Limits and Piecewise functions help please

Answer:

( 10 , -3 )

Step-by-step explanation:

→ See which coordinate is affected by a translation right

x

→ Apply

( 10 , y )

→ See which coordinate is affected by a translation down

y

→ Apply

( 10 , -3 )

The function F(g(9))= 179

Given ,Function F (n) = 3n-1

g(n) = n² - 2n-3

g(9)= 9²-2(9)-3

= 81-18-3

g(9) = 60

F(g(9))=F(60)

= 3(60)-1

 = 179

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain.

The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.

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The projected attendance for 2014 in the form of linear equation is written as y = 2x.

A linear equation in two variables is one that is written in the form ax + by + c = 0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero.

Now, for the given question;

Let us consider that the total attendance in 2012 be 'x'.

And the total attendance in 2014 be 'y'.

Then,  the total attendance for 2014 will be twice the attendance in 2012.

Thus,

y = 2x.

Therefore, the linear equation which shows the condition that the total attendance for 2014 will be twice the attendance in 2012 is y = 2x.

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The Number of Gallons drained per minute from the pool is; 931.5 gallons drained per minute

Constant rate is simply a rate that remains unchanged regardless of change in parameters.

Now, we are told that One hundred three and one half gallons drained in the last 9 minutes from a pool. Thus;

Amount of gallons that drained from pool = 103¹/₂ gallons = 207/2 gallons

Time it took to drain = 9 minutes

Thus;

Number of Gallons drained per minute from the pool = (207/2)/9

Number of Gallons drained per minute from the pool = (207 * 9)/2

Number of Gallons drained per minute from the pool = 931.5 gallons drained per minute

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Proportionality constant of p is = 14 t

The constant proportional relationship between two variables. The proportionality constant, k, is defined as k = y/x. This is equivalent to the equation for the slope of a line through the origin, m = y/x. The value of m, which will be the same as the value of k, or the constant or proportionality, can be discovered using the equation for the slope of the line.

y = kx

The rate k = 210 ÷ 15 = 14 gel pens per minute

"p" is number of pens, "t" is number of minutes

p = 14t

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Answer:

I think it's, Y = 2x + 5

Step-by-step explanation:

* You move the -4x to the right side.

* Divide 2 from both sides

And you will end up with this answer.

F(x) means the equation

and we are solving for Y here.

Answer:

x=82.7

Step-by-step explanation:

3x+6-6=248

3x=248

x=82.7

Answer:  

Step-by-step explanation:

3x   +  6  −  6  =  248

3x  +  6  +  −  6  =  248

(  3x  )   +  (   6   +  −  6  )  =  248      (ℂ  )

3x  =  248

3x  /  3  = 248  /  3

x   =   248  /  3

x  =  82.6

Using proportions, it is found that they traveled a total of 3066 miles around the lake.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships.

One example of application of proportions is for unit rate problems, in which we find the unit rate for a single person, and then the total amount for a number n of people is given by n multiplied by the unit rate.

For this problem, we have that:

Hence the total distance traveled by all these people is given as follows:

200 x 15.33 = 3066 miles.

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The expression [tex]-2\vec C+6\vec D[/tex] in the ordered pair notation is (16,-16).

The vector components of a vector are represented as the ordered pair of its x and y components.

For example, if a vector has x - component 'a' and y- component 'b' , then the ordered pair notation for the vector is (a, b), where the vector is [tex]a \vec i+b \vec j[/tex].

Now the vector C has its x- component = -2

y- component of C = -1

Therefore, ordered pair notation of C = (-2, -1)

x- component of D = 2

y-component of D = -3

Therefore, ordered pair notation of D = (2,-3)

So the expression  [tex]-2\vec C+6\vec D[/tex] = -2 (-2,-1) +6 (2,-3) = (4,2) + (12, -18)

= (16, -16)  in the ordered pair notation.

That is, the vector [tex]\bold {-2\vec C+6\vec D}[/tex] is a vector with x-component 16 and y-component -16.

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The value of the given expression is equivalent to [tex]y^{-5} x^{-2}[/tex], that is, option 5.

An exponent is a number or variable that is placed above and to the right of the expression to which it applies. It tells us the number of times the expression is used as a factor.

Here, we are given an expression as follows-

To simplify this expression we can use the following property of exponentials-

[tex]a^{l} a^{k} = a^{k+l}[/tex]

This holds true for all real values of a, k and l.

