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dybincka [34]
3 years ago
12

A circle is centered at (5, -9) and has a radius of 12. What is the equation for this circle

Mathematics
1 answer:
WINSTONCH [101]3 years ago
3 0
(x - 5)² + (y + 9)² = 144
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Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select t
nignag [31]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

y = mx + b

Where:

m: It's the slope

b: It is the cut-off point with the y axis

On the other hand we have that if two lines are perpendicular, then the product of their slopes is -1. So:

m_ {1} * m_ {2} = - 1

The given line is:

5x-2y = -6\\-2y = -6-5x\\2y = 5x + 6\\y = \frac {5} {2} x + \frac {6} {2}\\y = \frac {5} {2} x + 3

So we have:

m_ {1} = \frac {5} {2}

We find m_ {2}:m_ {2} = \frac {-1} {\frac {5} {2}}\\m = - \frac {2} {5}

So, a line perpendicular to the one given is of the form:

y = - \frac {2} {5} x + b

We substitute the given point to find "b":

-4 = - \frac {2} {5} (5) + b\\-4 = -2 + b\\-4 + 2 = b\\b = -2

Finally we have:

y = - \frac {2} {5} x-2

In point-slope form we have:

y - (- 4) = - \frac {2} {5} (x-5)\\y + 4 = - \frac {2} {5} (x-5)

ANswer:

y = - \frac {2} {5} x-2\\y + 4 = - \frac {2} {5} (x-5)

3 0
3 years ago
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David is 4 times older than Adan. Adan is 2 times older than julio. Julio is 12, how old is David?
dem82 [27]
12 x 2 = 24 (Julio), 24 x 4 = 96 (David).
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3 years ago
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Find the minimum cost of producing 50,000 units of a product, where x is the number of units of labor (at $36 per unit) and y is
erastovalidia [21]

Answer:

Step-by-step explanation:

Given problem: C(x,y) = 36x + 48y

constraint: 100x^0.6y^0.4

Using langrange Multiplier,

36 = 0.6(100)x^-0.4y^0.4λ         i

48 = 0.4(100)x^0.6y^-0.6λ         ii

dividing the equations we have:

x = 2y

substituting into the constraint

p(x,y) = 100 *(2y)^0.6 y^0.4 = 100*2^0.6 *y

5000  = 151.572y

y = 329.876 labor units

x = 659.752 capital units

Minimum cost = 36(659.752) +48(329.876) = $39585.12

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3 years ago
PLSSSSSSS HELP QUICK PLSSSSSSS!!
lozanna [386]

Answer:

Step-by-step explanation:

8 0
3 years ago
HELP giving brainless and 100 points!!
Ksivusya [100]

Answer:

b

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3 1/2 x 3 x 1/2= 5.25 or 5 and 1/4

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