The length of a rectangle exceeds the breadth by 8 cm. Find the area of the rectangle, if its perimeter is 180 cm

Yes, rectangles and squares are similar polygons.

Similar polygons are two or more polygons with the same shape but different sizes. This means that the sides of the polygons are proportional, and the angles are congruent. The formula to determine if two polygons are similar is A/a = B/b = C/c = D/d = …, where A, B, C, and D are the sides of one polygon and a, b, c, and d are the sides of the other polygon. For instance, if a rectangle has sides of 4 and 8, and a square has sides of 6 and 6, the ratio of the sides of the rectangle to the sides of the square is 4/6 = 8/6. This means that the two shapes are similar.

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The 4 types of triangle with respect to angle measurement :

Acute Triangle

Obtuse Triangle

Right triangle

Equivalent triangle

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.

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There are four different triangles for measuring angles:

sharp triangle

Sharp triangle

correct triangle

comparable triangle

If all three sides of a triangle are the same length, the triangle is equilateral. Equiangular triangles are equilateral triangles in well-known Euclidean geometry. His three internal angles, which are all 60 degrees, are therefore consistent with one another.

An acute triangle is a triangle having three acute angles. Obtuse triangles are those with one obtuse angle and two acute angles. Euclidean geometry mandates that the total of all the angles of a triangle be 180°, hence a triangle cannot have more than one obtuse angle.

A right triangle, also known as a right triangle, right triangle, right triangle, right triangle, right triangle, or formerly right triangle, is a triangle with one or two right sides. The basis of trigonometry is the relationship between the sides of a right triangle and different angles.

An obtuse or obtuse triangle is a triangle with one of its angles obtuse or greater than 90°. An acute triangle has only 180° interior angles.

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Answer:

9/4

Step-by-step explanation:

Use the process of elimination. Divide each number's numerator by its denominator; if the outcome repeats itself, it isn't a terminating decimal. Therefore, when you divide 9/4, it equals 2.25, which is a terminating decimal.

A quadrilateral is a four-sided shape. The perimeter of a quadrilateral is the sum of all its sides. If the perimeter of a quadrilateral is 54 cm, and we know that all four sides are equal, we can divide 54 by 4 to find the length of each side.

54 cm / 4 = 13.5 cmTherefore, the length of each side of the quadrilateral is 13.5 cm.

It's important to note that this is only one possibility, since quadrilaterals can have different shapes and different side lengths.

Answer:

(-3,5)

Step-by-step explanation:

8x+3(23+6x)=-9

x=-3

y=23+6x(-3)

y=5

(-3,5)

A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions is not true.

Linear equations are equations that graph as a line, while the quadratic equations are that graph as a parabola. Lines and parabolas in the xy-plane are convenient representations of linear and quadratic systems, respectively. One solution to the system is shown by each point where the line and parabola intersect. It is possible for a line and a parabola to intersect zero, one, or two times. This indicates that a linear and quadratic system may have zero, one, or two solutions.

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The correct measure of center to determine which shop typically sells the most amount of coffee per hour will be C. Coffee Ground, with a mean value of about 5 gallons.

The mean is calculated by adding all the data points together and dividing by the number of data points.

When comparing the mean values of the two shops, Coffee Ground has a higher value of 5 gallons compared to Wide Awake's mean value of about 4.5 gallons. This indicates that Coffee Ground typically sells more coffee per hour on average.

The correct option is C.

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The area of the triangle is 54 square centimetres, which is calculated by multiplying the base (12 cm) and height (9 cm) and dividing by 2.

A = (12 cm * 9 cm) / 2

A = (108 cm²) / 2

A = 54 cm²

The area of a triangle is calculated by multiplying the base of the triangle and its height, and then dividing the result by 2. To calculate the area of the triangle with a base of 12 cm and a height of 9 cm, first the base and height must be multiplied together. 12 cm multiplied by 9 cm equals 108 cm². Then, the result of the multiplication, 108 cm², must be divided by 2. 108 cm² divided by 2 equals 54 cm². Therefore, the area of the triangle is 54 cm². To summarize, the area of a triangle is found by multiplying the base and height of the triangle, and then dividing the result by 2. In this case, the area of the triangle with a base of 12 cm and a height of 9 cm is 54 cm².

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3/4 divided by 2 in the fraction is equal to 3/8.

A fraction is used to represent the portion of the whole quantity. Also, we know that every integer is a rational number and any whole number can be written in the form of n/1, where n is any whole number.

On the given data, we need to use the concept of the division of fractions.

3/4 ÷ 2

=3/4 × 1/2 [ Reciprocal of 2 is 1/2]

=3/8

Therefore, 3/4 divided by 2 in the fraction is equal to 3/8.

Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form: 3/8=0.375

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The 4 physical properties of solutions are:

1) Concentration

2) Solubility

3) Viscosity

4) Transparency

In chemistry, a solution is a homogeneous mixture of two or more substances. The four common physical properties of solutions are:

1) Concentration: The amount of solute present in a given amount of solvent, typically measured in molarity, molality, or mass percentage.

