Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.

If x∆y = 3x - y², then

5∆1 = 3×5 - 1² = 15 - 1 = 14

and

14∆6 = 3×14 - 6² = 42 - 36 = 6

So (5∆1)∆6 = 6.

Answer:

when (-1, -4) is substituted into the first equation it's true

when (-1, -4) is substituted into the second equation it's true

the ordered pair (-1, -4) is a solution to the systems of equation

Step-by-step explanation:

original equation

x-y=3

multiply both sides by 7

7x-7y = 21

add 7y to both sides

7x=7y + 21

substitute into second equation

(7y+21)-y=-3

simplify

6y+21=-3

subtract 21 from both sides

6y=-24

y=-4

substitute y into original equation

x-(-4) = 3

cancel out negative signs

x+4=3

subtract -4 from both sides

x=-1

Answer:

8/3

Step-by-step explanation:

4 x 2 = 8, so (4 × 2)/2 = 8/3.

Answer:

Maybe    9     and 12   ?

Step-by-step explanation:

-6 + 9 = 3  

    then   3 + 9 = 12

           then 12 + 3 = 15      

                 each term is the sum of the two that are before it

Answer: 189/760

Step-by-step explanation:

The series can be represented in sigma notation as:

[tex]\sum^{18}_{n=1} \frac{1}{n(n+1)(n+2)}[/tex]

We can perform partial fraction decomposition as follows:

[tex]\frac{1}{n(n+1)(n+2)}=\frac{A}{n}+\frac{B}{n+1}+\frac{C}{n+2}\\\\ \implies 1=A(n+1)(n+2)+B(n)(n+2)+C(n)(n+1)[/tex]

If n = 0, then [tex]1=A(0+1)(0+2) \implies A=\frac{1}{2}[/tex]

If n = -1, then [tex]1=B(-1)(-1+2) \longrightarrow B=-1[/tex]

If n = -2, then [tex]1=C(-2)(-2+1) \longrightarrow C=\frac{1}{2}[/tex]

This means the series can be expressed as:

[tex]\sum^{k}_{n=1} \left(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2(n+2)} \right)=\frac{k(k+3)}{4(k+1)(k+2)}[/tex]

Substituting in k=18,

[tex]\frac{18(21)}{4(19)(20}=\boxed{\frac{189}{760}}[/tex]

Answer:

The answer is y = -4x+11

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Answer:  [tex]\textsf{Option D, y = 2x - 3}[/tex]

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Given: [tex]\textsf{The graph}[/tex]

Find: [tex]\textsf{The equation in slope intercept form}[/tex]

Solution: Looking at the graph, we can see that the line intersects the y-axis at -3 therefore that is the y-intercept.  All we need to do now is find a second point so we can determine the slope.  The line crosses at (1, -1) so we will use that as the second point.  Then we just plug all of the values into the slope intercept form.

Determine the slope

Plug in the values

Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.

Answer:

[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]

Step-by-step explanation:

(3a³-6b³) (4a² + 5b²) -> Simplify not Multiply

Expand (3a³-6b³) (4a² + 5b²) using the FOIL Method.

Apply the distributive property.

[tex]3a^3(4a^2+5b^2)-6b^3(4a^2+5b^2)[/tex]

[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2+5b^2)[/tex]

[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]

Simplify each term.

Rewrite using the commutative property of multiplication.

[tex]3*4a^3a^2+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]

↓

[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]

Equation Simplified.

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Hope this helped!

Answer:

  (b)  0.5431

Step-by-step explanation:

The proportion of adult tickets sold is the ratio of the total number of adult tickets sold to the total number of tickets sold. Those totals are found on the bottom line of the table.

__

  proportion = (adult tickets)/(total tickets) = 126/232 ≈ 0.5431

Approximately 0.5431 of the tickets sold were adult tickets.

Answer:

B) 0.5431

Step-by-step explanation:

edge 2023

Answer:

1.37

Step-by-step explanation:

3^1=3/2=1.5

2^(1/3)=1.26

1.5×1.26=1.89

1.89^(1/2)=1.37

We found a counterexample, so the statement is false.

Let's use the matrix:

[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]

This is a 4x4 matrix with determinant equal to -2.

The inverse matrix is:

[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]

If we multiply it by 2, we get:

[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]

The adjoint of that is the original matrix, actually:

[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]

Which we already know, has a determinant of -2.

So the statement is false, as we found a counterexample.

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The statement is false, as the system can have no solutions or infinite solutions.

The statement says that a system of linear equations with 3 variables and 3 equations has one solution.

If the variables are x, y, and z, then the system can be written as:

[tex]a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3[/tex]

Now, the statement is clearly false. Suppose that we have:

[tex]a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3[/tex]

Then we have 3 parallel equations. Parallel equations never do intercept, then this system has no solutions.

Then there are systems of 3 variables with 3 equations where there are no solutions, so the statement is false.

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Answer:

D)

Step-by-step explanation:

47 is the right answer! Have an cool day!

The area of the piece of red paper after the hole for the photograph has been cut is,

⇒ 47 square units.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Now, First, find the area of the two squares:

The photograph have vertices:

(-3, -2), (-2, 2), (2, 1), and (1, -3).

Since, The square is diagonally aligned, so we need to find the length between two points in order to find the area.

For (1, -3) and (2, 1).

There is a 1 unit length and a 4 unit height.

We can use the Pythagorean theorem to find the hypotenuse of the triangle, which is the length of the square's side:

1² + 4² = x²

1 + 16 = x²

x = √17

The side length for the square of the photograph is the square root of 17,

so the area of the photograph is 17 units²

Now, The red paper has side lengths of 8. The distance between (-4, 4) and (4, 4) is 8 units wide, so we do not need to use the Pythagorean theorem.

