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The number of sides of the regular polygon with the sum of interior angles  900 degrees is equal to 7 .

As given in the question,

Sum of the interior angles of any regular polygon is equal to 900 degrees.

Let us consider 'n' represents the number of sides of the regular polygon.

Relation between number of sides with the sum of the interior angles in the regular polygon is given by :

( n - 2 ) × 180° = Sum of the measure of interior angles of regular polygon

⇒ ( n - 2 ) × 180° = 900°

Divide both the sides by 180°

⇒ ( n - 2 ) = 900° /180°

⇒ ( n - 2 ) = 5

⇒ n = 5 + 2

⇒n = 7 sides

Therefore, the number of sides of the regular polygon whose sum of interior angles 900 degrees is equal to 7 sides.

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Answer:

x = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{16}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 16[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 8[tex]\sqrt{3}[/tex]

Answer:

Step-by-step explanation:

?

In this problem, x stands for the original quantity. To solve the problem, we can use algebra to rearrange the equation.

2x + 2x/3 = 19

Multiply each side by 3

6x + 2x = 57

Subtract 2x from each side

4x = 57

Divide each side by 4

x = 14.25

Therefore, x stands for 14.25, which is the original quantity.

Step-by-step explanation:

the other answer started correctly and then did a strange (to put it mildly) and wrong turn.

that is why I have to add my answer :

2x + 2x/3 = 19

yes, we need to multiply both sides by 3 to get rid of the fraction :

6x + 2x = 57

now we add terms of the same base and get

8x = 57

x = 57/8 = 7.125

Answer:

Step-by-step explanation:

1.The square root function is a mathematical function that returns the positive number that, when multiplied by itself, gives the original number. It can be represented using the symbol √ or using the exponent 1/2. The cube root function is a mathematical function that returns the number that, when multiplied by itself three times, gives the original number. It can be represented using the symbol ∛ or using the exponent 1/3.

2.The ancient civilizations of Babylonia, Greece, and India all independently discovered the square root function. The concept of cube root was first mentioned in the ancient Indian text "Sulbasutras" around 800 BCE. The Greek mathematician Euclid also described the cube root function in his work "Elements" around 300 BCE.

3.The square root function is used in many areas of mathematics and science, including geometry, trigonometry, and physics. In real life, square root functions are used in many areas such as engineering, architecture, and finance. For example, in engineering, square root functions are used to calculate the stress and strain on materials. In architecture, square root functions are used to calculate the area of a building or room. In finance, square root functions are used to calculate the volatility of an asset. Similarly, cube root function is used in mathematics, physics, engineering, economics, and other fields. It is used to find the cube root of a number, to find the volume of a cube, to solve equations, and to calculate the cube root of a complex number.

Three-degree polynomials have 3 roots. Three-degree polynomials are called cubic polynomials.

Any cubic equation having a degree three has 3 roots. Just like linear polynomials have only one root which has only one degree and a polynomial of degree two is known as a quadratic polynomial. A Quadratic polynomial has two roots. The degree of zero polynomial is not defined. The degree of a non-zero constant polynomial is zero. Non-zero constant polynomials are represented in the equation as a constant real number.

A cubic polynomial can be represented as:

[tex]ax^3+bx^2+c[/tex]

We can find the roots of a quadratic polynomial using splitting the middle term and the Quadratic formula.

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Answer:

if m stands for number of tickets

then amount would be

12+2.75*m

14.75m

Step-by-step explanation:

The answer to the question is 90.

The sum of the five products x1x2x3 x2x3x4 x3x4x5 x4x5x1 x5x1x2 is divisible by 3 if and only if the sum of the exponents of each of the numbers 1, 2, 3, 4, and 5 in the expression is divisible by 3.

Since there are 5 numbers, and each number can appear in the exponent of each of the 5 products, there are 5^5 = 3125 ways to arrange the numbers. However, we need to subtract the cases where the exponents of each number don't add up to a multiple of 3.

For example, if the exponents of 1, 2, 3, 4, and 5 are (1, 1, 1, 1, 1), the sum of the exponents is 5, which is not divisible by 3. Similarly, if the exponents are (2, 1, 1, 1, 1), the sum of the exponents is 6, which is not divisible by 3.

After calculating this, we get that there are only 90 permutations that meet the condition. So the answer to the question is 90.

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-(24/5)x(1/2)  is the final result of the integral, tells us  that the integral of 4xy(x^2 + y^2) upon  the specified rectangular domain is explained as:

The given integral is in the form of  an iterated integral, which is known as  we need to integrate with respect to x first, and then integrate the resulting expression with respect to y.

