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3 years ago

For each part below, use the figure to fill in the blank.

Mathematics

1 answer:

kobusy [5.1K]3 years ago

8 0

Answer:

a) m<F = 70

b) AB = 6

Step-by-step explanation:

Since this is an isoceles triangle, the base angles are equal so:

2x + 40 = 180

2x = 140

x = 70

Since all of the angles are equal, this is an equilateral triangle. This also makes all of the sides equal and the same.

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A bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. After 6 hours there will be 3960 bacte

scoray [572]

Answer:

a) $P(t) = 660 e^{\frac{ln(6)}{6} t}$

b) $P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

Step-by-step explanation:

For this case we have the following info:

$P(0) = 660$ represent the initial amount of bacteria

$P(6) = 3960$ represent the population of bacteria after 6 hours

Part a

For this case we use the proportional model given by:

$\frac{dP}{dt}= kP$

Where P represent the population at time t and k is a constant of proportionality.

We can rewrite the model like this:

$\frac{dP}{P} = k dt$

And if we integrate both sides we got:

$ln |P|= kt + C$

Now if we apply exponential we got:

$P = e^{kt +c}= e^{kt} e^C$

$P(t)= P_o e^{kt}$

For this case using the initial condition:

$660 = P_o e^{0k}, P_o = 660$

We have the following model:

$P(t) = 660 e^{kt}$

Using the second condition $P(6) = 3960$ we have this:

$3960 = 660e^{6k}$

We can divide both sides by 660 and we got:

$6= e^{6k}$

Now we can apply natural log on both sides and we got:

$ln (6)= 6k$

$k = \frac{ln(6)}{6}=0.2986265782$

So then the model would be given by:

$P(t) = 660 e^{\frac{ln(6)}{6} t}$

Part b

For this case we just need to replace t=3 into the model and we got:

$P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

4 0

3 years ago

Rewrite 7x + 4 = x – 2 as a system. y = –(7x + 3) y = –(x – 2) y = (7x + 4) y = –(x – 2) y = (7x + 4) y = x – 2

Slav-nsk [51]

Answer: $\left \{ {{y=7x+4} \atop {y=x-2}} \right.$ (LAST OPTION)

Step-by-step explanation:

You have the following expression given in the problem:

$7x+4=x-2$

If the expression on the left side of the equation is equal to the expression on the right side of the equation, and the problem asks to rewrite it as a system, you can conclude that the first equation is:

$y=7x+4$

And the second equation is:

$y=x-2$

Therefore, you can set up the following system of equations:

$\left \{ {{y=7x+4} \atop {y=x-2}} \right.$

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That it wiil not equal out to be the same unless one of them start with money

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Plus answer now Find 3/5 of 3000.

stealth61 [152]

3000/5 = 600*3 = 1800

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