find the volume and surface area of three-dimensional shapes (examples: rectangular and right prisms, cylinders, right pyramids). find the side lengths, radius, or diameter of a three-dimensional figure when given the volume or surface area

Por lo tanto, hace 50 años que el Abuelo era 10 veces mayor que el Nieto.

Primero, definimos las edades en una ecuación.

Padre = 25

Hijo = 20

Abuelo = 4 × Nieto = 1

Para encontrar cuántos años han pasado desde que el Abuelo era 10 veces mayor que el Nieto, restamos 25-20=5 años desde que el Padre era 5 años mayor que el Hijo. Luego, multiplicamos esto por 10 para encontrar los años transcurridos desde que el Abuelo era 10 veces mayor que el Nieto. Entonces, 5 x 10 = 50 años. Por lo tanto, hace 50 años que el Abuelo era 10 veces mayor que el Nieto.

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The value of the equations are

a) A = ( x + 4 ) ( x - 4 )

b) B = ( x - 3 ) ( x² - 3x + 9 )

c) C = ( x + 6i ) ( x - 6i )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = x² - 16   be equation (1)

On simplifying the equation , we get

Taking the common factor of the equation , we get

A = ( x - 4 ) ( x + 4 )

On factorizing the equation , we get

A = ( x - 4 ) ( x + 4 )

b)

B = x³ + 27   be equation (2)

On simplifying the equation , we get

Taking the common factor of the equation , we get

B = ( x - 3 ) ( x² - 3x + 9 )

On factorizing the equation , we get

B = ( x - 3 ) ( x² - 3x + 9 )

c)

C = x² + 36   be equation (3)

On simplifying the equation , we get

Taking the common factor of the equation , we get

C = ( x + 6i ) ( x - 6i )

where i² = -1

On factorizing the equation , we get

C = ( x + 6i ) ( x - 6i )

Hence , the equations are solved

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Answer:

A. two table cloths

B. 24$

Step-by-step explanation:

First, develop your functions:

[tex]f(x)=3x+18\\g(x)=2x+20[/tex]

f(x) is the first company, g(x) is the second company.

A.

Set the two equations to be equal to each other and solve for x:

[tex]f(x)=g(x)\\3x+18=2x+20\\3x-2x=20-18\\x=2\\[/tex]

B.

Just plug in the value you got from A into either function:

[tex]f(2)=3(2)+18\\f(2)=24[/tex]

Answer:

F, M, J

Step-by-step explanation:

The slope of the line AB by joining the coordinates x and y is equal to 2.

Let the coordinates of the points A and B to form a line AB by joining them are:

A ( x₁ , y₁ ) = A ( x₁ = 50 , y₁ = 30 )

B ( x₂ , y₂ ) = B  ( x₂ = 60 , y₂ = 50 )

Slope of the line by joining two points is :

= ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value in the formula we get,

Slope of the line

= ( 50 - 30 ) / ( 60 - 50 )

= ( 20 ) / ( 10 )

= 2 / 1

= 2

Therefore, the slope of the function y and x for line AB by joining the coordinates of A and B  is equal to 2.

The given question is incomplete, I answer the question in general according to my knowledge:

If the point is at A ( x = 50 , y = 30 ) and point B is at ( x = 60 , y = 50 ) , what is the slope of the function described by y and x for line AB?

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The correct answer is option c. 50%;

50% of scores in a normal distribution are above the mean.

A normal distribution is symmetrical, which means that the mean, median, and mode are all equal and that the percentage of scores below the mean is equal to the percentage of scores above the mean.

For a normal distribution with a mean of 40, exactly half of the scores (50%) will be above the mean, and the other half (50%) will be below the mean. This is true for any normal distribution, regardless of the standard deviation or any other characteristic of the distribution.

In a normal distribution, the data is symmetrically distributed around the mean. This means that if the mean is represented by a line, the same number of data points will be on either side of the line.

