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klasskru [66]
2 years ago
12

Find the equation of the line through (8,−6) which is perpendicular to the line y=x3−7.

Mathematics
1 answer:
ycow [4]2 years ago
8 0

Answer:

y = (-1/3)(x + 10)

Step-by-step explanation:

The slope of the new (perpendicular) line is the negative reciprocal of the slope of the given line, which appears to be 3.  Thus, the perpendicular line has the slope -1/3.

Using the slope-intercept form y = mx + b, and substituting the givens, we obtain:

y = mx + b    =>    -6 = (-1/3)(8) + b, or

-6 = -8/3 + b.  We must solve for the y-intercept, b:

Multiplying all three terms by 3 removes the fraction:

-18 = -8 + 3b.  Thus, -10 = 3b, and so b must be -10/3.

The desired equation is    

y = (-1/3)x - 10/3, or

y = (-1/3)(x + 10)

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Divide 85 into the ratio of 2:3:5
alukav5142 [94]
The actual amount that needs to be divided = 85
The ratio in which the amount needs to be divided = 2:3:5
Let us assume the common ratio to be = x
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2x + 3x + 5x = 85
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x = 85/10
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Then
The ratio in which the number 85 will be divided = 2 * 8.5:3 * 8.5:5 * 8.5
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san4es73 [151]

Answer:

m∠M = 79°

m∠N = 66°

Step-by-step explanation:

∠MPN is supplementary to ∠MPQ, so m∠MPN = 35

The sum of the measures of a triangle is 180.

So, m∠M + m∠N + m∠MPN = 180

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m∠N = 4y + 6 = 4(15) + 6 = 66

Another way to do this problem, which is easier, is to know that an exterior angle of a triangle is equal to the sum of the two remote interior angles.

That means 5y + 4 + 4y + 6 = 145

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                         y = 15

From knowing the value of y you can now find the measures of angles M and N

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