\text{triangle congruence theorem: }\color{blue}{\text{s}}\color{purple}{\text{a}}\color{red}{\text{s}} triangle congruence theorem

The values on a number line that are less than -2 include -3, -4 etc

A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that each real number and each point on a number line correspond to one another.

The horizontal straight lines known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. This line continues forever at both ends.

It should be noted that -3, and above are less than -2.

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With all this information, and reading our question carefully, we can decipher the following:

9(n-3) = 3 + (9n + 3n)

9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)

9n - 27 = 3 + 12n       (Step 2. Combine like terms; 9n + 3n = 12n)

-9n                  -9n    (Step 3. Subtract 9n from both sides to isolate the variable)

______________

  -27 = 3 + 3n            

     -3      -3               (Step 4. Subtract 3 from both sides)

________________

-30 =       3n                        

 -----         ----

  3            3              (Step 5. Divide 3 from both sides)

________________

 -10 = n

Therefore, n = -10

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Answer:

  a. 31 months

  b. $818.32

  c. $168.32 interest

Step-by-step explanation:

Given that Joe makes a minimum payment of $21.45 on his credit card purchase of $650 with an APR of 19.85%, you want to know ...

If the balance is reduced by $21.45 per month, it will take ...

  $650/($21.45/mo) ≈ 30.3 months

to pay off the balance.

Joe will be making payments for 31 months.

The total amount Joe pays for his sound system is the sum of its initial cost and the total of interest payments. That sum is ...

  cost + interest = total paid

  $650 +168.32 = $818.32

Joe will pay a total of $818.32.

The total amount of interest Joe pays is $168.32.

__

Additional comment

If the total payment each month is $21.45, then it will take 43 months to pay off the system, for a total cost of $909.61, of which $259.61 is the cost of the credit. (The finance charge is paid first from this payment amount, so the amount that goes to reduce the balance is less.)

The average grade received on two tests and the final exam is 78.67%

What is average?

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

The average formula has numerous practical uses. If we were asked to determine the average male height in India or the average age of the men and women in a group, we would add up all the data and divide it by the total number of data points.

Given, the grades in tests are 74% and 82%. Also, the grade on final exam is 80%.

Now, considering that we have to find the average grade in tests and final exams combined, we put the average formula.

Average grade = Sum of percentages of each exam/Total exams

Thus, average is

= (74+82+80)%/3

= 236%/3

= 78.67%

The average grade received on two tests and the final exam is 78.67%.

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c is the answer. jdjsisiao

Answer:

The answer is 2x + 6 or 2(x + 3)

Step-by-step explanation:

2/3 (9x + 6) -1/2(8x - 4)

(18x + 12)/3 - (8x + 4)/2

6x + 4 - 4x + 2

Rearrange it

6x - 4x + 4 + 2

Combine like terms

2x + 6

Take 2 as common

2(x + 3)

Thus, The answer is 2x + 6 or 2(x + 3)

The required equivalent expression is given as 5(w - 3).

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
An equivalent expression of any expression is given as the simplifying the expression using various operations such as factors.
So,
Given expression,
=  5w - 15
As in the expression 5 is a common term between 5w and 15.
Take 5 commons and put the rest of the expression in the parenthesis.
= 5(w - 3)

Thus, the required expression is 5(w - 3).

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Step-by-step explanation:

Area of circle 1= pie r²

=3.14 x 5²

=3.14x 25

= 78.5km²

Area of circle 2=3.14 x 5.2²

= 3.14 x 27.04

= 84.9km²

change in area= 84.9-78.5

=6.4

radius²= 6.4/ 3.14

r²=2.03

r =√2.03

r=1.42

Answer: D; 360

Step-by-step explanation: To find percentages, I like to set up proportional relationships to find the amount. It would look like this:

[tex]\frac{90}{100}[/tex] = [tex]\frac{?}{400}[/tex]

90=  part %

100= whole %

?= amount of the %

400= all of the item(s)

So, we would cross multiply the 90 and the 400, then divide it by 100. That would be 36,000. So, that divided by 100 leaves us with 360. I hope this helped!

Answer:

125+25n

Step-by-step explanation:

We are given that

Heather opens a bank account with=$125

Each week she deposited money  into her account=$25

We have to find the explicit rule for the amount of money that has Heather after n weeks.

