Solve 100x+y+10x+y=1002

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{501}{55}

Evaluate

100 x + y + 10 x + y = 1002

To find the x -intercept,set y =0

100 x + 0 + 10 x + 0 = 1002

Simplify

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Evaluate

100 x + 0 + 10 x + 0

Removing 0 doesn't change the value,so remove it from the expression

100 x + 10 x

Collect like terms by calculating the sum or difference of their coefficients

(100 + 10) x

Add the numbers

110 x

110 x = 1002

Divide both sides

\frac{110 x}{110} = \frac{1002}{110}

Divide the numbers

x = \frac{1002}{110}

Solution

x = \frac{501}{55}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{501 - y}{55}

Evaluate

100 x + y + 10 x + y = 1002

Add the terms

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Evaluate

100 x + y + 10 x + y

Add the terms

More Steps

Evaluate

100 x + 10 x

Collect like terms by calculating the sum or difference of their coefficients

(100 + 10) x

Add the numbers

110 x

110 x + y + y

Add the terms

More Steps

Evaluate

y + y

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1) y

Add the numbers

2 y

110 x + 2 y

110 x + 2 y = 1002

Move the expression to the right-hand side and change its sign

110 x = 1002 - 2 y

Divide both sides

\frac{110 x}{110} = \frac{1002 - 2 y}{110}

Divide the numbers

x = \frac{1002 - 2 y}{110}

Solution

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Evaluate

\frac{1002 - 2 y}{110}

Rewrite the expression

\frac{2 ( 501 - y )}{110}

Cancel out the common factor 2

\frac{501 - y}{55}

x = \frac{501 - y}{55}

Show Solution

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Evaluate

100 x + y + 10 x + y = 1002

Simplify the expression

110 x + 2 y = 1002

To test if the graph of 110 x + 2 y = 1002 is symmetry with respect to the origin,substitute -x for x and -y for y

110 (- x) + 2 (- y) = 1002

Evaluate

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Evaluate

110 (- x) + 2 (- y)

Multiply the numbers

- 110 x + 2 (- y)

Multiply the numbers

- 110 x - 2 y

- 110 x - 2 y = 1002

Solution

Not symmetry with respect to the origin

Show Solution

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

r = \frac{501}{55 cos ( θ ) + sin ( θ )}

Evaluate

100 x + y + 10 x + y = 1002

Evaluate

More Steps

Evaluate

100 x + y + 10 x + y

Add the terms

More Steps

Evaluate

100 x + 10 x

Collect like terms by calculating the sum or difference of their coefficients

(100 + 10) x

Add the numbers

110 x

110 x + y + y

Add the terms

More Steps

Evaluate

y + y

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1) y

Add the numbers

2 y

110 x + 2 y

110 x + 2 y = 1002

To convert the equation to polar coordinates,substitute x for r cos (θ) and y for r sin (θ)

110 cos (θ) \times r + 2 sin (θ) \times r = 1002

Factor the expression

(110 cos (θ) + 2 sin (θ)) r = 1002

Solution

r = \frac{501}{55 cos ( θ ) + sin ( θ )}

Show Solution

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = - 55

Calculate

100 x + y + 10 x + y = 1002

Simplify the expression

110 x + 2 y = 1002

Take the derivative of both sides

\frac{d}{d x} (110 x + 2 y) = \frac{d}{d x} (1002)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (110 x + 2 y)

Use differentiation rules

\frac{d}{d x} (110 x) + \frac{d}{d x} (2 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (110 x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

110 \times \frac{d}{d x} (x)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

110 \times 1

Any expression multiplied by 1 remains the same

110

110 + \frac{d}{d x} (2 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 y)

Use differentiation rules

\frac{d}{d y} (2 y) \times \frac{d y}{d x}

Evaluate the derivative

2 \frac{d y}{d x}

110 + 2 \frac{d y}{d x}

110 + 2 \frac{d y}{d x} = \frac{d}{d x} (1002)

Calculate the derivative

110 + 2 \frac{d y}{d x} = 0

Move the constant to the right-hand side and change its sign

2 \frac{d y}{d x} = 0 - 110

Removing 0 doesn't change the value,so remove it from the expression

2 \frac{d y}{d x} = - 110

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{- 110}{2}

Divide the numbers

\frac{d y}{d x} = \frac{- 110}{2}

Solution

More Steps

Evaluate

\frac{- 110}{2}

Reduce the numbers

\frac{- 55}{1}

Calculate

- 55

\frac{d y}{d x} = - 55

Show Solution

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = 0

Calculate

100 x + y + 10 x + y = 1002

Simplify the expression

110 x + 2 y = 1002

Take the derivative of both sides

\frac{d}{d x} (110 x + 2 y) = \frac{d}{d x} (1002)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (110 x + 2 y)

Use differentiation rules

\frac{d}{d x} (110 x) + \frac{d}{d x} (2 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (110 x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

110 \times \frac{d}{d x} (x)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

110 \times 1

Any expression multiplied by 1 remains the same

110

110 + \frac{d}{d x} (2 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 y)

Use differentiation rules

\frac{d}{d y} (2 y) \times \frac{d y}{d x}

Evaluate the derivative

2 \frac{d y}{d x}

110 + 2 \frac{d y}{d x}

110 + 2 \frac{d y}{d x} = \frac{d}{d x} (1002)

Calculate the derivative

110 + 2 \frac{d y}{d x} = 0

Move the constant to the right-hand side and change its sign

2 \frac{d y}{d x} = 0 - 110

Removing 0 doesn't change the value,so remove it from the expression

2 \frac{d y}{d x} = - 110

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{- 110}{2}

Divide the numbers

\frac{d y}{d x} = \frac{- 110}{2}

Divide the numbers

More Steps

Evaluate

\frac{- 110}{2}

Reduce the numbers

\frac{- 55}{1}

Calculate

- 55

\frac{d y}{d x} = - 55

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- 55)

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 55)

Solution

\frac{d ^{2} y}{d x ^{2}} = 0

Show Solution

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph