⁵

P ≈ $2,208.2

Therefore, Kenya needs to initially put in approximately $2,208.2in the account to have at least $7,000 after 15 years.

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Answer:

  23/41

Step-by-step explanation:

You want to know the fraction who failed, given they predicted they would fail.

The attached 2-way table shows the given numbers (black) and the numbers that make the totals correct (blue).

It shows 23 of the 41 who thought they would fail actually did. That fraction is ...

  23/41 . . . . failed who thought they would

<95141404393>

The graph that shows the solution set of the inequality is the second one.

Here we have the following inequality:

y < |x + 3|

Notice that we have the symbol "<", then we know that the graph of the absolute value must be with dashed lines (because the points that lie on the graph aren't solutions).

Also, y is smaller than that, then the shaded region must be below the graph.

With that in mind, we conclude that the correct option is the second one.

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The total surface area of the cylinder is 414.7 cm².

The curved surface area of the cylinder is calculated as follows;

C.S.A = 2πrh

where;

The curved surface area of the cylinder is calculated as;

C.S.A = 2π(6 cm) x (5 cm)

C.S.A = 188.5 cm²

The total surface area of the cylinder is calculated as follows;

T.S.A = 2πrh + 2πr²

circular area = 2πr² = 2π x (6cm)² = 226.2 cm²

The total surface area = 188.5 cm² + 226.2 cm² = 414.7 cm²

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Our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use a proof by contradiction.

Assume that for every vertex u in T, the distance between u and v is greater than (n-1)/2.

Since T is a tree with n vertices, it has n-1 edges. We can select a longest path P in T, which has a length of at least n-1. Let's denote the endpoints of this path as u and w, where u is the starting vertex and w is the ending vertex.

Now, consider the distance between u and v. Since we assumed that the distance between any vertex u and v is greater than (n-1)/2, the distance between u and v must be greater than (n-1)/2.

However, let's consider the distance between w and v. Since the path P is the longest path in the tree, the distance between w and v must be greater than or equal to the length of path P, which is at least n-1.

Now, let's consider the total number of vertices in the tree, which is n. Since n is an odd integer, (n-1)/2 is an integer as well.

If the distance between w and v is greater than or equal to n-1, and (n-1)/2 is an integer, then there must be a contradiction. This is because the distance between w and v is greater than (n-1)/2, violating our assumption.

Therefore, our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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