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gavmur [86]
3 years ago
13

Find an equation for the line perpendicular to 4x+12y=72 and goes through the point (-9,6)

Mathematics
1 answer:
il63 [147K]3 years ago
7 0

Answer:

Step-by-step explanation:

Given the equation

4x+12y=72

The equation of a line can written as

y=mx+c

Where m is the slope

And c is the intercept on y axis

Then, we need to write the equation given in the form of equation of a line (y=mx+c), by making y subject of the formula

4x+12y=72

12y=-4x+72

Divide through by 12

y=-4x/12 + 72/12

y=-⅓x+6

Then, comparing with equation of a line shows that

m=-⅓ and c=6

So we need to get another linen that is perpendicular to this line and passes through the point (-9,6)

The slope of the line perpendicular to another line is given as

m1=-1/m2

Then, m1=-1÷-⅓

Then, the slope of the perpendicular line is 3

Then, m=3

So apply this to equation of the line

y=mx+c

Then, y=3x+c

So to know c, we will insert the point given(-9,6), x=-9 and y=6

y=3x+c

6=3(-9)+c

6=-27+c

Then, c=6+27

c=33

Then, the equation of line becomes

y=3x+33

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Answer:

200 mg sodium is in 1 oz of chips and 50 mg sodium is in 1 cup of soda.

Step-by-step explanation:

Let x mg sodium is in 1 oz of chips and and y mg is in 1 cup of soda.

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i.e. 3x + 2y = 700 --------(1),

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i.e. x + 3y = 350 ---------(2),

Equation (1) - 3 × equation (2),

We get,

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From equation (1),

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3x + 100 = 700

3x = 700 - 100

3x = 600

\implies x = \frac{600}{3}=200

Hence, 200 mg sodium is in 1 oz of chips and 50 mg sodium is in 1 cup of soda.

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Step-by-step explanation:

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