2) Solubility: The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature and pressure.

3) Viscosity: The resistance of a fluid to flow, which can be affected by the presence of a solute.

4) Transparency or Opacity: The property of a solution by which it allows light to pass through it or not.

These are the 4 common physical properties of solutions, but there are many other physical properties that can be used to describe solutions depending on the context.

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Answer: a. In this situation, 0 likely represents sea level or the baseline from which water levels are measured.

b. To find the average water level relative to high tide, you need to take the average of high tide and low tide.

Since high tide is 5 feet higher than low tide, you can assume that low tide is 0 ft. Therefore, the high tide is 5 ft.

The average of two values is the sum of the values divided by the number of values. So average of 0ft and 5ft is (0+5)ft / 2 = 2.5 ft.

Therefore, an integer that represents the average water level relative to high tide would be 2.5 ft.

It's worth noting that relative to high tide means how much the average water level varies (higher or lower) from the high tide, so the answer was not an integer in this case.

The fraction of Jon original pay is 4/10

Jon earns  £90  one week

The following week he earns  £130

His pay rise is

130-90

= 40

The fraction of his original pay is

= 40/100

= 4/10

Hence the fraction of Jon original pay is 4/10

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Claire's current account balance would be -$50.

The amount that Clare has in his bank account initially = $150

The amount that he used from his bank account to buy the bike =  $200

As we can see that the amount that Clare used to buy the bike is more than the amount that he has in his account, therefore his account balance becomes negative, that is:

$150 - $200 = -$50

Here, it means that Clare has to pay the bank the amount of $50 that he used more than the amount that he had in his account.

Therefore, Claire's account balance would be -$50.

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Cells share many cοmmon features, yet they can look wildly different. In fact, cells have adapted οver billions of years to a wide array of environments and functional rοles.

The lοwest common element of life is a cell. Some cells function as independent entities, while οthers are a component of multicellular οrganisms.

Nucleic acids, prteins, carbohydrates, and lipids make up the four main types of οrganic molecules that all οrganisms are composed of. In part because they arrive in distinct, distinguishable packets, cells are regarded as the fundamental building blοcks of life.

The reasοn for this is that, like a hοuse's walls, the cell membrane that surrounds every cell acts as a definite border between its interiοr and exterior envirοnments. The plasma membrane is anοther name for the cell membrane. Phοspholipids are a framework οf fat-based molecules that serve as the fοundation of cell membranes.

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The total playground area is 280 square meter, if the dome cover an area of 1+2/3 = 5/3 square meter.

The area covered by the dome = 5/3 square meter

The area covered by the dome is 5/840 times of the total playground area.

Let the total area of the playground = A

5/3 = 5/840 × A

A = (5 × 840)/(3 × 5)

A = 280 square meter

--The given question is incomplete, the complete question is " Ben like to go in the covered dome, when he feels overexcited. The dome covers an area of 5/3 square meter, which is 5/840 of the total playground area. What is the total playground's area?"--

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The number of images that will be formed when two mirrors are positioned at an angle of 45 degrees is 7.

The formula that you have provided for calculating the number of images formed by two mirrors positioned at a specific angle is (360/n) - 1, where n is the angle between the mirrors in degrees.

When two mirrors are positioned at an angle of 45 degrees, n = 45. So, using the formula, the number of images formed would be: (360/45) -1 = 8 - 1= 7

It's important to note that this formula only gives you the approximate number of images that will be formed. In reality, due to the nature of light and the reflective properties of mirrors, it is impossible to determine the exact number of images that will be formed.

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The equation of the line perpendicular to the line A is given by the

x-4y +29=0

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a  Line A pass through the point (1,5) and (5,7).

Find the equation of the line perpendicular to A that pae through point (-1,7)

line A is y= 1/4 x+c

x-4y +4c=0

it passes through ( -1,7)

c= 29/4

equation becomes x-4y +29=0

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Answer:

I don't care for the points

Step-by-step explanation:

The answer is the last one

Answer:

See below

Step-by-step explanation:

I'm guessing this is what you're looking for:

[tex]45^2=(40+5)^2=(40+5)(40+5)=40(40)+2(40)(5)+5(5)=1600+400+25=2025[/tex]

The volume of the biggest possible cube inside the right cylinder is approximately 1193.243 cubic centimeters.

Cubes are hexahedrons with one same side length and only right angles. In this case, the cube is constrained by cross area of right cylinder in accordance to image attached below. The maximum possible volume for a cube inside the cylinder is described by following expression:

V = (√2 / 2)³ · R³

Where:

If we know that R = 15 cm, then the volume of biggest possible cube is:

V = (√2 / 2)³ · (15 cm)³

V ≈ 1193.243 cm³

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the other equation is missing, the solution cannot be found.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of an ounce per second.

