A rectangle has a length of
2,000 cm and a width of 23 cm.
What is the area?
What is the perimeter?

Expression: x² - 6x + 9

Factored form: (x - 3)²

Using the concept of factorization.

The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.

Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.

Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.

Given that,

x² - 6x

Now, to find the value of c = (b/2)²

divide the coefficient of x by 2.

So, divide 6 by 2 we get: ( -1.3)²

Next, multiply -1 by 3: (-3)²

Now, raise -3 to the power of 2, we get: 9

So, the expression becomes: x² - 6x + 9

Factorized form: (x - 3) (x -3)

or we can write (x - 3)²

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The number of sheets of stickers that Kyle needs will be 7 sheets.

The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

From the information, Kyle has a notebook for each of his 13 classes. He puts 5 stickers on

each notebook and there are 10 stickers on each sheet.

The number of sheets of stickers that Kyle needs will be:

= (13 × 5) / 10

= 65 / 10.

= 6.5

= 7 approximately

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Therefore , the solution of the given problem of median comes out to be

confidence interval = [ 51.708 , 64.558 ].

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.

Here,

(48, 51, 65, 71, 61, 45, 48, 72, 74, 66, 43, 47, 70, 66, 45) sample data; sample mean, x = 58.133; sample size, n = 15; standard deviation, s = 11.6;

Standard deviation equals sd/√(n)

where, n = sample size and sd = standard deviation

Margin of error is equal to t alpha/2 and the standard error is (11.6/√( (15)) = 2.995. (standard error)

where ta/2 is the t-table level of significance, alpha is 0.05 from the standard normal table, the two-tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145, and the margin of error is 2.145 * 2.995, which equals 6.425. The confidence interval for this margin of error is [58.133 6.425] = [51.708, 64.558].

being that,

sample data: (48 , 51 , 65 , 71 , 61 , 45 , 48 , 72 , 74 , 66 , 43 , 47 , 70 , 66 , 45 )

sample mean, x =58.133

standard deviation, s =11.6

sample size, n =15

level of significance, alpha = 0.05

from standard normal table, two tailed  value of |t alpha/2| with n-1 = 14 d.f is 2.145

we use CI = x ± t a/2 * (sd/ √((n))

where,

x    = mean

sd   = standard deviation

a    = 1 - (confidence level/100)

ta/2 = t-table value

CI   = confidence interval

confidence interval = [ 58.133 ± t a/2 ( 11.6/ sqrt ( 15) ]

= [ 58.133-(2.145 * 2.995) , 58.133+(2.145 * 2.995) ]

=  [ 51.708 , 64.558 ]

Therefore , the solution of the given problem of median comes out to be

confidence interval = [ 51.708 , 64.558 ].

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An Example of a caravan is eight covered wagons traveling together on the trail. Meaning, option A is correct.

A caravan, travel trailer, camper, tourer, or camper trailer is a trailer towed behind a road vehicle to provide a more comfortable and secure sleeping space than a tent.

It allows people to have their own home on a trip or vacation without relying on a motel or hotel, and it allows them to stay in places where none are available. However, in some countries, campers are restricted to designated sites where fees must be paid.

Caravans range from basic models that are little more than a tent on wheels to those that have several rooms with all of the furniture, furnishings, and equipment of a home. The solid-wall trailers can be made of metal or fibreglass.

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Answer:

Here is an example. Check out the uploaded image.

Step-by-step explanation:

Draw Points   XY  using a Straight Line

Draw a bisector in the middle of the line

Repeat Procedure for lines XZ  and YZ

Where the two lines meet is the Center

Extend the compass from the center to any point and complete the circle.

Step-by-step explanation:

please refer to the sketch

The system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, is an equation, x² = 2x+3, we need to find a system of equations that can be graphed to give the solution of the equation given,

So, the equation is x² = 2x+3

We can write this as,

x²-2x-3 = 0

Now, factorize to find the solution of the equation,

x²-3x+x-3 = 0

x(x-3)+1(x-3) = 0

(x+1)(x-3) = 0

x = -1 and x = 3

So, the solution of the equation is -1 and 3

However, if we consider the equation to be two different systems combined, that is the equation of the straight line and the equation of the basic quadratic function,

y = x² and y = 2x+3

Then the solution to is the intersection of the graph of the straight line and the graph of the quadratic curve.

That is the x-coordinates of the points of intersection are the solutions.

Since, the graphs are intersecting at (3, 9) and (-1, 1) [see the graph]

Therefore, the system of equation is y = x² and y = 2x+3

Hence, the system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

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Answer:

QS = 12

Step-by-step explanation:

Hello!

We can see that QS is the sum of QR and RS, which is equal to 6x.

We can substitute the given values to solve for x, and then use that to find QS.