The integral with respect to x is:

∫(4xy)(x^2 + y^2)dx from x=3 to x=0

This can be evaluated as shown below:

(2/5)(4xy)(x^3 + 3xy^2) evaluated at x=0 and x=3

= (2/5)(4xy)(0^3 + 30^2y^2) - (2/5)(4xy)(3^3 + 33^2y^2)

= 0 - (2/5)(4xy)(27 + 27y^2)

= -(24/5)xy(1 + y^2)

The integral with respect to y is:

∫( -(24/5)xy(1 + y^2)) dy from y=0 to y=1

This can be evaluated as shown below:

-(24/5)x(1/2)y^2(1+y^2) evaluated at y=0 and y=1

= -(24/5)x(1/2)1^2(1+1^2) - -(24/5)x(1/2)0^2(1+0^2)

= -(24/5)x(1/2)

hence  the final result of the iterated integral is:

-(24/5)x(1/2)

therefore it  is the final result of the integral, indicating that the integral of 4xy(x^2 + y^2) over the specified rectangular domain is -(24/5)x(1/2).

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Answer:

The 6th one is x=70 and <BCX=145

The equation represents the function on the graph is f(x)= cos 4x.

What is the function on the graph?

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.

We have given,

A: f(x)= cos 1/4x

B: f(x)= sin 4x

C: f(x)= cos 4x

D: f(x)= sin 1/4x

To find the equation represent the function on the graph:

f(x) = cos 4x

let take the values on the x-axis of the graph,

x = п/2, п, 3п/2, 2п, 5п/2

For cos 360 degrees, the angle 360° lies on the positive x-axis. Thus cos 360° value = 1

Since the cosine function is a periodic function, we can represent cos 360° as, cos 360 degrees = cos(360° + n × 360°), n ∈ Z.

⇒ cos 360° = cos 720° = cos 1080°, and so on.

so, cos 4( п/2) = cos 4( 3п/2) = cos 4( 2п) = cos 4( 5п/2) = 1.

Hence, the equation represents the function on the graph is f(x)= cos 4x.

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

30.22 minutes taken to cover the distance.

Speed at a distance is a measure of how swiftly something is moving. A moving object's speed determines how far it travels in a given amount of time. Speed is determined by the formula: speed = distance x  time. Meters every second (m/s), kilometers / hour (km/h), and kilometres per second (mph) are the most often used units for measuring speed (mph).

Here,

Similar to part b, but with the knowledge of the cruise distance and the necessity to solve for time, maximum cruising time is achieved.

1) Accelerating: 13.2 seconds, d = 871.2 feet.

2) Deceleration: 13.2 seconds, d = 871.2 feet.

3) When cruising: d = 45 miles - 871.2 feet - 871.2 feet = 237600 feet - 1742.4 feet = 235857.6 feet

t = 235857.6/132 = 1786.8s

Total: 1786.8 + 13.2 + 13.2 = 1813.2 seconds, or 30.22 minutes.

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

30.22 minutes taken to cover the distance.

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Answer:

-4a²b

5a²b

Step-by-step explanation:

A monomial is a polynomial that has one term only but can have multiple variables.

Given monomial:

[tex]-20a^4b^2[/tex]

The coefficient of the given monomial is -20.

Therefore, we need to find two numbers that multiply to -20 and sum to 1.

Factors of -20:

Therefore, the two numbers that multiply to -20 and sum to 1 are:

Rewrite -20 as the product of -4 and 5:

[tex]\implies -4 \cdot 5 \cdot a^4b^2[/tex]

Rewrite the exponents as sums of equal numbers:

[tex]\implies -4 \cdot 5 \cdot a^{2+2} \cdot b^{1+1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]

[tex]\implies -4 \cdot 5 \cdot a^2 \cdot a^2\cdot b^{1}\cdot b^{1}[/tex]

Rearrange as the product of two monomials with the same variables:

[tex]\implies -4a^2 b^{1}\cdot 5 a^2 b^{1}[/tex]

[tex]\implies -4a^2 b\cdot 5 a^2 b[/tex]

Therefore, the two monomials whose product equals -20a⁴b², and whose sum is a monomial with a coefficient of 1 are:

Check the sum of the two found monomials:

[tex]\begin{aligned}\implies -4a^2b+5a^2b&=(-4+5)a^2b\\&=(1)a^2b\\&=a^2b\end{aligned}[/tex]

Thus proving that the sum of the monomials has a coefficient of 1.

The measure of angle MQS is 18°.

In mathematics, angles are typically measured in degrees or radians.

An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of an angle, and the endpoint is called the vertex.

There are different types of angles:

Acute angle: an angle measuring between 0 and 90 degrees.

