What is the solution to the system of equations?
{x+y=4
{x=y=1
O (3, 1)
O (2, 2)
O (1/2, 3/2)

Answer:

5

Step-by-step explanation:

8235

Answer:

a. dQ/dt = -kQ

b. [tex]Q = 9e^{-kt}[/tex]

c. k = 0.178

d. Q = 1.063 mg

Step-by-step explanation:

a) Write a differential equation for the quantity Q of hydrocodone bitartrate in the body at time t, in hours, since the drug was fully absorbed.

Let Q be the quantity of drug left in the body.

Since the rate of decrease of the quantity of drug -dQ/dt is directly proportional to the quantity of drug left, Q then

-dQ/dt ∝ Q

-dQ/dt = kQ

dQ/dt = -kQ

This is the required differential equation.

b) Solve your differential equation, assuming that at the patient has just absorbed the full 9 mg dose of the drug.

with t = 0, Q(0) = 9 mg

dQ/dt = -kQ

separating the variables, we have

dQ/Q = -kdt

Integrating we have

∫dQ/Q = ∫-kdt

㏑Q = -kt + c

[tex]Q = e^{-kt + c}\\Q = e^{-kt}e^{c}\\Q = Ae^{-kt} (A = e^{c})[/tex]

when t = 0, Q = 9

[tex]Q = Ae^{-kt} \\9 = Ae^{-k0}\\9 = Ae^{0}\\9 = A\\A = 9[/tex]

So, [tex]Q = 9e^{-kt}[/tex]

c) Use the half-life to find the constant of proportionality k.

At half-life, Q = 9/2 = 4.5 mg and t = 3.9 hours

So,

[tex]Q = 9e^{-kt}\\4.5 = 9e^{-kX3.9}\\\frac{4.5}{9} = e^{-kX3.9}\\\frac{1}{2} = e^{-3.9k}\\[/tex]

taking natural logarithm of both sides, we have

[tex]ln\frac{1}{2} = ln(e^{-3.9k})\\\\-ln2 = -3.9k\\k = -ln2/-3,9 \\k = -0.693/-3.9\\k = 0.178[/tex]

d) How much of the 9 mg dose is still in the body after 12 hours?

Since k = 0.178,

[tex]Q = 9e^{-0.178t}[/tex]

when t = 12 hours,

[tex]Q = 9e^{-0.178t}\\Q = 9e^{-0.178X12}\\Q = 9e^{-2.136}\\Q = 9 X 0.1181\\Q = 1.063 mg[/tex]

Answer: It is 16/21

Step-by-step explanation: Once you find a common denominator just add the top and leave the bottom alone

Answer:

16/21

Step-by-step explanation:

Answer:

rational expressions

hope I helped! :)

Answer:

f(-2) ≈ 2.00

Step-by-step explanation:

f(x) = e^(4x + 2) + 2

At x = -2

f(-2) = e^(4(-2) + 2) + 2

f(-2) = e^(-8 + 2) + 2

f(-2) = e^(-6) + 2

use calculator

f(-2) = 0.002478752176666 + 2

f(-2) = 2.002478752176666

Rounded to 2DP

f(-2) ≈ 2.00

Answer:

x = 9

Step-by-step explanation:

first, you would subtract 1 from 80 and get -9x = -81 then you can just divide -81 by -9 or 9 from 81, either way, you'll have x = 9

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\boxed{x=9}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving the Equation for 'x':}}\\\\-9x+1=-80\\---------\\\rightarrow -9x+1-1=-80-1\\\\\rightarrow -9x=-81\\\\\rightarrow\frac{-9x=-81}{-9}\\\\\rightarrow \boxed{x=9}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

B. n + 6 = 12

C. 4 • 6 = 24

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

The answer is b. n+6 and c. 4×n=24.

hope this helps,have a great day!!

~Pinky~

Answer:

any number goes down 3 places

Step-by-step explanation:

EX:10 to the power of -3 = 0.001

The standard deviation of 83 million eggs and 2,655 millions eggs represent that of 3% of the farmers, of the production that is normally distributed, indicates that the mean egg production by Queensland farmers is about 2498.1 million eggs.

A normal distribution is a probability distribution such that the values of the distribution are symmetrical around the mean value of the distribution.

The standard deviation, σ = 83 million eggs

The percentage of farmers that produce more than 2,655 million eggs, x = 3%

The formula for the z-score is; [tex]Z = \dfrac{x - \mu}{\sigma}[/tex]

Therefore, we get;

[tex]Z = \dfrac{2655 - \mu}{83}[/tex]

From the z-score table for P(Z > Z₁), where Z₁ is the z-score corresponding to Φ(1 - 0.03) = Φ(0.97)

The z-value corresponding to Φ(0.97) is about 1.89

Therefore;

[tex]Z = \dfrac{2655 - \mu}{83} \approx 1.89[/tex]

83 × 1.89 ≈ 2655 - μ

μ ≈ 2655 - 83 × 1.89 = 2498.1

The mean egg production by Queensland farmers is about 2498.1 million eggs per year

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Answer:

6 the last one

Step-by-step explanation:

4704/6=784

784 squared is 28

making it a perfect square unlike the rest which have excess numbers after the decimal

Answer:

6

Step-by-step explanation:

WHEN YOU DIVIDE 4704 BY 6 YOU GET 784

IN ORDER TO GE THE PERFECT SQUARE YOU HAVE TO FIND THE LCM O 4704

Answer: 70

Step-by-step explanation:

the correct answer is 70

The lines FE and GH are parallel to each orther.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Given that

ΔPEI = ΔGHI

here ∠pie = ∠gih

PI =HI

GI=EI

So both triangles are congruent

So the FE║GH.