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Answer:

the first expression is equivalent to this sum

Step-by-step explanation:

3(7+3)

3×7+3×3

21+9

30

Answer:

Van = 9

Bus = 58

Step-by-step explanation:

Based on the given,

School A = 2 Vans + 6 Busses = 366 Seniors

School B = 5 Vans + 4 Busses = 277 Seniors.

Question to answer:

How many students can a van carry?

How many students can a bus carry?

Solution:

Let's put it into equations.

Let,

x = Vans      [x represent the number of Vans]

y = Busses [y represent the number of Busses]

School A equation: 2x + 6y = 366

School B equation: 5x + 4y = 277

Now since we have the equations we can start solving;

2x + 6y = 366

5x + 4y = 277

Let's use substitution method.

Substitution method is basically substitute one equation to the other one.

Before we do that we have to get y by itself.

Thus,

5x + 4y = 277

5x - 5x + 4y = 277 - 5x [Subtract 5x and put it to the other side]

4y = -5x + 277

4y/4 = -5x/4 + 277/4 [Divide all side by 4]

y = -5/4x + 69.25

Now substitute it in:

2x + 6(5/4x + 69.25) = 366

-11 = -99

x = 9

Now we know that x = 9, we can use top or bottom equation and substitute to find x.

Or we can also use;

y = -5/4x + 69.25

y = -5/4(9) + 69.25

y = 58.

As a result,

A van can carry 9 students and a bus can carry 58 students.

To check answer:

2x + 6y = 366

2(9) + 6(58) = 366

18 + 348 = 366

366 = 366

5x + 4y = 277

5(9) + 4(58) = 277

45 + 232 = 277

277 = 277

RevyBreeze

Answer:

In this Equation x = 44.78  = 24 + 12root3

The values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

The concept of the integral is a fundamental part of calculus and it is used to calculate the area under a curve or the volume of a 3-dimensional object. In this context, we will be exploring the integral of a two-dimensional set in the R^2 plane.

For every two-dimensional set C contained in R^2 for which the integral exists, the function Q(C) is defined as the double integral of the function (x^2 + y^2) over the set C. The double integral is a mathematical tool for finding the total volume under a surface.

Let's consider the three sets C1, C2, and C3 and find Q(C1), Q(C2), and Q(C3).

C1={(x,y) : −1 ≤ x ≤ 1, −1 ≤ y ≤ 1}

Q(C1) = ∬C1 (x^2 + y^2) dxdy = ∫^1_{-1}∫^1_{-1} (x^2 + y^2) dxdy = ∫^1_{-1} [(x^2 + y^2)/2]^1_{-1} dx = 4.

C2 ={(x,y):−1≤x≤1,−1≤y≤1}

Q(C2) = Q(C1) = 4.

C3 = {(x,y):x^2 + y^2 ≤1}

Q(C3) = ∬C3 (x^2 + y^2) dxdy = π.

In conclusion, the values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

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Answer:

$352

Step-by-step explanation:

David Gave 1/5 of his money to charity

$2640 / 5 = $528

$2640 - $528 = $2112

1/3 of it to his mom

$2112 / 3 = $704

$2112 - $704 = $1408

He shared the rest of it among his 4 sisters equally

$1408 / 4 = $352

So, each of his sisters get $352

It as 2.24m far from the origin. The location in polar coordinates is 26.6°.

The fly is located at the point having coordinates (2.00, 1.00) m

Cartesian and Polar Coordinates:

In the Cartesian system the coordinates are perpendicular to one another with the same unit length on both axes. A Polar coordinate system is determined by a fixed point, a origin or pole, and a zero direction or axis. Each point is determined by an angle and a distance relative to the zero axis and the origin.

If the cartesian coordinates of a point is given (x,y), the polar coordinates r,θ is given by the following relation

Take the wall as the xy plane so that the coordinates are x=2.00m and y=1.00m; and the fly is located at point P.