Rate= 1/3 ounce milkshake per second

Initial = 20 ounces

Lin's condition is thus represented by the equation:

[tex]y = \frac{1}{3} x +20[/tex]

Since the other equation is missing, the solution cannot be found.

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By evaluating the quadratic equation we can get some points, and with them we can estimate the graph.

The graph can be seen in the image at the end.

Here we want to graph the function:

y = x^2 + 2x - 2

To do so, we can evaluate the quadratic equation in some values of x to get points, and then just connect the points with a general parabola.

when x = 0

y = 0^2 + 2*0 - 2 = -2

So the point is (0, -2)

when x = 1

y = 1^2 + 2*1 - 2 = 1 + 2 - 2 = 1

So the point is (1, 1)

when x = -1

y = (-1)^2 + 2*(-1) - 2

y = 1 - 2-  2 = -3

So the point is (-1, -3)

when x = -2

y = (-2)^2 + 2*(-2) - 2

y = 4 - 4 - 2 = -2

So we have the point (-2, -2)

And so on..., eventually, you will get enough points to connect, and you should get something like:

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Answer:

the answer is 45°

Step-by-step explanation:

because they mirror eachother

Answer:

Step-by-step explanation:

I'm not sure but I think that is 45

Answer:

25 :)

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

given the system of equations

x + 3y = 76 → (1)

x + y = 36 → (2)

1

subtracting (2) from (1) term by term will eliminate x

(x - x) + (3y - y) = 76 - 36

0 + 2y = 40

2y = 40 ( divide both sides by 2 )

y = 20

3

substitute y = 20 into either of the 2 equations and solve for x

substituting into (2)

x + 20 = 36 ( subtract 20 from both sides )

x = 16

4

that is 16 students bought orange juice and 20 bought a sandwich

As a check

substitute the values for x and y into the equations and if both sides are equal then they are the solution

(1) :  16 + 3(20) = 16 + 60 = 76 ← True

(2) : 16 + 20 = 36 ← True

since both equations are true, then

x = 16 and y = 20 are the solutions to the system

Step-by-step explanation:

1.y = x * (1-0.4)

2.y = x - 0.4x

3.x = y / (1-0.4)

4.x = y + 0.4y

The equation 1 and 2 correctly represent the situation. In the first equation, we are multiplying the initial amount of water (x) with (1-0.4) which is the percentage of the water that is remaining after drinking 40% of it. In the second equation, we are subtracting 0.4x from x, which is equivalent to multiplying x by (1-0.4).

The equation 3 and 4 are not correct, as they are trying to calculate the initial amount of water from the remaining amount, but it's not possible to know the initial amount once it has been consumed.

You have 0.6X amount water remaining.

The amount of water remaining in the water bottle is X minus 40%. This means that if you had X amount of water at start you now have 60% of X left.  That is, you have 0.6X amount of water remaining.

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The equation written is: x + 18 + x = 84

The lengths of each piece of the cable are: 33 meters and 51 meters.

To write an equation, let the unknown quantity be represented as a variable, which would be used in creating an algebraic expression.

For example, we are given the following:

Length of a cable = 84 meters

The length of one the pieces that the cable is cut into is represented as x.

The second pieces = x + 18 meters.

The equation that would be created for this problem would be:

x + 18 + x = 84

Solve for x:

2x + 18 = 84

2x = 84 - 18

2x = 66

2x/2 = 66/2

x = 33

The length of one of the pieces = 33 meters

Length of the second piece = x + 18 = 33 + 18 = 51 meters.

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Using the cosine rule calculate the magnitude of angle B when did the b=20.8cm c= 14.5cm and a= 9.3cm is [tex]\approx 37.02364^{\circ}[/tex]

​

Given,

b=20.8cm c= 14.5cm and a= 9.3cm

[tex]\gamma=\cos ^{-1}\left(\frac{a^2+b^2-c^2}{2 a b}\right)[/tex]

[tex]=\cos ^{-1}\left(\frac{9.3^2+20.8^2-14.5^2}{2 \cdot 9.3 \cdot 20.8}\right)[/tex]

[tex]\approx 37.02364^{\circ}[/tex]

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The option that describes the center and variability of simulation A and simulation B is The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B. The correct answer is C.

Considering the details provided in the query,

The two simulations will be run with sampling proportions from a population with a true percentage of 0.325.

Simulacrum A:

100 samples were used.

Tests: 1500

Exercise B -

50 samples total.

2000 trials

Due to the relationship between simulations A and B, they are now nearly equal.

1500 x 100 is the overall sample size for Simulation A.

= 150000

The simulation B sample size is 2000 x 50.

= 100000

We can observe from the simulations A and B calculations above that when comparing the,

Sample Size = Comparison of Simulations A and B

Simulation B + Simulation = Variability

Your question is incomplete but most probably your full question was

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

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David's annual gross pay is $2 730.00 * 12 = $32 760.00.

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