A chord of the circle with centre O and radiu 10 cm, ubtend an angle
of 120° at the centre of the circle. Find the area of the major ector and
the area of minor egment. (Ue = 3. 14 √3 = 1. 732

The pair of equations y = 0 and y = -5 has no solutions.

The pair of equations y = 0 and y = -5 can be written as:

y = 0

y = -5

Since both equations have the same value of y, 0 and -5, the equations are not equal and therefore there is no solution.

The pair of equations y = 0 and y = -5 have no solutions. This is because the equations have the same value of y, 0 and -5, which means that the equations are not equal. Therefore, there is no solution to this pair of equations. To determine if the pair of equations has a solution, you must check to see if the equations are equal. If the equations are not equal, then there is no solution. In this case, the equations are not equal, and thus there is no solution.

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The value of the SW is 12 units.

What is a chord in a circle?

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle that passes through the center of the circle.

Since we want to find SW to get SV, we can change SW to x.

We already know the other lengths:

ST = 3

SU = 18

SW=x

SV=x-3

So, 3(18)=x(x-3).

From here, we see that when expanded, this becomes 54 = x² - 3x.

Solving the quadratic, we see that SW is 12, therefore SV is 9.

Hence, the value of the SW is 12 units.

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complete question: Let TU and VW be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.

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:

-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.

Answer:

(6, 2 )

Step-by-step explanation:

3x - 2y = 14 → (1)

5x + 6y = 42 → (2)

multiply (1) through by - 1

- 3x + 2y = - 14 ( add 3x to both sides )

2y = 3x - 14

substitute 2y = 3x - 14 into (2)

5x + 3(2y) = 42

5x + 3(3x - 14) = 42

5x + 9x - 42 = 42

14x - 42 = 42 ( add 42 to both sides )

14x = 84 ( divide both sides by 14 )

x = 6

substitute x = 6 into either of the 2 equations and solve for y

substituting into (2)

5(6) + 6y = 42

30 + 6y = 42 ( subtract 30 from both sides )

6y = 12 ( divide both sides by 6 )

y = 2

solution is (6, 2 )

The sum of the series:

1 - 2/3 + 4/9 - 8/27+16/81 - 32/243 + .... = 2/3

All geometric sequences have a starting term a and a common ratio r.

The common ratio r is the number that the terms of the sequence are multiplied to find the next term, hence the name "ratio". All terms in the sequence are the same, hence the name "common".

The common ratios here are the numbers multiplied by 2/3 to get −4/9

and the numbers multiplied by−4/9 to get 8/27.

2/3⋅ 2/3 = [tex]\frac{2*2}{3*3 }[/tex]  = 4/9 .

2/3 × (-2/3) = -4/9

The infinite sum of the geometric series can only be found in a specific case: r lies between −1 and 1.

When r is between these values, adding the series will converge - close on both sides - to a certain number.

Otherwise the sum diverges - further apart - i.e. there is no specific value that the series approaches. is in This means that an infinite series can be computed as the number to which the series converges.

This calculation is done using the formula

S∞ = a₁ − r.

a, the first term of the sequence is 2/3.

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A polynomial with the given zeros can be written as:

P(x) = x^3 - 6x^2 - 27x

If we have a polynomial of degree N with the given N zeros:

{x₁, x₂, ..., xₙ}

Then we can write that polynomial as:

P(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)

In this case we know that the degree is 3, and the zeros are:

{-3, 0, 9}

Then we can write that polynomial as:

P(x) = (x + 3)*(x - 0)*(x - 9)

Expanding that we will get:

P(x) = (x^2 + 3x)*(x - 9)

P(x) = x^3 + 3x^2 - 9x^2 - 27x

P(x) = x^3 - 6x^2 - 27x

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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

A graph of the image of the given triangle, rotated 270° about the origin is shown in the image attached below.

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).

By applying a rotation of 270° about the origin to the given triangle, the location of P" is given by:

(x, y)                                   →         (y, -x)

Ordered pair A (3, 2)        →    Ordered pair A' (2 -(3)) =  (2, -3).

Ordered pair B (-2, -6)      →    Ordered pair B' (-6, -(-2)) = (-6, 2).

Ordered pair C (10, -8)     →     Ordered pair C' (-8, -(10) = (-8, -10).

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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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-(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:

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.

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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The absolute value is used to represent the magnitude of a number, regardless of its sign.

The absolute value is commonly used in mathematical equations, particularly in situations where the sign of a number does not carry any significance or when a distance or a difference is being measured.

For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. This is useful when working with negative numbers in calculations, as the absolute value allows them to be treated as positive numbers. Additionally, it is used to define the distance between two points on a number line.

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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

Answer:

2.4%

Step-by-step explanation:

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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The squares represent a visual representation of equivalent fractions. Each square is divided into a certain number of equal parts, and the number of parts that are shaded in represents the numerator of the fraction. The total number of parts the square is divided into represents the denominator of the fraction.

In the first square, it is divided into 23 equal parts and 8 of them are shaded in. Therefore, the fraction represented by that square is 8/23.

In the second square, it is divided into 812 equal parts and 23 of them are shaded in. Therefore, the fraction represented by that square is 23/812. Since both squares are divided into the same number of equal parts, the fractions 8/23 and 23/812 represent the same quantity, just in different forms. Therefore, they are equivalent fractions.

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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:

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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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.

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

Check the picture below.

[tex]\tan(37^o )=\cfrac{\stackrel{opposite}{49}}{\underset{adjacent}{DB}}\implies DB=\cfrac{49}{\tan(37^o )} \\\\\\ \sin(56^o )=\cfrac{\stackrel{opposite}{DB}}{\underset{hypotenuse}{AD}}\implies AD=\cfrac{DB}{\sin(56^o )} \\\\\\ AD=\cfrac{ ~~ \frac{49}{\tan(37^o )} ~~ }{\sin(56^o )}\implies AD=\cfrac{49}{\tan(37^o ) \sin(56^o )}\implies AD\approx 78.43[/tex]

Make sure your calculator is in Degree mode.

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

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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You are designing a 5 kilometer course for charity run. The design now has been covers 4,908.5 meters, hence, you need to add more 91.5 meters on the course.

The conversion from yard to meter is:

1 yard = 0.9144 meters

The course streets and the distances after converted into meters are:

main street to 6th ave.  781 yards = 714.15 meters

6th ave. to pleasant road 1,250 yards = 1143 meters.

pleasant road to city park 275 yards = 251.46 meters

route through city park 2,337 yards = 2,136.95 meters

city park to main street 725 yards = 662.94 meters

Total course = 714.15 + 1143 + 251.46 +  2,136.95 +  662.94

Total course = 4,908.5 meters

The design is 5 km = 5000 meters. Therefore, you still need to add:

5000 - 4,908.5 = 91.5 meters more course.

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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 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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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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