circles with centers at o and p have radii 2 and 4, respectively, and are externally tangent. points a and b on the circle with center o and points c and d on the circle with center p are such that ad and bc are common external tangents to the circles. what is the area of the concave hexagon aobcpd?

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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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

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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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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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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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 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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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 )

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.

-(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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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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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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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:

2.4%

Step-by-step explanation:

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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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

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:

if m stands for number of tickets

then amount would be

12+2.75*m

14.75m

Step-by-step explanation:

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.

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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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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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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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

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:

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