Right angle: an angle measuring exactly 90 degrees.

Obtuse angle: an angle measuring between 90 and 180 degrees.

Straight angle: an angle measuring exactly 180 degrees.

Reflex angle: an angle measuring between 180 and 360 degrees.

Draw QT  and QS

Angles TQP, SQT, and  SQR  will trisect the interior angle PQR

And PQR  = 108

So  ...angle  SQT  = 108 / 3   = 36

But...by symmetry....angle XQS  =  (1/2)angle SQT  = (1/2)36  = 18°

Therefore, The measure of angle MQS is 18°.

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Answer:

Step-by-step explanation:

all internal angles in a triangle add to 180 degrees.

77+36=113

180-113=67

we know that the final angle in the triangle is 67 degrees

the left parallel line makes another triangle in the bottom left. we know that one angle is 41 and we just calculated that the other is 67.

41+67=108

180-108=72

so now we know that the small triangle in the bottom left has angles of 41,67 and 72.

all straight lines are 180 degrees, and we just figures out that the left side of the left parallel line is 72 degrees. therefore the other side is 108 degrees.

since they are parallel lines, the left angle of both of them on the bottom line is 72, while the right angle is 108.

this means that x=108 degrees

i hope this is right and it helps if it is correct. really sorry if it is wrong. have a good day :)

Answer:

£2.50+5b>21

Step-by-step explanation:

this is because a bag is b and they cost £5 so therefore it's 5b then they have to be under 21 pounds so you use the less than symbol.

The solid figure that has the given net is C.rectangular prism.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Six faces, eight vertices (or corners), and twelve edges to up a rectangular prism. We would require either 12 edge pieces and 8 corner pieces to create the rectangular prism's frame or 6 rectangles that connect at the edges to form a closed three-dimensional shape.

Therefore, option C is correct.

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missing options:

square pyramid

cube

rectangular prism

square prism

By parallelogram opposite angles converse, the given quadrilateral is a parallelogram.

What is quadrilateral?

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. Four non-collinear points are connected to form it. A quadrilateral's interior angles add up to 360 degrees in all cases.

There are four closed sides to a quadrilateral. These shapes below are quadrilaterals: a four-sided shape. One set of parallel sides make up the shape, and there are no right angles.

In given figure we can see that there is a quadrilateral given.

The opposite angles of quadrilateral are same.

Also the opposite sides of the quadrilateral are same.

It defines the properties of parallelogram.

Hence, by parallelogram opposite angles converse, the given quadrilateral is a parallelogram.

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The rule for the given pattern is to subtract 13, then add 24.

The correct Option is (A.) subtract 13, then add 24.

A pattern or sequence in a series of numbers is called a number pattern. In general, this pattern builds a connection between all integers.

In this question we have the following pattern:

1, -12, 12, -1

Here we need to find the rule for this pattern.

Let's take the first number of the pattern, which is 1:

1

To obtain the second number of the pattern, which is -12, we must subtract 13, because:

1 - 13 = -12

To obtain the third number of the pattern, which is 12, we must add 24, because:

-12 + 24 = 12

Therefore, the correct answer is A.) subtract 13, then add 24

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The complete question is: "Which best describes the rule for this pattern? 1,-12,12,-1 A.) subtract 13, then add 24 B.) subtract -13, then add 24 C.) subtract -24, then add 13 D.) subtract 24, then add 13"

The product of two matrices L and P is given as L × P = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex].

A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,
The product of matrices is only possible when the matrices have one of the matching orders with rows and columns.
Since among the given matrices, only matrix P and matrix L has the same order so,
[tex]L\times P = \left[\begin{array}{cc}2&-3\\1&2\end{array}\right]\times \left[\begin{array}{cc}0&0\\0&0\end{array}\right]\\L \times P = \left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

Thus, the product of two matrices L and P is given as L × P = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex].

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Answer: 3 ovals and 3 rectangles and an even amount of rectangles and ovals

The scale factor from the cliff in the drawing to the actual cliff is equal to 1/3.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (actual figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = 12/36

Scale factor = 1/3.

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Answer:

Step-by-step explanation:

36ft/12in

36 divided by 12 =3 feet per inch

There are 7 motorcycles and 4 cars in the parking lot

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the number of motorcycle and y represent the car. There could be a 2 wheel motorcycle or a 4 wheel car.

There are 11 vehicles in the parking lot, hence:

x + y = 11    (1)

There are 30 wheels, hence:

2x + 4y = 30    (2)

From both equations:

x = 7, y = 4

There are 7 motorcycles

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a) The cube-shaped sculpture has edges that are 4 ft long, so the volume of the sculpture is 4^3 = 64 ft^3. The density of the marble is 170 lb/ft^3, so the weight of the sculpture is 64 ft^3 * 170 lb/ft^3 = 10,880 lb.

