Seth is planning a route for a train that travels at a constant rate of
220 kilometers per hour. They want to write an equation that shows how many hours (t) a trip takes in terms of the trip's distance (d) .

Answers:
A: d/t = 220
B: t = d/220
C: d = 220t

Answer:

39.60

Step-by-step explanation:

9.90 x 4 = 39.60

The equation of the line passing through points \(A(a,b)\) and \(B(b,a)\) is \(x + y = a + b\)  , and the length of   \(AB\) is  \(\sqrt(2(a - b)^2).\)

To find the equation of the line passing through points A(a,b) and B(b,a), we can first find the slope of the line. using the two given points, and then use the point-slope form of a line equation.

The slope of a line passing through two points (\(x_{1} , y_{1}\)) and (\(x_{2}, y_{2}\)) is given by:

\(m = (y_{2} - y_{1} ) / (x_{2} - x_{1} )\)

Applying this formula, we can find the slope of the line passing through points A(a,b) and B(b,a):

Slope \((m) = (a - b) / (b - a)\)

Since a and b can take any real values, we can see that the slope of the line passing through points A and B is -1.

Now, let's find the equation of the line passing through points A and B using the point-slope form of a line equation:

Point-slope form: \(y - y_{1} = m(x - x_{1} )\)

Substituting the slope (-1) and the coordinates of point A(a,b) into the point-slope form, we get:

\(y - b = -1(x - a)\)

Expanding the equation, we get:

\(y - b = -x + a\)

Rearranging the terms, we get the equation of the line passing through points A(a,b) and B(b,a):

\(x + y = a + b\)

Now, let's find the length of AB using the distance formula:

The distance between two points \((x_{1} , y_{1} )\) and  \((x_{2} , y_{2} )\) is given by:

\(d = \sqrt((x_{2} - x_{1} )^2 + (y_{2} - y_{1} )^2)\)

Applying this formula, we can find the length of AB using the coordinates of points A(a,b) and B(b,a):

Length of  \(AB (d) = \sqrt((b - a)^2 + (a - b)^2)\)

Simplifying the expression, we get:

Length of \(AB (d) = \sqrt(2(a - b)^2)\)

Therefore, The equation of the line passing through points \(A(a,b)\) and \(B(b,a)\) is \(x + y = a + b\)  , and the length of   \(AB\) is  \(\sqrt(2(a - b)^2).\)

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5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:What is 464,943 rounded to the nearest ten thousand?

Step-by-step explanation:

What is 464,943 rounded to the nearest ten thousand?

3172.97 joules is the value of x when the Richter scale rating is 3.2

The equation that relates earthquake magnitude (M) and energy (E) is:

M = 2/3 × log(E) - 1.8

We have to find the value of X when the richer scale rating is 3.1

If an earthquake with a rating of 3.2 is not usually felt, then we can assume that x corresponds to the energy released by an earthquake that is just barely felt.

According to the United States Geological Survey, an earthquake with a magnitude of 2.5 corresponds to an energy release of about 1.3 × 10⁸ joules.

Using this as a reference point, we can set up the following equation:

3.2 = 2/3 × log(x) - 1.8

Solving for x, we get:

2.3 = 2/3 × log(x)

log(x) = 3.45

x = 3172.97

Therefore, the value of x when the Richter scale rating is 3.2 is approximately 3172.97 joules.

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The value of the vase 65 years ago was $115.38

The value of the vase now is $415.38.

Percentage is a measure of frequency. Percentage is the fraction of an amount that is expressed as a number out of 100. The sign that is used to represent percentage is %.

The equation that can be used to represent the increase in the value of the vase is:

Increase in the value of the vase = percentage increase x value of the vase 65 years ago

300 = 2.6v

In order to determine the value of v, divide both sides of the equation by 2.65.

v = 300 / 2.60

v = $115.38

Value of the vase now = value of the vase 65 years ago + increase

$115.38 + $300 = $415.38

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Answer:

The formula for finding the area of a circle using its radius is:

The formula for finding the area of a circle using its radius is:A = πr²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14

Step-by-step explanation:

Hope it Helps

The formula for finding the area of a circle using its radius is π * r².

The formula for finding the area of a circle using its diameter is (π/4) * d².

The formula for finding the area of a circle using its radius is:

A = π * r²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

r represents the radius of the circle.

If you have the diameter of the circle instead of the radius, you can use the following formula:

A = (π/4) * d²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

d is the diameter of the circle.

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The correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

What is decagonal pyramid?

A decagonal pyramid is a solid whose base is a decagon or a ten sided figure, regular or irregular. The surfaces are ten isosceles triangles, in case of a regular decagonal pyramid with all the ten vertices meeting at a point.

Here The decagonal prism is formed by two regular decagons as its bases and 10 squares as its other faces. the top of the decagonal prism is a regular decagon, so is the bottom face.

We know that decagonal pyramid has 11 faces and 20 edges and 11 vertices.

Hence the correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

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Answer:

90units²

Step-by-step explanation:

area of a triangle= ½base *height

area = ½*12*15

area= 90units²

The domain of the function → y = √√√x is -

Domain → [0, + ∞)

Domain is the set of {x} - values for which a function {y - values} exists. It is one of the important parameter while defining the characteristics of a function.

