<img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%3D%20%20-%205x" id="TexFormula1" title=" {x}^{2} =

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marta [7]

2 years ago

} = - 5x" align="absmiddle" class="latex-formula">

Mathematics

2 answers:

fomenos2 years ago

7 0

Step-by-step explanation:

${x}^{2} - 5x \\ x(x + 5)$

aliina [53]2 years ago

3 0

Answer:

x(x + 5) = 0

Step-by-step explanation:

x² = - 5x

x² + 5x = 0

x(x + 5) = 0

hope it's helpful

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A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

2 years ago

Subtract j from 9, then subtract 3 from the result

Lera25 [3.4K]

Answer:

(9-j)-3

Step-by-step explanation:

Let's start from the beginning and subtract j from 9. Because the word "from" is used, 9 will be the first number and j will be the second number.

We have 9-j

Now, we have to subtract 3 from the final answer. So, we have (9-j)-3

7 0

3 years ago

Simplify (4i)(–5i)(6i) –120 –120i(incorrect) 120i 120

professor190 [17]

Answer:

120i

Step-by-step explanation:

;i × i = -1....so hence

4i × (-5i) = -20 i^2...which is -20(-1) = 20....

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20(6i) = 120i

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3 years ago

In each of the following scenarios, determine if the data are paired.

zmey [24]

Answer:

1. Can be Paired or Not Paired

2. Paired

3. Not Paired

Step-by-step explanation:

Two sets of observations are paired if each observation in one set has a special correspondence or connection with exactly one observation in the other data set.

1. Can be Paired or Not paired

Reason -

We might look at testing the difference of means using a two sample t-test. However, we may also try running a paired t-test.

But its used in cases where the observations are usually from the same populations at different times or through different sources etc.

Hence can't conclude that it is paired or not paired.

2. Paired

Reason -

Each record is a price of the same item from different stores.

3. Not paired

Reason -

This is again a case of testing the difference of means of two-samples (2 independent samples precisely) that are not paired.

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3 years ago

Which equation is represented by the graph below?

marta [7]

Answer:

Hello,

Answer C

Step-by-step explanation:

Since ln(1)=0

if x=1 then y=4 ==> y=ln(x)+4

y=ln(x) is translated up for 4 units.

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2 years ago