Hence the lines FE and GH are parallel to each orther.

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Answer: 12/13, i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope of a line given two points [tex](x_0,y_0)[/tex] and [tex](x_1,y_1)[/tex] is

[tex]m=\frac{y_1-y_0}{x_1-x_0}=\frac{15-(-12)}{18-2}=\frac{27}{16}[/tex]

An equation may have more than one solution.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The variable's value for which the equation holds true is referred to as the equation's solution. If the LHS and RHS are switched, an equation doesn't change. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.

Steps to solve a linear equation:

1. If necessary, remove the parentheses and use the distributive property.

2. By merging like terms, make both sides of the equation simpler.

3. The LCD (least common denominator) of all the fractions should be multiplied by both sides of the equation if there are any fractions.

4. If the equation contains decimals, multiply both sides by the lowest power of 10 to make the result a whole number.

5. Using the addition and subtraction properties of equality, move the constant terms to the other side of the equation and the variable terms to the other.

6. Using the equality properties of multiplication or division, set the variable's coefficient to 1.

7. Get the answer by isolating the variable.

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The length of AB in the line segment is 21 units.

A line segment is bounded by two distinct points on a line. In other words, a line segment is a part of a line that connects two points which are considered to be its endpoints.

Therefore, let's find the length AB, in the line segment AC.

Hence,

AC = AB + BC

AC = 23

AB = 2x + 7

BC = 3x - 19

Therefore,

23 = 2x + 7 + 3x - 19

23 = 5x  - 12

23 + 12 = 5x

35 = 5x

divide both sides by 5

x = 35 / 5

x = 7

Therefore,

AB = 2x + 7 = 2(7) + 7 = 14 + 7 = 21

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9514 1404 393

Answer:

  (c)  Not parallel: corresponding angles are not congruent

Step-by-step explanation:

The two angles shows are both "east" of the respective points of intersection, so are "corresponding" angles. If (and only if) lines r and s are parallel, corresponding angles are congruent. These angles have different measures, so lines r and s are not parallel.

Its 336 sorry if I'm wrong

Answer:

  c : d : u = 8 : 6 : 27

Step-by-step explanation:

Given c:d = 4:3 and d:u = 2:9, you want c:d:u.

To write the desired ratio, we need to convert the others so they have the same number of ratio units representing 'd'. That number can be the least common multiple of 3 and 2, which is 6. Knowing this, we can write ...

  c:d = 4:3 = 8:6

  d:u = 2:9 = 6:27

Then the desired ratio is ...

  c:d:u = 8:6:27

Answer:

5

Step-by-step explanation:

Answer:

y is 40.54 degrees

x is 49.46 degrees

Step-by-step explanation:

Recall that Pythagoras theorem states that

a^2 + b ^2 = c^2

where a and b are the opposite and adjacent sides of a right angled triangle and c is the hypotenuse side

Using the notation SOH CAH TOA

Sin y = 13/20 where 13 is the length of the opposite side and 20 is that of the hypotenuse side.

y = sin^-1 0.65

y = 40.54 degrees

Considering angle x,

Cos x = 13/20 where 13 is the adjacent side and 20 is the hypotenuse side

x = Cos^-1 0.65

= 49.46 degrees

Answer:

x=49

y=41

Step-by-step explanation:

Answer:

Graph 1: The slope is -1/1 or -1

Graph 2: The slope is -1/1 or -1

Step-by-step explanation:

I hope this helps!

Answer: The answer is 9.

Answer:

9

Step-by-step explanation:

4mp + 3n

Given:

m = 2

n = 3

p = 0

Work:

4mp + 3n

4(2)(0) + 3(3)

0 + 9

9

Answer:

1. true

2. false

3. false

4. true

Answer:

25%

Step-by-step explanation:

slope = (175-100)/300 = 75/300 = ¼

the percent slope = ¼×100%= 25%

Answer: y = -4

Step-by-step explanation:

y = 4x-6

y = 4(1/2)-6

y = 2-6

y = -4

Answer:

Step-by-step explanation:

Y = 4x - 6

Putting value of x = 1/2 in the equation

Y = 4(1/2) - 6

= 2 - 6

= - 4

Answer:

the flag is 50 feet long and 160 feet wide

Answer: The width is 330 feet and the length is 790 feet.

Step-by-step explanation:

     We will write a system of equations to help us solve. Let w be the width and l be the length.

2w + 2l = 2,240 ft

l = 460 ft + w

     Now, we will solve for w, the width, by substituting one equation into the other.

2w + 2l = 2,240 ft,       l = 460 ft + w

2w + 2(460 ft + w) = 2,240 ft

2w + 920 ft + 2w = 2,240 ft

4w + 920 ft = 2,240 ft

4w = 1,320 ft

w = 330 ft

     The width is 330 feet.

     Now, we will solve for l, the length.

l = 460 ft + w,          w = 330 ft

l = 460 ft + 330 ft

l = 790 ft

     The length is 790 feet.

Answer:

x = 2

Step-by-step explanation:

2 + 3 = 5

Answer:

The right answer is C ( π/2)