Heather has money after 1 week=125+25=$150

Heather has money after 2 week=125+2(25)=$175

Heather has money after 3 weeks=125+3(25)=$200

Heather has money after n weeks=125+25(n)

Hence, the explicit rule for the amount of money that has Heather after n weeks is given by

125+25n

Answer:

I was willing to pay $20 more for the toy than I actually paid.

Step-by-step explanation:

Let us take the maximum bid be y

So,

(y × 60) ÷ 100 = 30

60y/100 = 30

60y/100 × 100 = 30 × 100

60y = 3000

60y/60 = 3000/60

y = 50

60% of $50 is $30

So,

50 - 30 = 20

Thus, I was willing to pay $20 more for the toy than I actually paid.

Answer:

Your answer is x = 47.

Step-by-step explanation:

First, you need to move the constant to the right-hand side and change its sign.

4x = 180 + 8

Now, you need to add the numbers.

4x = 188

Last but not least, you need to divide both sides of the equation by 4, which gets you to:

x = 47

Answer:

(-2, 1.5)

Step-by-step explanation:

When graphed their solution is (the point where both the line intercept/touch) (-2,1.5)

I graphed this equations online**

Answer:

x = 58, y = 61

Step-by-step explanation:

We can use two properties of a parallelogram to solve this

1. The opposite angles of a parallelogram are equal

2. The sum of the 4 interior angles of a parallelogram equal 360

Using property 1,

Using property 2
(2x - 3) + y + (y + x) + y = 360

3x + 3y + 3 = 360

3x + 3y = 360 - 3 = 357

Divide both sides by 3 to get
x + y = 357/3
x + y = 119  [2]

Add [1] and [2] together to eliminate y and get

x - y + x + y = -3 + 119

2x = 116

x = 116/2 = 58

Use equation [2]

x + y = 119
58 + y = 119

y = 119 - 58

y = 61

Answer: percent: 25% amount: 40 base: unknown

Base after finding it: 160

Step-by-step explanation:

40/x = 25%/100

butterfly method

25x/25 = 4000/25

simplify; cancel out

x (aka the base) = 160

Answer:

21/79

Step-by-step explanation:

(7x6)÷2[{45÷3(7×2-15+6)}+4)​

(7*6)/2[{15(7*2-15+6)}+4)

(42)/2[{15(14-15+6)}+4)

(42)/2[{15(5))}+4)

(42)/2[{75}+4)

(42)/2[75 + 4]

(42)/2 * 79

42/2 * 79

21/79

Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

What is differentiation?

In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.

Main body:

by using product rule;

Let = u = x² + 4x + 6

⇒ du/dx = 2x + 4 .

Now y = u⁵

⇒ dy/dx = 5u⁴ .

dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)

= 5 * (x² + 4x + 6)⁴ * (2x + 4)

= 5(2x + 4) * (x² + 4x + 6)⁴

hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

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The supplement of BIE equals the supplement of GMD is a false assertion if lines BG and CF are parallel.

Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the total of angle 130° and angle 50° is 180°, hence they are supplementary angles.

Lines BG and CF are parallel, as shown in the figure.

If BIE = X, then its supplement of BIE will be 180 - X;

similarly, if GMD = Y, then its supplement of GMD will be 180 - Y.

Since BG and CF are parallel, the supplements of BIE and GMD are interior angles on the same side ( as shown in figure)

and for parallel line the interior angle on the same side is 180

so 180 - X and 180 -Y there sum should be 180

They cannot be equal

line BG and CF are parallel, then the supplement of BIE = the supplement of GMD are not equal.

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The sum will be an odd integer.

What is an integer?

An integer  is an integer (not a fraction) that is positive, negative, or zero.

In mathematics, integers are collections of integers and negative numbers. Like whole numbers, whole numbers do not contain fractions. Therefore, we can say that integers are numbers that can be positive, negative, or zero, but which are not fractions.

Let p,q,r be three random numbers

Let S be the sum of two even integers and one odd integer

S = 2p + 2q + (2r + 1)

S = 2p + 2q + 2r + 1

S = 2(p+q+r)+1

This shows that S is odd integer for all values ​​of p,q,r

Therefore, the sum will be an odd integer.

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The value will be 13.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

According to the given graph of

⇒ f(x) = 3ˣ

The point for f(x) = 12

We can see that such x is situated between 2.2 and 2.3

Thus the solution for this be;

⇒ (2.2 + 2.3)/2

⇒ 2.25

As above the solution of 3ˣ = 12

Is x = 2.25 which is about 2

Now, put x = 2.3

Therefore;

3²°³  = 12.51 ≈ 13

Thus it is about 13.

