Why is the 4th interval called perfect?

The shorter side should be 200 ft and the longer side should be 200 ft. This would give the garden the greatest possible area of 40,000 square-feet.

1. The area of a rectangle can be calculated by multiplying the length and width together.

A = L * W

2. We know that the total amount of fencing is 400 ft.

3. We also know that one side of the garden is a river and so it doesn't require fencing.

4. Therefore, the remaining fencing must be divided equally between the two other sides of the garden (200 ft per side).

5. We now know that the length and width of the garden are both 200 ft.

6. Plugging these values into the area equation, we get:

A = 200 ft * 200 ft = 40,000 sqft

7. Therefore, the greatest possible area of the garden is 40,000 square-feet..

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Answer:

C

Step-by-step explanation:

Yes, [tex]9x^2-30x +25[/tex]  is a perfect square trinomial.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial of the form [tex]ax^2 + bx + c[/tex] meets the requirement [tex]b^2 = 4ac[/tex], it is said to be a perfect square.

Two of your terms will be perfect squares in a perfect square trinomial. This trinomial is not a perfect square trinomial if it lacks two perfect square terms. The square root of each perfect square word should now be determined, combine the two square roots, then multiply the result by two.

This trinomial is a perfect square. The only thing left to determine is whether the middle term matches when you square (3x-5) because both [tex]9x^2=(3x)^2\ and\ 25=52[/tex] are perfect squares. The minus sign was used to at least produce a negative coefficient for the middle term.

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Answer:

2/5

Step-by-step explanation:

Answer:

1)95

2)180

3)77

4)120

5)244

6)74

I think

Answer:

D = (-4, -4)

Step-by-step explanation:

Given;

midpoint of line CD = M(-3, -7)

coordinate of C = (-2, -10)

The coordinate of D is calculated as follows;

C(-2, -10)---------------------M(-3, -7)--------------------D

[tex]M = \frac{D_1 + C_1}{2} \ , \ \frac{D_2 + C_2}{2} \\\\(-3, \ -7) = \frac{D_1 + (-2)}{2} , \ \frac{D_2 + (-10)}{2} \\\\(-3, \ -7) = \frac{D_1 \ - \ 2}{2} , \ \frac{D_2 -10}{2} \\\\-3 = \frac{D_1 \ - \ 2}{2} \ \ ----(1)\\\\-7 = \frac{D_2 -10}{2} \ -----(2)\\\\From \ (1): 2(-3) = D_1\ - \ 2\\\\-6 = D_1 - 2\\\\-6 + 2 = D_1\\\\-4 = D_1\\\\From \ (2) : \ 2(-7) = D_2 - 10\\\\-14 = D_2 - 10\\\\ -14 + 10 = D_2\\\\-4 = D_2\\\\The \ coordinate \ of \ D = (D_1\ , \ D_2)\\\\D = (-4 \ , \ -4)[/tex]

Therefore, the coordinate of D = (-4, -4)

The value of x is 14.7224.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Sin 60° = x/17 ____(1)

Sin 60° = √3/2 _____(2)

From (1) and (2) we get,

√3/2 = x/17

x = 17√3/2

x = 17 x 1.73205 / 2

x = 14.7224

Thus,

The value of x is 14.7224.

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Answer:

%120

Step-by-step explanation:

The original cost was $10 then it went to $12, so 100 percent representing the 10, then with 2 dollars left it is 20 percent. You can check by multiplying 1.2 by 10.

Hope I helped :]

Answer:

20.00%

Step-by-step explanation:

$12-$10=$2

2/100

2/100 / 2 = 1/50

1/50=0.02

0.02×100=20%

Answer:

y = [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line

On solving the provided question we can say that the new Mean = 610 mean .

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). is 50.

What is mean?

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean).

The mean score is calculated by dividing the total number of tests taken by all of the scores. The mean will therefore rise if you give each test a higher mark. The standard deviation is calculated as the square root of the product of the power of two of all test results, multiplied by the number of tests, and then subtracted from the mean.

Each score you raise by 10 will result in a 10 change in the mean. But as there will be no change in the distance between each score and the mean, the standard deviations will also not change.

Mean = 600

Average deviation is 50.

Scores went up by 10

Mean = 610

Average deviation is 50.

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Answer:

the first one is x=7 and the second one is x=6

Answer:

2

Step-by-step explanation:

The parent graph is the one used to create a new function by any of the transformations (reflection about an axis, horizontal/vertical shifts, stretches/compressions).

Start with the square root function

[tex]f(x)=\sqrt{x}[/tex]

Multiply by 3 (vertical stretch)

[tex]h(x)=3\sqrt{x}[/tex]

Replace  x  with  x - 2 (shift to right 2 units)

[tex]g(x)=3\sqrt{x-2}[/tex]

The parent function of a line (usually of the form y = ax + b) is y = x.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

Linear functions have x as the term with the highest degree and a general form of y = a + bx. All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers.

These functions represent relationships between two objects that are linearly proportional to each other.

Therefore, the parent function of a line (usually of the form y = ax + b) is y = x.

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The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line.