The distance between two points in the xy plane is

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

⇒d=[tex]\sqrt{(2-0)^{2}+(1-0)^{2} }[/tex]

⇒d=[tex]\sqrt{4+1} =\sqrt{5}[/tex]

⇒d=2.24 m

Therefore, 2.24m far from the origin.

(b).

⇒tanθ=[tex]\frac{y}{x}[/tex]

⇒θ=[tex]tan^{-1}(\frac{y}{x} )=tan^{-1}(\frac {1.00}{2.00})[/tex]

=26.6°

Therefore, the location in polar coordinates is 26.6°.

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The length of one side of the box, in meters, is 0.138 meters.

The density of water is approximately 1000 kg/m^3 or 1 g/cm^3. If a cubic box is filled with 2650 g of water, we can find the volume of the box and then find one side length.

Volume = Mass / Density = 2650 g/(1 g/cm^3) = 2650 cm^3

Since the box is cubic, one side length is the cube root of the volume.

Side length = (Volume)^(1/3) = (2650 cm^3)^(1/3) = 13.8 cm

To convert cm to meters, divide by 100:

Side length = 13.8 cm/100 cm/m = 0.138 m

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Answer:

C s = k÷8

Step-by-step explanation:

Kylies Farm is 8 times larger than Sean's. So if we divide the size of Kylie's farm by 8, we have the size of Sean's farm.

s = k ÷ 8

k = 8s

k ÷ 8 = s

s × 8 = k

Answer: look below :))

Step-by-step explanation: To solve the equation X^2+x-6=0, we can use the Quadratic Formula:

X = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -6.

Substituting these values into the formula, we get:

X = (-1 ± √(1 - 4(1)(-6))) / 2(1)

Which gives us:

X = (-1 ± √(1 + 24)) / 2

X = (-1 ± √25) / 2

So the solutions to the equation are:

X = ( -1 + √25) / 2 or X = (-1 - √25) / 2

X = ( -1 + 5) / 2 or X = (-1 - 5) / 2

X = 2 or X = -3

So the solutions of the equation X^2+x-6=0 are X = 2 and X = -3.

Mowing Andre's uncle's lawn paid better than the other two jobs.

The job that paid better compared to the others is mowing Andre's uncle's lawn. He earned $30 for 1 hour of work, which is more than the $10 he earned for mowing a neighbor's lawn for 1 hour or the $15 he earned each hour for mowing the community's lawn for 2 hours.

The thinking behind this is basic. The rate of pay for mowing Andre's uncle's lawn was higher than the rate of pay for the other two jobs.

This is still up in the air by isolating the sum earned by the number of hours worked.

For the uncle's lawn, the rate was $30/1 hour = $30 each hour.

For the neighbor's lawn, the rate was $10/1 hour = $10 each hour. Furthermore, for the community center's lawn, the rate was $30/2 hours = $15 each hour.

Therefore, Mowing Andre's uncle's lawn paid better compared to the next two jobs.

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Step-by-step explanation:

then let's change that. you don't want to stay a dumdum, right ?

midpoint. what does that mean ? it is the point exactly in the middle between 2 other points.

what does that mean to be in the middle between 2 other things ?

well, it means that the distance is the same to both other things. otherwise it would not be the middle.

therefore,

4.

QS = 56 ft

exactly the same distance as PQ.

PS = PQ + QS

because Q is the point in the middle between P and S.

it is really that simple.

5.

the line segment PQ is bisected (cut in half) by the line segment MN at point R.

so, we know what the intersection of PQ and MN did to PQ (cut PQ in half). but this does not tell us what it did to MN. it could be also one of the ends of MN that cut PQ in half. we simply don't know.

therefore, we cannot say anything about the midpoint of MN.

and therefore the first 2 answer options are not generally correct. they COULD be correct, but they could be also wrong. therefore they are mathematically and logically not a true statement per se. for that the statement needs to be true unconditionally = in all possible cases.