Since the sculpture weighs more than 10,000 lb, the pedestal should not be able to support it. The sculpture would require a pedestal that can support more than 10,000 lb.

b) The density of the marble is determined by the mass of the marble per unit volume. If the sculpture was half the size, it would have half the volume, but the same mass. So, the density of the marble would not change.

To estimate the number of sticks of butter needed to fill an empty bathtub, we can use the Fermi process.

First, we need to find the volume of the bathtub. A rectangular prism has a length of 60 inches, a height of 40 inches and a width of 20 inches. So, the volume of the bathtub is 604020 = 48000 cubic inches.

Next, we need to find the volume of a stick of butter. A stick of butter has a length of 4 inches, a width of 2 inches, and a height of 2 inches, so the volume of a stick of butter is 422 = 16 cubic inches.

Finally, we can divide the volume of the bathtub by the volume of a stick of butter to find the number of sticks of butter needed to fill the bathtub:

48000/16 = 3000 sticks of butter.

We can estimate that it would take around 3000 sticks of butter to fill an empty bathtub with the given measurements.

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Line formed by joining the given points ( 1,3) and ( 2,1) divided in the ratio by the given equation of the line 3x + y = 9 is equal to 3 :2.

As given in the question,

Equation of the given line : 3x + y = 9 __(1)

Standard equation line formed by joining the two points :

( x₁ , y₁ ) = ( 1,3)

(x₂ , y₂) = ( 2,1 )

( y - y₁) / (y₂ -y₁ ) = ( x -x₁)/(x₂ - x₁ )

⇒(y - 3)/(1 - 3) = ( x -1)/(2 -1)

⇒(y -3)/-2 = (x -1)/1

⇒-2x +2 = y - 3

⇒ y + 2x = 5 __(2)

Subtract (2) from (1) we get,

3x + y = 9

2x + y = 5

x = 4

⇒y = -3

Point of intersection is ( 4, -3)

Distance between ( 4, -3) and ( 1,3) is:

= √ ( 4 -1)² + ( -3 -3 )²

= √9 + 36

= √45

= 3√5

Distance between ( 4, -3) and ( 2 ,1) is:

= √ ( 4 -2)² + ( -3 -1 )²

= √4 + 16

= √20

= 2√5

Required ratio to divide a line by given points is :

= 3√5 / 2√5

= 3/2

Therefore, the equation of the line 3x + y =9  divides the line formed by joining the given points in the ratio is 3:2.

The above question is incomplete, the complete question is:

In what ratio is the line joining the points (1,3) and (2,1 ) divided by the line 3x+y=9?

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Josh will cover a total distance of 38 kilometres while trekking in Glacier National Park, having already covered 17 km of the park's trails.

The idea that will be applied in this situation is the usage of models to simplify expression.

Josh was able to hike 17 km, and since this is 2 km short of being halfway done, we can create the equation that models the situation.

The model can be written as  [17 + 2 = (1/2)h ]

h =length of the hike.

then  we can substitute the values so that we can know the value of h,

[17 + 2 = (1/2)h ]

[19 =0.5h]

h = 38 km

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The properly written question:

Josh is hiking Glacier National Park. He has now hiked a total of 17 \text{ km}17 km17, space, k, m and is 2 \text{ km}2 km2, space, k, m short of being \dfrac12 ​2 ​ ​1 ​​ start fraction, 1, divided by, 2, end fraction of the way done with his hike.

The required time for Cormac to catch Leif is, 2.85 minute

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

Given that,

Cormac runs at a speed = 105 m/minute

Leif runs at a speed = 65 m/minute

Leif is 100 m away from the Cormac,

So, total distance covered by Leif =  100 + Distance covered After Cormac started

Distance covered After Cormac started = 65t

Distance covered by Cormac =  100t

To catch Leif,

100t = 65t + 100

35t  =  100

   t  = 2.85 minute

Hence, the required time is 2.85 minute

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The fraction of the students that played the trumpet is 1/6

The school band has several students

1/4 play a brass instrument

2/3 of those students play the trumpet

Therefore the fraction of students that paly the trumpet can be calculated as follows

1/4 × 2/3

= 1/6

Hence the fraction of students that play the trumpet is 1/6

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Answer:

2.4%

Step-by-step explanation:

Answer:

6700

Step-by-step explanation:

6.7*10³ to ordinary form. You simply move the decimal point three steps back because it's positive and put zeros before the decimal point which you have moved