Now , we know the area of the red paper and photograph, you can subtract the area to find the red paper with the hole:

64 - 17 = 47 square units.

Thus, The area of the piece of red paper after the hole for the photograph has been cut is,

⇒ 47 square units.

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Answer:

5√2, 5

Step-by-step explanation:

in a 90 45 45 triangle, each leg is the same legnth

the hypotenuse of a 90 45 45 triangle is x√2

x being the measure of the leg

Answer:

slope: -1

y-intercept: 6

Step-by-step explanation:

y-intercept is when x is 0 so it's 8 and the slope can be found using the slope formula (y2-y1)/(x2-x1)

(6-8)/(0 - (-2)) = -2/2 = -1

Answer:

For plato users, the answer would be letter C.

Step-by-step explanation:

A.

It represents neither a relation nor a function.

B.

It represents a relation only.

C.

It represents both a relation and a function.

D.

It represents a function only.

This equation represents both a relation and a function.

Took the test, hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

answer D    ( if i interpreted your question correctly )

Step-by-step explanation:

Sqrt (c^2)  = √(c^2) = C

The sum of the geometric series will be 1/4. And the sum of the series will be the negative 0.13.

The complete question is attached below.

Let a be the first term and r be the common ratio. Then the sum of the geometric series will be

S = a / (1 – r)     if r < 1

S = a / (r – 1)     if r > 1

The series is given below.

1/16 + 3/64 + 9/256 + 27/1024 ....

Then we have

a = 1/16

r = (3/64) / (1/16) = 3/4

Then the sum of the series will be

S = (1/16) / [1 – (3/4)]

S = (1/16) / (1/4)

S = 1/4

Let [tex]\rm S = (-0.13)^m[/tex], where m = 1

Then the value of S will be

S = (-0.13)¹

S = -0.13

Hence, the sum of the series will be the negative 0.13.

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y equals short dash 2 x minus 1

In other words, y = -2x - 1 is the equation

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Explanation:

Slope = m = -2

Point on the line is (x,y) = (1, -3)

Use these three items to find the y intercept b

y = mx+b

-3 = -2*1 + b

-3 = -2 + b

-3+2 = b

-1 = b

b = -1

The slope intercept form of y = mx+b turns into y = -2x-1 after plugging m = -2 and b = -1

Answer:

[tex]3^2=x+5[/tex]

Step-by-step explanation:

Given equation:

[tex]\log_3(x+5)=2[/tex]

Method 1

[tex]\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b[/tex]

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^2=x+5[/tex]

Method 2

Make both sides of the equation the index to base 3:

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^{\log_3(x+5)}=3^2[/tex]

Apply the log law [tex]a^{\log_ax}=x[/tex] :

[tex]\implies x+5=3^2[/tex]

Swap sides:

[tex]\implies 3^2=x+5[/tex]

Solve for x

Although the question hasn't asked to solve for x, here is the solution:

[tex]\implies 3^2=x+5[/tex]

[tex]\implies 9=x+5[/tex]

[tex]\implies x=9-5[/tex]

[tex]\implies x=4[/tex]

Check

Substitute the found value of x into the original equation:

[tex]x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}[/tex]

[tex]\\ \rm\Rrightarrow log_3(x+5)=2[/tex]

[tex]\\ \rm\Rrightarrow x+5=3^2[/tex]

[tex]\\ \rm\Rrightarrow x+5=9[/tex]

[tex]\\ \rm\Rrightarrow x=9-5[/tex]

[tex]\\ \rm\Rrightarrow x=4[/tex]

Question 1

We want to choose a white marble, then a black marble.

Multiplying these probabilities, we get (9/24)(8/24) = 1/8.

Question 2

Thus, the probability is 5/10 = 1/2.

Question 3

Multiplying these probabilities, we get (7/24)(9/23) = 21/184.

Answer:

Sorry I don't know the answer

The equation of the line with points (2,10) and (0,0) is: y = 5x.

The line given has two points which are stated as:

(2,10) and (0,0).

Find the slope(m):

Slope (m) = change in y / change in x = (10 - 0)/(2 - 0)

Slope (m) = 10/2

Slope (m) = 5

The y-intercept (b) = 0

Substitute m = 5 and b = 0 into y = mx + b

y = 5x + 0

y = 5x

The equation of the line is: y = 5x.

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Answer:

22/7

Step-by-step explanation:

22/7 is not very close to pi, but it is sometimes used as an estimation for pi

Answer:

22/7 is estimation

Answer: [tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]-3x(4x^2-81)(x^2+64)=0\\[/tex]

multiply the terms together

[tex]-12x^5-525x^3+15552x=0[/tex]

factor left side of the equation

[tex]3x(-x^2-64)(2x+9)(2x-9)=0[/tex]

set factors equal to 0

[tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]

Answer:

x = 4

Step-by-step explanation:

6x - 8 = 16 (add 8 to both sides)

6x = 24 (divide by 6 on both sides)

x = 4

Brainliest, please :)

Step-by-step explanation:

6x=16+8

6x=24

6x/6=24/6

x=4

so the answer is 4

Step-by-step explanation:

3x - 2 is formatted in the formula y = mx + c

To substitute for 3x - 2

y = 3x -2

Given the parameterization

[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]

take the normal vector to be

[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]

(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)

Compute the magnitude of the normal vector.

[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]

so that the area element reduces to

[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]

Evaluate the integrand at [tex]\vec r[/tex] to get

[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]

The surface integral reduces to

[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]