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Your chances of being killed or injured in such a crash are 5 times greater when you are thrown from your car than when you are buckled up

The safest decision that drivers and passengers can make is to use their seatbelts.

The national seat belt use rate was 90.4% in 2021, indicating that many Americans are aware of the life-saving benefits of seat belts.

In 2017, it is projected that 14,955 lives were saved by seat belt use in passenger automobiles.

Recognize the potentially devastating repercussions of not using a seat belt and discover how to always buckle up properly for you and your family.

Buckling up keeps you safe and secure within your car, whereas not doing so increases your chance of being completely ejected from the vehicle in an accident, which is virtually always fatal.

You need more protection than air bags.

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The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

Given that,

Give the equation for the parabola's axis of symmetry by sketching the graph of each quadratic function using its vertex and intercepts.

We have to determine the function domain and range using the graph is f(x) = (x-1)²+2

We know that,

Its vertex A quadratic function's form is provided by

f(x) = a(x-h)²+k

So, (h,k) is the vertex of the parabola

Take

f(x) = (x-1)²+2

(1,2) is the vertex of the parabola.

Therefore, The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

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The matrix equation Ax=b with one unique solution says that column A is linearly independent.

Two vectors are linearly dependent if at least one of them can be expressed as a linear combination of the others. If no vector can be expressed as a linear combination of the others, then two or more vectors are said to be linearly independent.

Given the matrix equation is Ax=b. And this equation has one unique solution. Then, let us assume this unique solution is x₁.  Let the column values of A be A₁, A₂, A₃, .... Aₙ.

If there is only one solution to the equation Ax = b for all b, then assume b = 0 and come to the conclusion that there is only one solution to the equation Ax = 0 as well. Consequently, the only solution is straightforward, and the columns of A are linearly independent.

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Computing on demand, on the cloud, and in real time IT Enviroment is most impacted by Are is known as gird computing.

What is Data Analysis?

Data analysis is the methodical application of logical and/or statistical approaches to describe and demonstrate, summarise and assess, and assess data.

Concept:

Step 1: A network of connected computers that act as a single supercomputer to complete complex tasks like modelling or data analysis is known as gird computing.

Step 2 : On-demand computing is a delivery method in which users are provided with computing resources as needed.

Step 3 : Real-time computing refers to a computer system that responds to an event by completing a task in a predetermined amount of time. a system for air traffic management as an example.

Grid computing, on-demand computing, and real-time computing

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(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

as the polynomial with rational coefficients that has zeros x=2 and x=3i

(x-2) and (x-3i) are factors of third-degree polynomial.

so ,

⇒(x-2)(x-3i)

solving (x-3i)

x = 3i

squaring both sides,

x² = -9

so , (x²+9) is a factor.

hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

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The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity

A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graph, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.

We are given the function;

g(x) = 2(x + 4)²/(x² - 16)

Simplifying the denominator gives;

(x² - 16) = (x + 4)(x - 4)

Thus, our function is;

g(x) = 2(x + 4)²/[(x + 4)(x - 4)]

(x + 4 ) will cancel out to give;

g(x) = 2(x + 4)/(x - 4)

Vertical asymptote:

Point in which the denominator is 0, so:

(x - 4) = 0

x = 4

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A widely used security technology called Transport Layer Protection, or TLS, enables privacy and data security for communications over the Internet. Encrypting communication between online applications and servers, such as when web browsers load a webpage, is one of the main applications of TLS.

When a user accesses a website through HTTPS and the browser initially starts to enquire about the website's origin server, a TLS handshake occurs

Together, the client and server will perform the following during a TLS handshake:

Indicate the TLS version (TLS 1.0, 1.2, 1.3, etc.) they'll be using.

Select the cipher suites they'll employ (see list below).

Using the server's public key and the SSL certificate authority's digital signature, confirm the server's identity.

After the handshake, generate session keys to enable symmetric encryption.

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Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

x=4-8y

3x+24=12

Taking first equation and rearranging it we get,

x+8y=4

multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.

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Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.

What do you mean by equations?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

What is a substitution method?

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

x=4-8y

3x+24=12

Taking first equation and rearranging it we get,

x+8y=4

multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.

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