A blood sample has 50,000 bacteria present. a drug fights the bacteria such that every hour the number of bacteria remaining, r(n), decreases by half. If r(n) is an exponential function of the number, n, of hours since the drug was taken, find the bacteria present four hours after administering the drug.

Answer:

a, 1,<Z b, 1,zy c,XZY

2,<Y 2, zx

3, <X 3, xy

Answer:

First rememeber that if we have a function like:

g(x) = x^n

then:

dg(x)/dx = g'(x) = n*x^(n - 1)

And also if we have:

g(x) = f(x) + h(x)

then:

dg(x)/dx = g'(x) = f'(x) + h'(x)

1) We have the function f(x) = (x + 1)^2

We can rewrite this as:

f(x) = x^2 + 2*x + 1

Using both things written above, we know that:

f'(x) = 2*x + 1*2 = 2*x + 2

And we want to find f'(-2), so we only need to evaluate the above function in x = -2, this is:

f'(-2) = 2*-2 + 2 = -4 + 2 = -2

f'(-2) = -2

b) I suppose that this refers to the inverse function of f(x)

An inverse function is such that:

g( f(x)) = x

f( g(x)) = x

For f(x) = (x + 1)^2

The inverse will be something that first cancels that square, and then subtracts 1.

Then:

g(x) = √x - 1

if we evaluate this in f(x) we get:

g( f(x)) = √(f(x)) - 1 = √(x + 1)^2 - 1 = (x + 1) - 1 = x

Then the inverse function of f(x) is:

g(x) = √x - 1

This can also be written as:

g(x) = x^(1/2) - 1

Then the derivative of this will be:

g'(x) = (1/2)*x^(1/2 - 1) = (1/2)*x^(-1/2) = (1/2)*(1/√x)

Answer:

Janelle is applying to work a full-time job next summer. So far, her only paid work experience has involved with babysitting. She's worried that she lacks the skills

£120.02

£130.98

£1,376

Answer:

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Remember that all triangles equal 180. Add 50 and 85. It equals 135. Subtract that from 180 and it equals 45.

Answer:

B. 13 units

Step-by-step explanation:

Hope this helps

Answer:

8

Step-by-step explanation:

40/5 = 8

56/7 = 8

64/8 = 8

Answer:

7, 12, 17, 22     rule: add 5.     1. 27  2. 32

Step-by-step explanation:

this is your equation all you have to do is count the sticks figure out the rule once done then you add to the numbers you already have based on the rule which is add 5.

Answer:

C= 45 + 19.95h

Step-by-step explanation:

45 for each home vist means one time payment

19.95 ever hour means you are charged 19.95 every hour

H= hour

Answer:

-64123.2679492

Step-by-step explanation:

I'm sorry if this is wrong!

Answer:

Slope: 10

Y-intercept= 30

Step-by-step explanation:

y= mx + b

m = slope

b = y-intercept

y= 10x + 30

Slope: 10

Y-intercept= 30

Answer:

A

Step-by-step explanation:

Answer:

A) (4,8) is the correct answer.

Step-by-step explanation:

Step: Solvey=2xfor y:

y=2x

Step: Substitute2xforyiny=x+4:

y=x+4

2x=x+4

2x+−x=x+4+−x(Add -x to both sides)

x=4

Step: Substitute4forxiny=2x:

y=2x

y=(2)(4)

y=8(Simplify both sides of the equation)

Hope this helps!

Answer:

The answer is 7z-7. Hope this helped!

Step-by-step explanation:

9514 1404 393

Answer:

  sin(63°) = 0.891

Step-by-step explanation:

The cosine of an angle is the sine of its complement. The angle with a sine of 0.891 is 90° -27° = 63°.

   sin(63°) = 0.891

Answer:

acute angle

Step-by-step explanation:

acute angle because it is under 90°

If the angle measure is less than 90 degrees then it's acute, if it is equal to 90 degrees it's right or square, if it's more than 90 degrees it's obtuse, and if it's equal to 180 degrees it's a straight angle but in this case it's straight and obtuse since 180 is greater than 90.

Question:

Which equation represents a proportional relationship that has a constant of proportionality equal to 4/5

Answer:

[tex]y = \frac{4}{5}x[/tex]

Step-by-step explanation:

Required

Equation with 4/5 as its constant of proportion

Two proportional quantities x and y have the following relationship:

[tex]y = kx[/tex]

Where k is the constant of proportion.

In this case:

[tex]k = \frac{4}{5}[/tex]

So.

[tex]y = kx[/tex] becomes

[tex]y = \frac{4}{5}x[/tex]

Answer:

1439.4702≈1439

Answer:

this question doesn't make sense

Answer:

the slope of the line that lies on those two points is 11/7

Step-by-step explanation:

insert the first point into y=mx+b

14=(-7)m+b

----------------

Do it again with the other point

3=(-14)m+b

-------------

Now put both equations in a system of equations

14=(-7)m+b

3=(-14)m+b

solve for m and b

m=11/7 and b=25

y=11/7x+25

m=slope

b=y-intercept

Hope that helps :)

Please give brainliest

Given two variables x and y, y is directly proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k such that

   y = kx,

The relation is often denoted, using the ∝ symbol, as

   y ∝ x

in this case k = 5/1

The answer is B............

Answer:

B

Step-by-step explanation:

Your answer is B because 0 is greater than any negative number. Also, it is a solid line and full dot meaning the less than sign gets a line under it.

Answer:

x=23

Step-by-step explanation:

90 - 65 = 25

25 - 2 =23

Answer:

arc RS = 116°

Step-by-step explanation:

Since the 2 chords are congruent then their minor arcs are congruent, that is

SR = TU, substitute values

6x - 28 = 4x + 20 ( subtract 4x from both sides )

2x - 28 = 20 ( add 28 to both sides )

2x = 48 ( divide both sides by 2 )

x = 24

Then

arc RS = 6x - 28 = 6(24) - 28 = 144 - 28 = 116°

Answer:

83 is the answer

Step-by-step explanation:

hope this helps

Answer:

[tex]\sin Y= \frac{XZ}{XY}[/tex]

[tex]\cos Y= \frac{YZ}{XY}[/tex]

[tex]\tan Y= \frac{XZ}{YZ}[/tex]

Step-by-step explanation:

Given

See attachment for triangle

Required

Find [tex]\sin, \cos[/tex] and [tex]\tan[/tex] of angle Y

For angle Y:

[tex]Opposite = XZ[/tex]

[tex]Adjacent = YZ[/tex]

[tex]Hypotenuse = XY[/tex]

The [tex]\sin[/tex] of an angle is calculated as:

[tex]\sin\theta = \frac{Opposite}{Hypotenuse}[/tex]

So:

[tex]\sin Y= \frac{XZ}{XY}[/tex]

The [tex]\cos[/tex] of an angle is calculated as:

[tex]\cos\theta = \frac{Adjacent}{Hypotenuse}[/tex]

So:

[tex]\cos Y= \frac{YZ}{XY}[/tex]

The [tex]\tan[/tex] of an angle is calculated as:

[tex]\tan\theta = \frac{Opposite}{Adjacent}[/tex]

So:

[tex]\tan Y= \frac{XZ}{YZ}[/tex]

Answer:

C, short answer

Step-by-step explanation:

trust