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2 years ago

Solve for x (12x-7)/4=(5x+18)/3

Mathematics

1 answer:

poizon [28]2 years ago

4 0

Answer:

x = 5.81

Step-by-step explanation:

3(12x-7) = 4(5x+18)

36x-21 = 20x +72

16x = 93

x = 5.81

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Suppose that a Petri dish initially contains 2000 bacteria cells. An antibiotic is introduced and after 4 hour, there are now 16

Sergeu [11.5K]

Answer:

a)The linear function for $P(t)$ is:

$P(t) = 2000 - 100*t$

b)The exponential function for $P(t)$ is:

$P(t) = 2000e^{-0.055t}$

Step-by-step explanation:

(a) Suppose that P(t) is a linear function. Find a formula for P(t):

$P(t)$ can be modeled by a linear function in the following format.

$P(t) = P_{0} - r*t$ , in which $P_{0}$ is the initial number of bacteria cells in the dish, t is the time and r is the rate that the number decreases.

Since the dish initially contains 2000 bacteria cells, $P_{0} = 2000$

We have

$P(t) = 2000 - r*t$

An antibiotic is introduced and after 4 hour, there are now 1600 bacteria cells present. So $P(4) = 1600$ . With this information, we can find the value of r.

$P(t) = 2000 - r*t$

$1600 = 2000 - r*(4)$

$4r = 400$

$r = \frac{400}{4}$

$r = 100$

So, the linear function for $P(t)$ is:

$P(t) = 2000 - 100*t$

b) Suppose that P(t) is an exponential function. Find a formula for P(t)

$P(t)$ can also be modeled by an exponential function in the following format:

$P(t) = P_{0}e^{rt}$

The values mean the same as in a). We use the fact that $P(4) = 1600$ to find r.

$P(t) = 2000e^{rt}$

$1600 = 2000e^{4r}$

$e^{4r} = \frac{1600}{2000}$

$e^{4r} = 0.8$

$ln e^{4r} = ln 0.8$

$4r = -0.22$

$r = \frac{-0.22}{4}$

$r = -0.055$

So, the exponential function for $P(t)$ is:

$P(t) = 2000e^{-0.055t}$

5 0

4 years ago

DaMarcus says the number 24/6 belongs only to the set of rational numbers. Explain his error.

ElenaW [278]

24/6 = 4. The eror is that 4 is not only in the set of rational numbers, but is also part of natural numbers, integers, and whole numbers.

7 0

3 years ago

For each ordered pair, determine when weather it’s a solution to 7x -6y=19

kumpel [21]

<h3>Answer:</h3>

Options A and B

<h3>Solution:</h3>

In order to determine whether or not an ordered pair is a solution to an equation, plug in the values of x and y:
7x-6y=19
7(7)-6(5)=19
49-30=19
19=19
We have a true statement. Therefore, the ordered pair is a solution to the equation 7x-6y=19.
Let's try the other ordered pairs.
7(1)-6(-2)=19
7+12=19
19=19
Here's another true statement.
Let's check the remaining two options:
7(-5)-6(3)=19
-35-18=19
-53≠19
Here we have a false statement.
7(-4)-6(0)=19
-28-6=19
-34≠19
Therefore, the ordered pairs that make this equation true are (7,5) and (1,-2)

Hope it helps.

Do comment if you have any query.

7 0

3 years ago

PLEASE HELP IM ON A TIMED TEST

Mila [183]

Answer:

third term

Step-by-step explanation:

hope this helped

6 0

3 years ago

A rectangle has a length 6 meters longer than double the width. The perimeters is i44 meters. Find the dimensions of the rectang

Oksana_A [137]

Use the information to form an equation
x = width
x + 6 = length
perimeter = length + length + width + width
x + x + x + 6 + x + 6 = 44
4x + 12 = 44
4x = 32
x = 32/4
x = 8
width = 8 meters
length = 8 + 6 = 14 meters

8 0

3 years ago