Solve 30x+35y=1125

Question

Function

$Find the x -intercept/zero$

Find the y-intercept

Find the slope

x = \frac{75}{2}

Evaluate

30 x + 35 y = 1125

To find the x -intercept,set y =0

30 x + 35 \times 0 = 1125

Any expression multiplied by 0 equals 0

30 x + 0 = 1125

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

30 x = 1125

Divide both sides

\frac{30 x}{30} = \frac{1125}{30}

Divide the numbers

x = \frac{1125}{30}

Solution

x = \frac{75}{2}

Show Solution

Solve the equation

$Solve for x$

$Solve for y$

x = \frac{225 - 7 y}{6}

Evaluate

30 x + 35 y = 1125

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

30 x = 1125 - 35 y

Divide both sides

\frac{30 x}{30} = \frac{1125 - 35 y}{30}

Divide the numbers

x = \frac{1125 - 35 y}{30}

Solution

More Steps

Evaluate

\frac{1125 - 35 y}{30}

Rewrite the expression

\frac{5 ( 225 - 7 y )}{30}

Cancel out the common factor 5

\frac{225 - 7 y}{6}

x = \frac{225 - 7 y}{6}

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

30 x + 35 y = 1125

To test if the graph of 30 x + 35 y = 1125 is symmetry with respect to the origin,substitute -x for x and -y for y

30 (- x) + 35 (- y) = 1125

Evaluate

More Steps

Evaluate

30 (- x) + 35 (- y)

Multiply the numbers

- 30 x + 35 (- y)

Multiply the numbers

- 30 x - 35 y

- 30 x - 35 y = 1125

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{225}{6 cos ( θ ) + 7 sin ( θ )}

Evaluate

30 x + 35 y = 1125

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

30 cos (θ) \times r + 35 sin (θ) \times r = 1125

Factor the expression

(30 cos (θ) + 35 sin (θ)) r = 1125

Solution

r = \frac{225}{6 cos ( θ ) + 7 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} = - \frac{6}{7}

Calculate

30 x + 35 y = 1125

Take the derivative of both sides

\frac{d}{d x} (30 x + 35 y) = \frac{d}{d x} (1125)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (30 x + 35 y)

Use differentiation rules

\frac{d}{d x} (30 x) + \frac{d}{d x} (35 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (30 x)

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

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

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

30 \times 1

Any expression multiplied by 1 remains the same

30

30 + \frac{d}{d x} (35 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (35 y)

Use differentiation rules

\frac{d}{d y} (35 y) \times \frac{d y}{d x}

Evaluate the derivative

35 \frac{d y}{d x}

30 + 35 \frac{d y}{d x}

30 + 35 \frac{d y}{d x} = \frac{d}{d x} (1125)

Calculate the derivative

30 + 35 \frac{d y}{d x} = 0

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

35 \frac{d y}{d x} = 0 - 30

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

35 \frac{d y}{d x} = - 30

Divide both sides

\frac{35 \frac{d y}{d x}}{35} = \frac{- 30}{35}

Divide the numbers

\frac{d y}{d x} = \frac{- 30}{35}

Solution

More Steps

Evaluate

\frac{- 30}{35}

Cancel out the common factor 5

\frac{- 6}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{6}{7}

\frac{d y}{d x} = - \frac{6}{7}

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

30 x + 35 y = 1125

Take the derivative of both sides

\frac{d}{d x} (30 x + 35 y) = \frac{d}{d x} (1125)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (30 x + 35 y)

Use differentiation rules

\frac{d}{d x} (30 x) + \frac{d}{d x} (35 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (30 x)

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

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

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

30 \times 1

Any expression multiplied by 1 remains the same

30

30 + \frac{d}{d x} (35 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (35 y)

Use differentiation rules

\frac{d}{d y} (35 y) \times \frac{d y}{d x}

Evaluate the derivative

35 \frac{d y}{d x}

30 + 35 \frac{d y}{d x}

30 + 35 \frac{d y}{d x} = \frac{d}{d x} (1125)

Calculate the derivative

30 + 35 \frac{d y}{d x} = 0

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

35 \frac{d y}{d x} = 0 - 30

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

35 \frac{d y}{d x} = - 30

Divide both sides

\frac{35 \frac{d y}{d x}}{35} = \frac{- 30}{35}

Divide the numbers

\frac{d y}{d x} = \frac{- 30}{35}

Divide the numbers

More Steps

Evaluate

\frac{- 30}{35}

Cancel out the common factor 5

\frac{- 6}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{6}{7}

\frac{d y}{d x} = - \frac{6}{7}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{6}{7})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- \frac{6}{7})

Solution

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

Show Solution

30x+35y=1125

Function

Find the x-intercept/zero

Find the y-intercept

Find the slope

Solve the equation

Solve for x

Solve for y

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

Graph

$Find the x -intercept/zero$

$Solve for x$

$Solve for y$

$Find the derivative with respect to x$

$Find the derivative with respect to y$

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$