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3 years ago

The angles shown below are supplementary: what is the value of x

Mathematics

2 answers:

Scorpion4ik [409]3 years ago

6 0

Answer:

x=12

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

10x+60=180

Subtract 60 from both sides:

10x=120

Divide 10 to both sides:

x=12

Annette [7]3 years ago

5 0

Answer:

$x=12$

Step-by-step explanation:

By definition, supplementary angles add up to 180 degrees. Therefore, we can set up the follow equation to solve for $x$ :

$10x+60=180,\\10x=120,\\x=\boxed{12}$

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3 years ago

Radius of a cone with a volume of 100.48 yds3 and a height of 6 yds

professor190 [17]

Answer:

r = 4

Step-by-step explanation:

Volume of a cone:

V = πr²(h/3)

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V = 100.48

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3 years ago

A culture started with 5000 bacteria after three hours it grew 6500 bacteria predict how many bacteria will be present after 13

charle [14.2K]

Answer:

15595 bacteria will be present after 13 hours.

Step-by-step explanation:

Continuous population growth:

The continuous population growth model, for the population after t hours, is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial population and r is the growth rate.

Started with 5000 bacteria

This means that $P(0) = 5000$

$P(t) = 5000e^{rt}$

After three hours it grew 6500 bacteria:

This means that $P(3) = 6500$ . We use this to find r.

$P(t) = 5000e^{rt}$

$6500 = 5000e^{3r}$

$e^{3r} = \frac{65}{50}$

$\ln{e^{3r}} = \ln{\frac{65}{50}}$

$3r = \ln{\frac{65}{50}}$

$r = \frac{\ln{\frac{65}{50}}}{3}$

$r = 0.0875$

$P(t) = 5000e^{0.0875t}$

How many bacteria will be present after 13 hours?

This is P(13). So

$P(13) = 5000e^{0.0875*13} = 15594.8$

Rounding to the nearest whole number

15595 bacteria will be present after 13 hours.

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