Given is the function -

y = √√√x

Domain is the set of values along the {x} - axis. The given function is -

y = √√√x

y = √√√x = \($x^{\frac{1}{8} }\)

Refer to the graph of the function attached. We can write the domain as -

Domain → [0, + ∞)

Therefore, the domain of the function is -

Domain → [0, + ∞)

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Step-by-step explanation:

the slope of a line or linear equation is always the factor of the driving variable.

usually in the form of

y = ax + b

x is the variable, and a the slope.

but in our case the variable is called "n".

it does not matter, the same principle applies.

the slope is the factor of n : 1050.

and as the slope is always the ratio y/x, we are looking for a fraction form, and that would be 1050/1.

so, the third answer is correct.

The sixth term of the sequence is 320

The definition of the function is given as

a₁= 10

aₙ = 2aₙ₋₁

The above definitions imply that we simply multiply 2 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a1 = 10

a2 = 2a1 = 2(10) = 20

a3 = 2a2 = 2(20) = 40

a4 = 2a3 = 2(40) = 80

a5 = 2a4 = 2(80) = 160

a6 = 2a5 = 2(160) = 320

Hence, the value of the 6th term is 320

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Answer:

Enter a problem...

Algebra Examples

Popular Problems Algebra Solve for x 2/3x-2=7

2

3

x

−

2

=

7

Combine

2

3

and

x

.

2

x

3

−

2

=

7

Move all terms not containing

x

to the right side of the equation.

Tap for more steps...

2

x

3

=

9

Multiply both sides of the equation by

3

2

.

3

2

⋅

2

x

3

=

3

2

⋅

9

Simplify both sides of the equation.

Tap for more steps...

x

=

27

2

The result can be shown in multiple forms.

Exact Form:

x

=

27

2

Decimal Form:

x

=

13.5

Mixed Number Form:

x

=

13

1

2

Step-by-step explanation:

Thank's………………………………

Answer: 27 x 1/3

Step-by-step explanation: 27/1 x 1/3 = 9 orchards per store

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

John manages 27 apple orchards in North Georgia. He wants to split the orchards into thirds so that he can open 3 local stores.

Then the number of orchards in each store will be

⇒ 27 / 3

Then the expression can be written as,

⇒ 27 x (1/3)

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

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Answer:

1.52%

Step-by-step explanation:

The value of the equation f ( x ) is

f ( x ) = x³ + x² - 8x - 12

What is an Equation?

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

f ( x ) = ( x + 2 )²( x -3 )   be equation (1)

Now , on simplifying the equation , we get

f ( x ) = ( x + 2 )²( x -3 )

f ( x ) = ( x² + 4x + 4 ) ( x - 3 )

Now , multiplying each term with ( x - 3 ) , we get

f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4

f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12

On simplifying the equation ,we get

f ( x ) = x³ + x² - 8x - 12

Now , the value of the equation f ( x ) = x³ + x² - 8x - 12

On graphing the equation , we get

The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below

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Answer:

what is the question? but I will answer it

Answer:

I think B and C is the answer.

The measure of the arc AT in this problem is given as follows:

mAT = 159º.

The measure of arc AT is obtained applying the two secant theorem, which states the angle measure of intersection of the two secant segments is half the difference of the measure of the far arc by the measure of the near arc.

The parameters for this problem are given as follows:

Hence the measure of the arc AT in this problem is given as follows:

(mAT - 59)/2 = 50

mAT - 59 = 100

mAT = 159º.

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Answer:

19.0285

Step-by-step explanation:

For this, we have to work backwards.

First, the equation for the circumference of a circle is:
\(2\pi r\)

We already know the circumference, so we can solve for r:
\(119.56=2\pi r\)

divide both sides by 2

\(59.78=\pi r\)

divide both sides by pi

\(19.0285...=r\)

So, depending on the answer choices, the answer is 19.0285 rounded to the according decimal place.

Hope this helps! :)

Answer:

2880 cubic meters.

Step-by-step explanation:

To find the area of a rectangular prism, multiply the length width and height.
20*12*12=144*20=2880

The volume of the Rectangular Prism is 2880 cubic meters.

Rectangular prism can be defined as a" 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid".

According to the question,

Length of the rectangular prism = 20 meters

Height of the rectangular prism = 12 meters

Width of the rectangular prism = 12 meters

Formula for Rectangular Prism = length × breadth × height

= 20 × 12 × 12

= 2880 cubic meters.

Hence, the volume of the Rectangular Prism is 2880 cubic meters.

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Answer:

I think it may be a but I am not completely sure

Step-by-step explanation:

The area of the sector in the circle shown above is given as follows:

32.3 in².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it is given as follows:

r = 10 in.

Then the area of the entire circle is given as follows:

A = π x 10²

A = 314 in².

The entire circumference of the circle is of 360º, while the angle is of 37º, hence the area of the sector is given as follows:

37/360 x 314 = 32.3 in².

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The number of chips and drinks are 46 chips and 56 drinks respectively.

Let the number of drinks be d.

Let the number of chips be c.

From the information, he works at a football concession stand selling drinks for $2 and bags of chips for $3 and he makes a total of $246 and sells a total of 100 drinks and bags of chips.

This will be:

c + d = 100 ........ i

2d + 3c = 246 ........ ii

From equation i, c = 100 - d

Substitute this into equation ii

2d + 3c = 246

2d + 3(100 - d) = 246

2d + 300 - 3d = 246

Collect like terms

2d - 3d = 246 - 300

-d = -54

d = 54

Number of drinks = 54

Since c + d = 100

c + 54 = 100

c = 100 - 54 = 46

Chips = 46

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Complete question

Russell works at a football concession stand selling drinks for $2 and bags of chips for $3. At one football game, Russell makes a total of $246 and sells a total of 100 drinks and bags of chips. Calculate the number of drinks and chips sold.

Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2