The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

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the question is of set of equations and the solution is as follows,

the equation is 2x -3 = 7,

First, add 3 to each side to get

2x - 3 + 3 = 7 +3

2x = 10

x = 10/2

x =5.

equations

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For Example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

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Step-by-step explanation:

w(idth) = 2.5 inches for both boxes

h(eight) = 10 inches for both boxes

l(ength)l(arge) = 8 inches

l(ength)s(mall) = 75% of ll (=> of 8 inches)

=> ls = 8 × 75/100 = 2 × 75/25 = 2 × 3 = 6 inches

vl (volume large) = 8 × 2.5 × 10 = 200 inches³

vs (volume small) = 6 × 2.5 × 10 = 150 inches³

the difference of these two volumes is 50 inches³

the units to be used is cubic inches (inches³). we are talking about volumes. not lengths (inches), not areas (inches²).

the reason - for a volume we need to multiply 3 lengths (measured in simple inches). so, inch multiplied by inch is inch². this multiplied by inch again is then inch³.

Answer:

8 he would be able to give 8 kids 1 dollor and 25 cents

Answer:

19,167

Step-by-step explanation:

Laura purchased a new vehicle for 27,382

She made a down payment of 30%

27,382×30/100

= 27,382×0.3

= 8,214.6

27382-8214.6

= 19,167

Hence Laura financed 19,167

TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. ccTLDs are two-letter domains that represent a specific country or region.

Domain names are used to identify websites on the internet. There are two main types of domain names: top-level domains (TLDs) and country code top-level domains (ccTLDs).

TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. Examples of TLDs include .com, .org, .net, .edu, and .gov.ccTLDs are two-letter domains that represent a specific country or region. Examples of ccTLDs include .us for the United States, .au for Australia, .ca for Canada, .uk for the United Kingdom, and .fr for France.

When registering a domain name, users should choose a TLD or ccTLD that best suits their needs. For example, if they are targeting a global audience, they should consider a .com TLD. If they wish to target a specific country, they should consider a ccTLD.

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Answer:

60:13

60 students to 13 teachers

Step-by-step explanation:

2×4=8

8×2/3

8×2=16

16×3=48

ans = 48

Translation is a rigid transformation. As such, it preserves sizes and angles. Isometric is an alternative way to say the size is preserved. Hence; B, C and E are the correct choices.

A triangle is a three-sided polygon. A closed shape consisting of three straight lines and three corners. The sum of the three angles of a triangle is always 180 degrees. Triangles come in a variety of shapes and sizes and can be classified according to their angles and sides. The most common type of triangle is the right triangle, which has 90 degree angles.

Translation is the transformation that happens when we move the image without changing anything in it. Therefore, the shape, size, and orientation remain the same.

In this case the triangle ABC has been transformed to A'B'C'. This means that the triangle has been moved in one direction to form a new triangle A'B'C' without changing its size or orientation. This is an example of translation transformation.

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The complete question is follows:

Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply

A. It is non rigid

B. The size is preserved

C. It is rigid

D. The angles are not preserved

E. It is isometric

Answer:

The largest integer is 29.

Step-by-step explanation:

Let the consecutive positive integers are x, x+1 and x+2.

The square of sum of squares of three consecutive positive integers is 2354 such that,

[tex]x^2+(x+1)^2+(x+2)^2=2354\\\\x^2+x^2+2x+1+x^2+4+4x=2354\\\\3x^2+6x+5=2354\\\\3x^2+6x- 2349=0[/tex]

It is a quadratic equation whose solution is given by :

x = 27 and x = -29

First positive integer = 27

Second positive integer = 27+1 = 28

Third positive integer = 27+2 = 29

Hence, the largest integer is 29.

The maximum height reached by the ball is 20 units at 1.2 unit time.

The extrema of a function are the maxima and minima. The highest and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, throughout its full range.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

The equation is given as

h = [tex]-10t\x^{2} + 24t + 5.6[/tex]

Differentiating both side with respect to t we get

[tex]\frac{dh}{dt} = -20t + 24[/tex]

To reach maximum value [tex]\frac{dh}{dt} = 0[/tex]

⇒20t = 24

⇒ t = 1.2

So the maximum height reached = [tex]-10 *(1.2)\x^{2} + 24*1.2 + 5.6 = 20[/tex]

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Answer: x=136 degrees

Step-by-step explanation: All 3 angles inside a triangle added together will get you 180 degrees. 46+90 degrees is 136. 180-136=44 degrees. Now a line is 180 degrees too. 180-44=136 degrees for x.

2x 11 is congruent to 13 mod 16, if 3x 7 is congruent to 2 mod 16.

If 3x 7 is congruent to 2 mod 16, then 2x 11 is congruent mod 16 to what integer between 0 and 15, is inclusive.

To find the solution of 2x 11 congruent mod 16, given 3x 7 congruent to 2 mod 16, we can first use the given equation to find the value of x and then substitute it into the second equation.

First, we can solve for x in the given equation:

3x 7 is congruent to 2 mod 16

3x is congruent to 2 mod 16

x is congruent to 6 mod 16

Now that we know that x is congruent to 6 mod 16, we can substitute it into the second equation:

2x 11 is congruent to 2(6) 11 which is congruent to 13 mod 16

So the solution is that 2x 11 is congruent to 13 mod 16.

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