In a classroom, 14 children have a dog as a pet, 11 children have cats and 3 who have both. If 24 children don't have either a cat of a dog, how many children are in the classroom.

Two column proof is a way to portray proofs in geometry.A two column proof always has two columns, one for statement and the other for reason.

The rules of a two column proof are, every statement should be numbered, every statement should have a reason. There is no order for the statements but it is better to maintain logocal order.Reasons for the statements are theories, previously proved theorems that justify the statement.

A,B,C,D are on a line and we have to prove that if AB=CD then AC=BD

Statements                                                  Reasons

1.A,B,C,D are collinear                               1.given

2.AB=CD                                                     2.given

3.BC=BC                                                     3.reflexive

4.AB+BC=BC+CD                                       4.adding 2 and 3

5.AB+BC=AC and BC+CD=BD                  5. Segment addition

6.AC=BD                                                     6.Substitution

Thus it is proved by two column proof that if AB=BC then AC=BD

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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:The space between the circle and the outside circle

Step-by-step explanation:

The space between the circle and the outside circle

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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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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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.

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

Answer:

8456/1000 Is the fraction of 8.456

Answer:

1057/125

Just write the number in a calculator and press equal. It'll give you the number in fraction

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.

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.

See attachment for the graph and the function is a continuous function.

The function definition is given as:

f(x) =  [ x-4 if x < 2

         [-2x+2 if x ≥2

The above function is a piecewise function.

So, we plot each function by its domain

Having said that, the next step is to plot the graph of the functions in f(x) according to their domain

See attachment for the graph

Also, the function is a continuous function.

This is so because there is no break in the function value i.e. domain and range are the set of all real values

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Answer:

-175

Step-by-step explanation:

thats the answer to the question

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

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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Using the concept of even and odd functions, it is found that, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

Hence, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

For even functions it will decrease because we have that f(4) > f(3), for example, hence f(-4) > f(-3).

For the odd function it will increase because if f(4) > f(3), then f(-3) > f(-4) due to the negative signal.

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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:

17

Step-by-step explanation:

[tex]\sf |-3d-6|+|-5-d^2| \quad for\:\: d = -3[/tex]

Given expression:

[tex]\sf |-3d-6|+|-5-d^2|[/tex]

substitute d = -3

[tex]\sf |-3(-3)-6|+|-5-(-3)^2|[/tex]

simplify following inside parenthesis

[tex]\sf |9-6|+|-5-9|[/tex]

simplify by combining integers

[tex]\sf |3|+|-14|[/tex]

if |-a| or |a| then equals to a

[tex]\sf 3+14[/tex]

evaluate:

[tex]\sf 17[/tex]

Answer:

17

Step-by-step explanation:

Given expression:

[tex]|-3d-6|+|-5-d^2|[/tex]

To evaluate for d = -3, substitute d = -3 into the expression:

[tex]\implies |-3(-3)-6|+|-5-(-3)^2|[/tex]

[tex]\textsf{Apply exponent rule} \quad a\cdot a=a^2:[/tex]

[tex]\implies |(-3)^2-6|+|-5-(-3)^2|[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^2=a^2:[/tex]

[tex]\implies |3^2-6|+|-5-3^2|[/tex]

[tex]\implies |9-6|+|-5-9|[/tex]

Subtract the numbers:

[tex]\implies |3|+|-14|[/tex]

[tex]\textsf{Apply absolute rule} \quad |a|=a, \quad a\geq 0[/tex]

[tex]\implies 3+|-14|[/tex]

[tex]\textsf{Apply absolute rule} \quad |-a|=a, \quad a > 0[/tex]

[tex]\implies 3+14[/tex]

Add the numbers:

[tex]\implies 17[/tex]

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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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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Each pound of brand B costs 0.33 dollars less than each pound of brand A.

Here we need to find the cost per pound for both brands, to get that, we need to get the quotient between the costs and the number of pounds.

For brand A the cost is $37.80 and you get 35 pounds, then the cost per pound is:

A = $37.80/35 = $1.08

Then each pound for brand A costs 1.08 dollars.

Now let's do the same for brand B, the cost is $33.75, and you get 45 pounds, then the cost per pound is:

B = $33.75/45 = $0.75

Then each pound for brand B costs 0.75 dollars.

So brand B is cheaper, and the difference is:

1.08 dollars -  0.75 dollars = 0.33 dollars.

Each pound of brand B costs 0.33 dollars less than each pound of brand A.

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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:

Step-by-step explanation:

4+2=6

6/2=3

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

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?

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 )

Using it's concept, the range of the function f(x) = -x + 5 in the domain [-3,2] is [3,8], and the graph is given at the end of the answer.

The range of a function is the set that contains all possible output values of the function for a given domain(set of input values). In a graph, the range is given by the vertical axis, that is, by the values of y.

From the graph shown at the end of the answer, y assumes values between 3 and 8, hence the range is of [3,8].

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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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