All categories

4 years ago

A population of rabbits triples every month.the population starts with two rabbits.how many rabbits are there after 3 month's

1 answer:

7 0

The answer would be 54. Because you start with 2.
2x3 = 6
6x3 = 18
18x3 = 54
Each month it triples so you continue
to add 3 to each result.

You might be interested in

Determine whether each function has an inverse function. If it does, find the inverse function and state any restrictions on its

Talja [164]

QUESTION 1

The given function is;

$f(x) = |x - 6|$

This is an absolute value function.

For this function to have an inverse it must be a one-to-one function.

This absolute value function is not one-to-one
because

$f( 5)=1$
and

$f(7) = 1$

Since this function has more than one x-value mapping onto one y-value, it is not one-to-one and cannot have an inverse.

You can see from the graph that this function cannot pass the horizontal line test.

QUESTION 2

The given function is

$f(x) = \sqrt{6 - {x}^{2} }$

Let

$y= \sqrt{6 - {x}^{2} }$

This implies that,

${y}^{2} + {x}^{2} = 6$

We see clearly that, this function is a circle that is centered at the origin.

This means that,

$f(x) = \sqrt{6 - {x}^{2} }$

is a semicircle.

This function will not pass the horizontal line test and hence does not have an inverse.

QUESTION 3

The given function is

$h(x) = \frac{x+4}{3x-5}$

If we put

$h(a) = h(b)$

We obtain,

$\frac{a+4}{3a-5} = \frac{b+4}{3b-5}$

$(a + 4)(3b - 5) = (b + 4)(3a - 5)$

$3ab - 5a + 12b - 20 = 3ab - 5b + 12a - 20$

$- 17a = - 17b$

$a = b$

This shows that h(x) has an inverse because it is one-to-one.

Let

$y=\frac{x+4}{3x-5}$

We interchange x and y to get,

$x=\frac{y+4}{3y-5}$

$x(3y - 5) = y + 4$

$3xy - 5x = y + 4$

Group like terms to get,

$3xy - y = 5x + 4$

Factor to get,

$y(3x - 1) = 5x + 4$
Solve for y,

$y = \frac{5x + 4}{3x - 1}$

Hence

${f}^{ - 1}(x) = \frac{5x + 4}{3x - 1}$

where

$x \ne \frac{1}{3}$

6 0

3 years ago

(29 points) <br><br> what is the slope of the line that passed through the points (3,-1) and (-2,-5)

Fynjy0 [20]

Hey there! We can get slope using the formula:

$\frac{y2 - y1}{x2 - x1}$

Let's gather our information:

X1 = 3

Y1 = -1

X2 = -2

Y2 = -5

$\frac{-5 -(-1)}{-2 - 3} = \frac{-4}{-5} = \frac{4}{5} = .80$

Slope(m) = .80

6 0

3 years ago

According to your model, as the population of San Francisco was revitalizing, for what value of the independent variable t did i

vampirchik [111]

Answer:

t =1.453 decades from 1980 i.e in year 1994.5

Step-by-step explanation:

Given:

- Population @ year 1980 P = 678.97 thousands.

- Population @ year 2000 P = 776.73 thousands.

- The rate of increase is linear - constant rate.

Find:

As the population of San Francisco was revitalizing, for what value of the independent variable t did it reach 750 thousand ?

Solution:

- Develop an expression of population P as a function of time t in decades elapsed from year 1980 on-wards

- The linear expression can take a form of :

P(t) = m*t + C

- Where, m is the rate of increase.

C is the initial population.

- Formulate m:

m = (776.73 - 678.97) / 2 = 48.88

- Formulate C:

C = P (@ 1980) = 678.97

- Evaluate P(t) = 750:

P(t) = 48.8*t + 678.97

750 = 48.8*t + 678.97

t = 71.03/48.8

t =1.453 decades

5 0

4 years ago

Review the work showing the first few steps in writing a partial fraction decomposition.

allochka39001 [22]

Answer:

8/(x + 2) - 4/(x + 6)

Step-by-step explanation:

4x + 40 = Ax + 6A + Bx + 2B

Equating coefficients of x

4 = A + B (1)

Equating constant terms:

40 = 6A + 2B (2)

Multiply equation (1) by -2:

-8 = -2A - 2B .. (3)

Add (2) and (3):

32 = 4A

A = 32/4

A = 8.

4 = 8 + B

B = 4 - 8

B = -4.

7 0

2 years ago

If mZDEC = (12x - 3), mZBCE =

kati45 [8]

Answer:

Step-by-step explanation:

12x - 3 = 180 - (7x - 26) supplementary angles

19x = 209

x = 11

m∠DEC = 12(11) - 3 = 129°

m∠BCE = 7(11) - 26 = 51°

M∠ADE = 129 - 72 = 57° exterior angle rule

m∠EDB = 180 - 57 = 123° supplementary angles

m∠DBC = 57° corresponding angle to ADE

3 0

3 years ago