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3 years ago

Find the measure of the angle indicated in bold. please include explanation.

Mathematics

2 answers:

My name is Ann [436]3 years ago

7 0

Answer:

D 95

Step-by-step explanation:

46x+3 = 48x-1 (corresponding angles are congruent)

now isolate x

2x = 4

2x/2 = 4/2

x = 2

plug x = 2 back into 48x-1 since it's the bold angle

48(2) - 1 = 96-1 = 95

Juliette [100K]3 years ago

4 0

Answer:

D 95

Step-by-step explanation:

The two angles are corresponding angles and corresponding angles are equal

46x+3 = 48x-1

Subtract 46x from each side

46x -46x+3 = 48x-46x-1

3 = 2x-1

Add 1 to each side

3+1 =2x-1+1

4 = 2x

Divide by 2 on each side

4/2 = 2x/2

2 =x

We need to find the bold angle 48x-1

48(2)-1

96-1

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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

Interest = $821.25, time = 1 year, rate = 12.42%. Find the principal

marta [7]

Step-by-step explanation:

P = l.100/t.r = $821.25×100/12.42×1 = $6612.318

hope this helps you.

4 0

2 years ago

May someone please help me out please?

Zanzabum

Step-by-step explanation:

First, we need to find that top angle, which we'll call angle x. We can say 26 is the hypotenuse, and 12 is the adjacent, so we know that:

$\cos(x) = \frac{12}{26}$

Let's solve this, to find X:

$x = { \cos }^{ - 1}( \frac{12}{26} )$

Now that we know what X is, we can use trig to find the missing side, which we'll call y. 48 is the adjacent, and y is the hypotenuse, therefore:

$\cos(x) = \frac{48}{y}$

To find y, let's rearrange:

$y = \frac{48}{ \cos(x) }$

And now let's figure out calculate the value of y (I'm leaving the value of X as just X for the equations, but you will need it to calculate first):

$y = 0.767833242$

8 0

2 years ago

How do you solve y=x-3 and<br> Y= -x +5

artcher [175]

Answer:

The answer is 4

Step-by-step explanation:

Set them equal so it would be X-3= -X+5 then add the negative X to get

2x-3=5 then add the -3 to 5 and get

2x=8 then divide 2 from both sides to get

x=4

5 0

4 years ago

What the image of (- 6, 5) after a reflection over the line y = x ?

zubka84 [21]

Answer:

Step-by-step explanation:

7 0

3 years ago