R is the midpoint of PQ. yes, correct. that's what is meant by being bisected or cut in half at that point.

since the 3rd answer option is correct, the 4th answer option (none of these) is incorrect.

Value of x for which defined function f(x) = x²e⁻ˣ² gives the relative maximum value is equal to option D. -1 or  1.

Function 'f' is defined by f(x) = x²e⁻ˣ²

To get the relative maximum value of the function f(x) =  x²e⁻ˣ² find the first derivative we have,

f(x) =  x²e⁻ˣ²

Apply product rule of derivative :

d/dx ( u × v ) = v du /dx + u dv /dx

f' ( x ) =  e⁻ˣ² d/dx (x²) + x² d/dx (e⁻ˣ²)

⇒ f' (x) = 2x  e⁻ˣ² - 2x (x² ) ( e⁻ˣ² )

⇒  f' (x) = 2x  e⁻ˣ² - 2x³ e⁻ˣ²

⇒ f' (x) = 2x  e⁻ˣ²( 1 - x² )

To get the value of x for maximum function f' (x ) = 0 we get,

2x  e⁻ˣ²( 1 - x² ) = 0

⇒ 2≠0 or x =0 or  e⁻ˣ² ≠ 0 or 1 - x² = 0

⇒ x = 0 or x = ± 1

When

x = 0 ⇒ f(x) = 0

x = 1 ⇒ f(x) = e⁻¹

x = -1 ⇒ f(x) = e⁻¹

x = -1 or 1 represents the relative maximum value of f(x).

Therefore , value of x which represents the relative maximum value of the function f(x) = x²e⁻ˣ² is equal to option D. -1 or 1.

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The paragraph proof to show that VUTS is a parallelogram is as shown below.

Generally for parallelograms we know that;

A) If any one pair of opposite side is congruent and parallel, then the quadrilateral is parallelogram.

B) If two pair of opposite sides are parallel then it is a parallelogram.

Thus, the paragraph proof is as follows;

ΔSVX ≅ ΔUTX                      Given

SV // TU                                 Given

SV ≅ TU                                Corresponding part of congruent triangle

VUTS parallelogram               Definition of parallelogram.

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Answer:

2 [tex]\leq[/tex] x < 7

Step-by-step explanation:

-9 [tex]\geq[/tex] -3x - 3 > -24

Step 1: Add 3 to all sides; -6 [tex]\geq[/tex] -3x > -21

Step 2: Divide all sides by -3 (when we divide an inequality, we flip the inequality signs); 2 [tex]\leq[/tex] x < 7

A park, in the figure of a quadrilateral ABCD, has ∠C = 90°, AB = 9m, BC = 12 m, CD = 5 m, and AD = 8 m. The area is 65.49 m² ≈ 65.5m²

Join BD in "BCD," and receive BC and DC.

In order to compute BD, we can use Pythagoras's theorem.

[tex]& \Rightarrow \mathrm{BD}=\sqrt{\mathrm{BC}^2+\mathrm{CD}^2} \\[/tex]

[tex]& \quad=\sqrt{12^2+5^2}=\sqrt{144+25}=13 \mathrm{~m}=\mathrm{BD}[/tex]

Area of triangle ABD

[tex]$ =\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \text { (Heron's formula) } \\[/tex]

[tex]& \Rightarrow 2 \mathrm{~S}=9+8+13, \mathrm{~S}=\frac{30}{2} \\[/tex]

[tex]& \Rightarrow \mathrm{S}=15 \mathrm{~m} \\[/tex]

[tex]& \Rightarrow \text { Area of } \triangle \mathrm{ABD} \\[/tex]

[tex]& =\sqrt{15(15-9)(15-8)(15-13)} \\[/tex]

[tex]& =\sqrt{15 \times 6 \times 7 \times 2}=\sqrt{630 \times 2} \\[/tex]