Thus, we can write the given expression as-

[tex]y^{-8} y^{3} x^{0} x^{-2} = y^{-8+3} x^{0-2}[/tex]

= [tex]y^{-5} x^{-2}[/tex]

Thus, the value of the given expression is equivalent to [tex]y^{-5} x^{-2}[/tex].

From the given options, thus, option number 5, is the correct answer.

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Answer:

-175

Step-by-step explanation:

thats the answer to the question

Answer:The space between the circle and the outside circle

Step-by-step explanation:

The space between the circle and the outside circle

Answer: 12

Step-by-step explanation: we know that a^2 + b^2 = c^2, pythagorean theorem. We're given a and c in this case, which are 16 and 20 respectively. so that means 16^2 + x^2 = 20^2. After evaluating the equation, we get 256+ x^2 =400. now subtract 256 from both sides and then we get x^2 = 144. take the square root of both sides and we end up with x = 12.

Evaluando la expresión:

b^2*(c + d) - a^2*(m + n) + 2x

En los corresopondientes valores obtendremos:

b^2*(c + d) - a^2*(m + n) + 2x = 161/6

Veamos la segunda expresión en la imagen, está es:

b^2*(c + d) - a^2*(m + n) + 2x

Uso está por que es la unica que puedo leer bien en la imagen.

Queremos evaluar está expresion, se nos dan los valores:

a = 1               d = 4

b = 2             m = 1/2

c = 3              n = 2/3

p = 1/4           x = 0

Solo hay que reemplazar las variables por los números correspondientes. Si reemplazamos x por 0 obtendremos:

b^2*(c + d) - a^2*(m + n) + 2*0 = b^2*(c + d) - a^2*(m + n)

Ahora reemplacemos c = 3 y d = 4:

b^2*(3+ 4) - a^2*(m + n) = b^2*7 - a^2*(m + n)

Ahora remplazamos m y n, asi obtendremos:

b^2*7 - a^2*(1/2 + 2/3) = 7*b^2 - (3/6 + 4/6)*a^2 = 7b^2 - (7/6)*a^2

Finalmente reemplazamos b y a, asi obtendremos:

7*(2)^2 - (7/6)*1^2 = 7*4 - 7/6 = 28 - 7/6 = 161/6

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The value of third consecutive odd is 23

• In Mathematics, algebra is a branch which only deals with symbols and the rule for  the manipulation of these symbols. Algebra is divided into different sub branches such as advanced algebra, linear algebra, elementary algebra, abstract algebra etc.

• The basics of algebra contains numbers, variables, constants, expressions and equations. The basic four operations of algebra are addition, subtraction, multiplication, division.

Let the first consecutive odd integer be x

Second consecutive integer = x+2

Third consecutive integer = x+4

We are given that

First + third = 5(Second) – 63

x + x + 4 = 5 (x+2) -63

2x + 4 = 5x +10 -63

-3x = -57

3x = 57

x = 19

First Consecutive odd = 19

Second Consecutive odd = 21

Third Consecutive odd = 23

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This is the random sampling is used in the statement.

According to the statement

We have to find that the about the sampling.

So, For this purpose, we know that the

A sample is an outcome of a random experiment. once we sample a chance variable, we obtain one specific value out of the set of its possible values. that exact value is termed a sample.

From the given information:

if she chooses a sample of the population that offers everyone an equal chance of participating, this might be a(n) sample.

Then

According to this, there is random sampling is used.

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

So, This is the random sampling is used in the statement.

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Here is a diagram of a straightedge and compass construction. c is the center of one circle, and b is the center of the other. Since both segments begin at point B, their lengths are equal.

Both segments begin at point B, their lengths are equal.

Since the radius of the smaller circle is the distance from its center (B) to its edge, length BD equals length AB.

Using the attached diagram

The larger circle's center is at C, while

Point B is the location of the smaller circle's center.

The smaller circle passes through the larger circle, dividing it into two segments, BD and AB, which extend from the smaller circle's center to their intersecting edges.

As a result, since both segments begin at point B, their lengths are equal.

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[tex] \large{ \star \boxed{ \tt \: Answer : \boxed{ \tt{4}}}}[/tex]

Please see the attached picture for full solution !

-------- Happy LearninG <3 --------

Answer:

Step-by-step explanation: We can begin by rewriting the equation. That would look like so:

3/9 = x/12

We need to solve for x. Our first step is to identify a common denominator. Let's list the multiples of each denominator.

9: 9, 18, 27, 36

12: 12, 24, 36

Our common denominator is 36.

