Divide the complex numbers. Write the answer in the form a + bi. (30 points)

Prefer work shown as it would be super helpful, thank you.

Answer: 26.34

Step-by-step explanation:

The bacteria will take 26.3409 minutes.

Exponents are used in exponential equations, as the name suggests. We are aware that a number's exponent (or base) tells us how many times the original number has been multiplied. But what occurs if a number's power is a variable? An exponential equation is one in which the power is a variable and a part of the equation.

Given f(t) = 256[tex]e^{0.0611t}[/tex]

initial condition when t = 0

f(0) = 256

to find the time when population reach 5 times its initial value

= 256 x 5 = 1280

f(t) = 1280,

to calculate t

1280 = 256[tex]e^{0.0611t}[/tex]

[tex]e^{0.0611t}[/tex] = 5

0.0611t = ln(5)

0.0611t = 1.60943

t = 1.60943/0.0611

t = 26.3409 minutes.

Hence Bacteria will take 26.3409 minutes to reach 5 times.

Learn more about Exponential Equations;

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Answer:

[tex]y=-\frac{4}{3} x+4[/tex]

Step-by-step explanation:

Slope-intercept form is written in [tex]y=mx+b[/tex]

So, to solve, we must separate y onto one side and make its coefficient one.

[tex]4x+3y=12[/tex]

Subtract 4x on both sides.

[tex]3y=12-4x[/tex]

Divide both sides by the coefficient of [tex]y[/tex], which is 3.

[tex]\frac{3y}{3} =\frac{12-4x}{3}[/tex]

Simplify.

[tex]y=4-\frac{4}{3} x[/tex]

Rewrite this equation into standard form by changing the order of [tex]mx[/tex] and [tex]b[/tex]

[tex]y=-\frac{4}{3} x+4[/tex]

Answer

y=4/5 times 2/3

Step-by-step explanation:

106 bags needed to pack all the brownies.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Jack and Dwayne made 318 Brownies.

Each small bag contain 3 Brownies.

So, the number of bags required

= 318 / 3

= 106 bags

Hence, 106 bags needed.

Learn more about Unitary Method here:

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Answer:

y-intercept: 5/3

Step-by-step explanation:

Our equation: y = mx + b

Given equation: y = -8/3 + 5/3

=> Now, let's compare.

=> y = mx + b = y = -8/3 + 5/3

=> we can tell that the y-intercept is b, which is 5/3.

Hoped this helped.

[tex]y = - \dfrac 83 x + \dfrac 53 \\\\\\\text{The above equation is in a form of y = mx +b where b is the y-intercept}\\\\\text{Hence}~ \dfrac 53~ \text{is the y-intercept}[/tex]

Answer:

11

Step-by-step explanation:

You would need to -3 on both sides to get:

-11x = -121.

To find x on it's own you would have to divide by -11 on both sides.

You would get a result of x = 11.

Hope this helps :)

Answer:

You would need the intial fee in dollars/cents

Expression:

c=initial fee

x=amount of miles

[tex]1.80x+c=12[/tex]

Step-by-step explanation:

You would need the intial fee in dollars/cents

Expression:

c=initial fee

x=amount of miles

[tex]1.80x+c=12[/tex]

Answer:

60

Step-by-step explanation:

y =  k/x ( as y is inversely proportional to x)

yx = k

--> k = yx

k = (6)(10)

k = 60

Enjoy it. I hope it will help you.

Answer:

Using function concepts, it is found that the domain of the function that model this phenomenon is [0, 12].

The domain of a function is the set that contains all possible input values.

In this problem, the function is the height of the bamboo according to the month of the year, hence, the input is the month of the year, which has values between 0 and 12, and thus, the domain of the function that model this phenomenon is [0, 12].

A similar problem is given at https://brainly.com/question/10891721

Answer:

E, -1/5

Step-by-step explanation:

The slope of a line, given the coordinates, can be written as m = (y2 - y1) / (x2 - x1), where x and y are points in the coordinates.

Let's look at the coordinates. (-5, 1), the first value in the brackets is always the x-coordinate and the second value is always the y-coordinate. So -5 is x and 1 is y. But we have to points, so -5 is x1 and 1 is y1, and -20 is x2 and 4 is y2.

By substituting

m = (4 - 1) / (-20 - [-5])

m = 3 / (-20 + 5)

m = 3 / -15

m = -1 / 5

[tex]\text{Given that,}~ (x_1,y_1) = (-5,1)~~ \text{and}~~ (x_2, y_2) =(-20,4)\\\\\\\text{Slope,}~ m =\dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{4 - 1}{-20 +5 } =-\dfrac 3{15} = - \dfrac 15[/tex]

we have: [tex]P=(7c-5) +(10c-2) + (7c-5) = 7c-5+10c-2 + 7c-5=24c-12[/tex]

ok done. Thank to me :>

Answer:

≈ 31.7 yd

Step-by-step explanation:

let the missing side be x , then using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 9² = 33²

x² + 81 = 1089 ( subtract 81 from both sides )

x² = 1008 ( take square root of both sides )

x = [tex]\sqrt{1008}[/tex] ≈ 31.7 yd ( to the nearest tenth )

Answer:

45*x-10

Step-by-step explanation:

10 less than a number would give you

x - 10

and the product of a number means your multiplying and your multiplying 45 so you would get

45*x

add them together and you get

45*x-10

The answer is P and R

Answer:

Q and R

Step-by-step explanation:

to be similar all sides must have the same scaling factor :

the factor from 2 to 8 is 4.

and the factor from 3 to 12 is also 4.

therefore, these 2 parallelograms are similar.

Answer:

9610/39

Step-by-step explanation:

You need to multiply 96.1 by the reciprocal of 39% to get the original number. 96.1x100/39 = 9610/39. This can also be rounded to 246.41

180 - 28 - 14 = 138

so 12x - 18 = 138

x = 13

Answer:

I hope this helps

Answer:

1/4

Step-by-step explanation:

The constant of proportionality is 1/4.

Answer:

b

Step-by-step explanation:

The form of an equation representing proportion is

y = kx ← k is the constant of proportionality

y = [tex]\frac{1}{4}[/tex] x ← is in standard form

with k = [tex]\frac{1}{4}[/tex]

I honestly don't know but I think it would come out to be 4/5

Answer:

-1+13=4v

12=4v

v=3

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