The value of x is 2. We can now find QS by substituting 2 for x in 6x.

QS = 12.

Answer:

(y+72)

I'm not sure because your answer is not very clear

Answer:

1/2 or 0.5 inches per hour

Step-by-step explanation:

5 divided by 10 will get you this answer

All of the equations that are true include the following:

B. 56 + 70 = 14(4 + 5).

C. 28 + 49 = 7(4 + 7).

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

In order to determine the true equation, we would apply the distributive property of multiplication and then check whether or not the right-hand side is equal to the left-hand side.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

32 + 96 = 8(4 + 14)

32 + 96 = 32 + 112 (False).

56 + 70 = 14(4 + 5).

56 + 70 = 56 + 70 (True).

28 + 49 = 7(4 + 7).

28 + 49 = 28 + 49 (True).

27 + 36 = 3(9 + 13)

27 + 36 = 27 + 39 (False).

25 + 35 = 5(5 + 6)

25 + 35 = 25 + 30 (False).

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The transformation in the graph is 1 units vertically downwards.

The correct option is A: The graph of g(x) is the graph of f(x) shifted down 1 unit.

Let the function f(x) and g(x) are two real functions.

And  g (x) = f (x) + k, where k is real numbers.

Function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given:

The function f(x) = eˣ,

and the function g(x):

g(x) = f(x)-1= eˣ-1.

The graph of both the functions are given in the attached images.

For the base function f (x) and a constant k, the function given by

The transformations in the graph is defined by:

g (x) = f (x) + k, where k is real numbers.

Function can be sketched by shifting f (x), k units vertically.

The value of k determines the direction of the shift. Specifically,

if k > 0, the base graph shifts k units upward, and

if k < 0, the base graph shifts k units downward.

Here, k = -1

And the graph of g(x) is the graph of f(x) is shifted down 1 unit.

Therefore, the f(x) is shifted to 1 unit downward.

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Answer:

Step-by-step explanation:

Well it would be funchen because as you see it just makes sence

Answer:

not a function

Step-by-step explanation:

In a function, an input gives only one output. As you can see from the graph, the input which is 4 produces 3 different outputs which are 2, 3 and 4, thus it cannot be a function.

Answer:

No, it is not a proportion

Step-by-step explanation:

10/12 and 40/64 is not a proportion since although the numerator is constant because when multiplied by 4, it gives us 40, however, when you multiply 4 by 12, you get 48, therefore, it is not a proportion since the changes in the value of a proportion must be constant in both the numerator and denominator.

Hope this helped!  :D

There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The function f(x) = x³ +7x² - 5x + 19 is a polynomial function of degree 3, which means it has 3 roots (also known as zeros or solutions) that could be real or complex.

To determine the number of negative real roots, we can use the fact that a cubic function has at least one real root.

x³ +7x² - 5x + 19

the first coefficient is positive, the second is positive, the third is negative, and the fourth is positive.

There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"

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Answer:

True

Step-by-step explanation:

First, you need to subtract a then that would make a 0

Answer: true

Step-by-step explanation: c and d are the same, so a+c and a+d will be the same

Answer:

perimeter = 70 yards

Step-by-step explanation:

⭐What is the area of a rectangle?

⭐What is the perimeter of a rectangle?

1. Make the equation for the area of the given rectangle and solve for x

2. Substitute x into the expressions of the length and width and solve for the perimeter

1. Define the expressions of the length and width of the rectangle

width: x

length: 4x

2. Make the equation for the area of the rectangle

[tex]196yd^2 = 4x * x\\196yd^2 = 4x^2[/tex]

3. Solve for x

[tex]\frac{196}{4} = x^2[/tex] . . . . . . . . . . divide both sides by 4

[tex]49 = x^2[/tex]

[tex]\sqrt{49} = \sqrt{x^2}[/tex] . . . . . . . . square root both sides to isolate x

∴ [tex]7 = x[/tex]

4. Substitute x into the expressions of the length and the width

width: x

width = 7

height: 4x

height = 4(7) = 28

5. Solve for the perimeter

[tex]perimeter = 2(length) + 2(width)[/tex]

[tex]perimeter = 2(28) + 2(7)\\perimeter = 56 + 14\\perimeter = 70[/tex]

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The angle of elevation of a 20-foot railroad crossing arm is fixed at 35 degrees. As necessary, round up to the next tenth. 20 ft, 35 ft, x -11.5 feet, y- 16.4 feet .

Between the horizontal line and the line of sight, an angle called the angle of elevation is created. The angle of elevation formula tan =QR/PR can be used to calculate the building's height (QR). Therefore, the building has 8 units of height. When it lies between the line of sight and the horizontal line, the angle of elevation is generated. The angle created, known as the angle of elevation, occurs when the line of sight is above the horizontal line. However, in the depression angle, the line of sight is downward and parallel to the ground.