[tex]& =6 \sqrt{1260}=35.49 \mathrm{~m}^2[/tex]

⇒ Area of Park = Quad ABCD

= 30+35.49

= 65.49 m² ≈ 65.5m²

The complete question is:

A park, in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

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Option 1 : In value market the hot dogs is pack of 8 so we have purchased 12 pack

  because, 96/8 =12

the cost of hot dogs is 12* $3.19 = $38.28

Option 2 : In Sammy's bulk store  the hot dogs is pack of 12 so we have purchased 8 pack

  because, 96/12 = 8  

the cost of hot dogs is 8 * $4.49  = $35.92

Costs are the monetary worth of expenditures for supplies, services, labor, goods, equipment, and other commodities acquired for use by a firm or other accounting entity in accounting. It is the amount marked as the price on invoices and documented as an expenditure or asset cost basis in book keeping records. price is the amount or equivalent paid or charged for anything. The average cost of a college education has skyrocketed. : the outlay or expenditure (as of work or sacrifice) made to attain a goal.

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With a 1.20 m/s velocity and an 8.8 m wavelength, this equation simulates ocean waves. The wave has an amplitude of 0.62 m and a wave number of 0.714 m-1. Position x and time t are both functions of the wave, with the time component being multiplied by velocity.

With a wavelength of 8.8 metres and a speed of 1.20 metres per second, this equation simulates the behaviour of ocean waves. According to the equation, the wave is a function of the position x, the time t, and the velocity times the time component. The wave's maximum size, or amplitude, is 0.62 m, which is the measurement of the wave's size. The wavelength of the wave is determined using the wave number, which is 0.714 m-1. The sine of the equation, which is 0.62 m multiplied by the sine of 0.714 m1, multiplied by (x vt), is used to determine the wave. This equation demonstrates how the wave is a dynamic entity that depends on both place and time.

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Answer:

Step-by-step explanation: by using the formula, volume of cylinder= πr2h

Answer:

Step-by-step explanation:

The measurement of the angle 7 is,

[tex]5+6+7=180\\ 5+90+7=180\\58+90+7=180\\ 7=180-90-58\\ 7=32[/tex]

Therefore, the desired angle is 32.

The distance far up the wall that the top of the ladder​ touches is 24 cm.

Given that a the ladder is 25 cm long and the foot of the ladder is 7 m away from the base of the wall.

This forms a right triangle.

From Pythagoras theorem;

Hypotenuse² = A leg² + B leg²

Plug the given values in and solve for B leg

Hypotenuse² - A leg² = B leg²

B leg = √( Hypotenuse² - A leg² )

B leg = √( 25² - 7² )

B leg = √( 625 - 49 )

B leg = √576

B leg = 24 cm

Therefore, the height at which the top of the ladder sits on the wall is 24cm.

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5x-3y+27=0 is the equation of the line passing between coordinates (-3,4) and (0,9).

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. A mathematical statement that expresses the connection between two values is simply characterized as an equation. In an equation, the two values are usually equated by an equal sign. Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). A linear equation can include several variables.

Here,

The point on the line is (-3,4) and (0,9).

m=(9-4)/(0+3)

m=5/3

y-4=5/3(x+3)

3y-12=5x+15

-5x+3y-27=0

5x-3y+27=0

The equation of the line that passes through coordinate (-3,4) and (0,9) is 5x-3y+27=0.

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An equation of product form of 3 and b is, 3b

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Two terms,

3

And b

by multiplying both the terms,

⇒  3 × b

⇒  3b

Hence, the product is 3b

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m<6 = 125° ( m<4 & m<6 are corresponding angles)

m<5 = 180°-125° (angles on a straight line)

= 55°

m<8 = 125° (corresponding angles)

m<7 = 55° (angles on a straight line)

Answer:

g(x) = x^2 -3

Step-by-step explanation: