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3 years ago

In a pen of goats and chickens, there are 40 heads and 150 feet. How many goats and chickens are in the pen?

Mathematics

1 answer:

s2008m [1.1K]3 years ago

6 0

Hey there!!

A chicken has 1 head and 2 feet . A goat has 1 head and 4 feet

For heads, total = 40

Let us take the number of chickens as ' x ' and goats as ' y '

x + y = 40 ------------- ( 1 )

2x + 4y = 150 ----------- ( 2 )

Multiply the first equation with 2

2x + 2y = 80

2x + 4y = 150

Subtract the first equation from the first

2y = 70

y = 35

Number of goats = 35

substitute this in other equation

x + y = 40

x + 35 = 40

x = 5

Number of chickens are 4

Hope it helps!

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Write an equation for a line perpendicular to y = -5x – 4 and passing through the point (15,5)

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The equation for the line in point-slope form that passes through (15, 5) and is perpendicular to $y = -5x - 4$ is $\mathbf{y -5 = \frac{1}{5} (x - 15)}$

Recall:

The equation of the line can be written in point-slope form (y - b = m(x - a)) and also in slope-intercept form (y = mx + b).

Given:

the point the line passes through: (15, 5)
the line it is perpendicular to: y = -5x - 4

Find the slope (m):

The slope value will be the negative reciprocal of the slope value of y = -5x - 4.

The slope of y = -5x - 4 is -5.

Therefore, the slope of the line perpendicular to y = -5x - 4 will be the negative reciprocal of -5 which is: 1/2.

Write the equation in point-slope form by substituting m = 1/2 and (a, b) = (15, 5) into y - b = m(x - a)

Thus:

$y -5 = \frac{1}{5} (x - 15)$

Therefore, the equation for the line that passes through (15, 5) and is perpendicular to $y = -5x - 4$ is $\mathbf{y -5 = \frac{1}{5} (x - 15)}$

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