When we multiply in algebra, we come before a variable with a number. In the same way, xy means to multiply variable x by variable y, while 7xy means to multiply variable x by variable y and then to multiply the entire expression by seven. Due to the complexity of how train-based questions are frequently presented, it is always advisable to read the question thoroughly before responding. After reading the question, try to use a formula in it; this may lead to a direct solution and save you time.

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to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{53}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{53}-\stackrel{y1}{32}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{8}}} \implies \cfrac{ 21 }{ 7 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{ 3}(x-\stackrel{x_1}{8}) \\\\\\ y-32=3x-24\implies {\Large \begin{array}{llll} y=3x+8 \end{array}}[/tex]

Answer:  -7/5

Step-by-step explanation:

Answer:

8.5

Step-by-step explanation:

there's a rule to get the distance between 2 points

√((1st x- 2nd x)²+(1st y- 2nd y)²)

√((-6-(-6))²+(5-(-3.5))²)

=√((-6+6))²+(5+3.5))²)

you can just type that on your calculator and you'll get the result

√((-6+6))²+(5+3.5))²)

=√((5+3.5))²)

= √((8.5))²)

the root goes away with the power (exponent)

so it equals 8.5

Answer:
Here is a sequence of numbers using the rule "x+8":

x+8=9 (x=1)

x+8=10 (x=2)

x+8=11 (x=3)

x+8=12 (x=4)

x+8=13 (x=5)

x+8=14 (x=6)

Here is the sequence of ordered pairs:

(1, 9)

(2, 10)

(3, 11)

(4, 12)

(5, 13)

(6, 14)

The listing of the given values from the least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.

A number line is defined as the expression that represents the location of real numbers as being a positive number or a negative number.

The negative values which are the least in the number line are usually higher in value than the greater numbers, while the greater values are higher for positive numbers.

Therefore,the arrangement of the given values from least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.

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Answer:

4|x|y²√(3yz)

She forgot the absolute value sign on x, and she left out the exponent on y.

Step-by-step explanation:

Step 1 is correct.

x may be positive, zero, or negative.

√x is always non-negative. To assure that √x² is non-negative, √x² = |x|.

√16 = 4

√3 = √3

√x² = |x|

√y² × √y² = √y^4 = y²

Since y² is always non-negative, there is no need for absolute value sign.

√y^4 = y²

Answer should be

4|x|y²√(3yz)

On solving the equation n = za the value of a is obtained as a = n/z.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

To solve for a in the equation n = za, isolate a on one side of the equation.

Do this by dividing both sides by z:

n/z = (za) / z

On the right side, the z's cancel out, leaving -

n/z = a

So the solution is -

a = n/z

Therefore, the value of a that satisfies the equation n = za is equal to n divided by z.

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The coordinates of Point D are (2.5, 8).

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

Given:

Parallelogram ABCD has vertices at A (-3, 6.5), B (-1, -1.5), and C (4.5, 0).

We have to find the coordinates of Point D.

Let its fourth vertex be D(a, b).

Join AC and BD. Let AC and BD intersect at point O.

We know that the diagonals of a parallelogram bisect each other.

So, O is the midpoint of AC as well as that of BD.

Using the midpoint formula,

Midpoint = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Here, ([tex](x_1, y_1) = (-3, 6.5), (x_2, y_2) = (4.5, 0)[/tex]

⇒  Midpoint of AC = [tex](\frac{-3 + 4.5}{2}, \frac{6.5 +0}{2}) = (\frac{1.5}{2}, \frac{6.5}{2}) = (0.75, 3.25)[/tex]

Now,

Midpoint of BD is = [tex](\frac{-1+a)}{2}, \frac{-1.5+b}{2})[/tex]

⇒

[tex]\frac{-1+a}{2} = 0.75, \frac{-1.5+b}{2} = 3.25 \\ -1 + a = 1.5, -1.5 + b = 6.50\\a = 2.5, b = 8[/tex]

Hence, the coordinates of Point D are (2.5, 8).

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Answer:

7

Step-by-step explanation:

In order to find the answer to the equation, you must substitute the given values into the equation.

A^3 - C + B

We know that A = 3, B = 6, and C = 8

(3)^3 - (8) + (6)

9 - 8 + 6

1 + 6

7

If you list the number of tickets sold over time, the kind of sequence will you see is a geometric sequence.

What is a geometric sequence?

A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Here,

We assume that the variable x represents the number of tickets sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression that models this situation is given by geometric sequence:

x, 7x, 49x, 343x, .....

Verification:

7/1 = 49/7 = 343/49 = 7

Hence, this is a geometric sequence.

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