Now, let's cross multiply:

3 x 12 = 36

9 x ? = 36

36 ÷ 9 = 4

x = 4

Final answer: 3/9 = 4/12, where x = 4.

yes proper subset  is different from a regular subset. The empty set is a proper subset of every set except for the empty set

A proper subset of a set A is a subset of A that cannot be equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.

Subset: If A and B are sets and every element of A is also an element of B, then:

A is a subset of B, denoted by A ⊆ B.

or equivalently, B is a superset of A, denoted by B ⊇ A.

Any set is considered to be a subset of itself. No set is a proper subset of itself. The empty set is a subset of every set. The empty set is a proper subset of every set except for the empty set.

For example, A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A = {1, 2, 3} and B = {1, 2, 3}

Here, A is a subset of B, or we can say that B is the superset of A.

Proper Subset: If A is a subset of B, but A is not equal to B (that is, there exists at least one element of B which is not an element of A), then

A is also a proper (or strict) subset of B; this is written as A ⊊ B.

For example A = {1, 2, 3} and B = {1, 2, 3, 4}.

Clearly, A is not equal to B and element {4} belongs to set B but is absent in set A, so we have one element in set B which is not an element of set A. Thus, A can be called a proper subset of B.

Hence, a proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B, thus the proper subset may or may not be the same.

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If two shapes can be mapped onto one another using rigid transformations, then yes, they can be said to be congruent.The preimage of right angle triangle and a right angle triangle are the example of congruent shapes.

Two shapes are considered to be congruent if they can be mapped onto one another using rigid transformations (a sequence of one or more rotations, translations, and reflections). A congruent triangle is produced by any series of rigid transformations applied to a triangle.

Now, let's learn about Rigid transformation

A rigid transformation of the plane, also known as an isometry, keeps length intact. "Rigid transformations" include reflections, translations, rotations, and combinations of these three transformations.

Example: The preimage of right angle triangle and a right angle triangle are the example of congruent shapes.

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The coordinates of the vertices of the image are Q'(x, y) = (- 1.5, 6), T'(x, y) = (0, - 3), R'(x, y) = (1.5, 3) and S'(x, y) = (3, - 3), respectively.

A dilation is a kind of rigid transformation, that is, a transformation applied on geometric loci such that its Euclidean distance is conserved. According to the statement, we must the following dilation to generate the image:

P'(x, y) = (3 / 2) · P(x, y)

If we know that Q(x, y) = (- 1, 4), T(x, y) = (0, - 2), S(x, y) = (2, - 2) and R(x, y) = (1, 2), then the vertices of the images are:

Q'(x, y) = (3 / 2) · (- 1, 4)

Q'(x, y) = (- 1.5, 6)

T'(x, y) = (3 / 2) · (0, - 2)

T'(x, y) = (0, - 3)

R'(x, y) = (3 / 2) · (1, 2)

R'(x, y) = (1.5, 3)

S'(x, y) = (3 / 2) · (2, - 2)

S'(x, y) = (3, - 3)

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Answer:x=6

Step-by-step explanation:

6x-4-4x+1=9

subtract 1 from both sides

6x-4-4x=8

add 4 to both sides

6x-4x=12

subtract 6x by 4x

2x=12

divide by 2 on both sides

x=6

Answer:

626 times 6261 plus 276262

Step-by-step explanation:

i buy 626 cookies and 1000 million water how much did i eat and drink?

[tex]450 - 300 = 150 \\ 150 \div 2 = 75t \\ the \: average \: rate \: of \: growth \: per \: year \: is \: 75 \: student \: per \: year[/tex]

Answer:

50 degrees

Step-by-step explanation:

The angle of ABE is opposite to angle CBD, which means that ABE = CBD

It is a math rule, all opposite angles are equal.

The fraction of the carpet covered by the rug will be 1/15.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L×W square units

A rectangular carpet estimates 10 m by 6m. Some portion of the rug is covered by a square rug of length 2 m.

The area of the carpet is given as,

A = 10 x 6

A = 60 square meters

The area of the rug is given as,

a = 2 x 2

a = 4 square meters

A fraction of the carpet is covered by the rug is given as,

⇒ 4 / 60

⇒ 1 / 15

A fraction of the carpet covered by the rug will be 1/15.

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The missing diagram is attached below.

Answer:

6x

Step-by-step explanation:

Because, 6 multiplied by x, we know that if there is just an x, we add a 1, so it would be 1x. 1x multiplied by 6 is 6x.

Hope this helps you!

Answer:

6x

Step-by-step explanation:

The product means multiply

6*x

6x