Using the proportion you found in Question 3, write an equation for the length of arc EF in terms of the radii of AB and AC and the length of arc CD.

Using exponential functions, it is found that:

a) Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.

b) The patient could have ingest 231 milligrams of caffeine.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem:

Then:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = A(0)(1 - 0.13)^t[/tex]

[tex]A(t) = A(0)(0.87)^t[/tex]

Item a:

The coffee cup contains 150 milligrams of caffeine, hence [tex]A(0) = 150[/tex].

At 6 a.m., it is 8 hours after drinking the coffee, hence we have to find A(8).

[tex]A(t) = A(0)(0.87)^t[/tex]

[tex]A(8) = 150(0.87)^8[/tex]

[tex]A(8) = 49.2[/tex]

Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.

Item b:

This A(0), considering A(11) = 50, hence:

[tex]50 = A(0)(0.87)^{11}[/tex]

[tex]A(0) = \frac{50}{(0.87)^{11}}[/tex]

[tex]A(0) = 231[/tex]

The patient could have ingest 231 milligrams of caffeine.

A similar problem is given at https://brainly.com/question/25537936

Proof:-

In ∆TOP and ∆ZAP

[tex]\because\sf\begin{cases}\sf <O\cong <A(Given)\\ \sf TO\cong AZ(Given)\\ \sf <TPO\cong <ZPA(Opposite angles)\end{cases}[/tex]

Hence

∆TOP[tex]\cong[/tex]∆ZPA(Side-Angle-Side)

Step-by-step explanation:

Statement                                                  Reason

∠O ≅ ∠A                                                    Given

TO ≅ AZ                                                    Given

∠OPT and ∠ZPA are vertical angles       Vertical angles theorem

∠OPT ≅ ∠ZPA                                           Definition of vertical angles

ΔTOP ≅ ΔZAP                                           Angle - angle -side AAS postulate

Answer:

Yes, it is a solution.

Step-by-step explanation:

Plug in 2 into x and 6 into y, because 2 is the x value of the ordered pair and 6 is the y value of the ordered pair.

1st linear equation: 2+6=8, this is true.

2nd linear equation: 3x2-6=0, this is also true.

Therefore, since the ordered pair is a solution to both equations, it is a solution of the linear system.

Answer:

Which Restaurant and aquarium

Step-by-step explanation:

If you tell the name I can answer it

Answer:

Step-by-step explanation:

9.43

Answer:

(7 , 7.75)

Step-by-step explanation:

Answer:

See attached

Step-by-step explanation:

A simpler form of the same equation is:

y = -4 +(4+2/5)

Answer:

A biconditional statement is a combination of a conditional statement Its converse written in the if and only form

Answer:

1, 3

Step-by-step explanation:

// Solve equation [2] for the variable  y  

  [2]    y = x - 2

// Plug this in for variable  y  in equation [1]

[1]    (x -2) + x = 4

  [1]    2x = 6

// Solve equation [1] for the variable  x  

[1]    2x = 6  

[1]    x = 3  

// By now we know this much :

y = x-2

x = 3

// Use the  x  value to solve for  y  

 y = (3)-2 = 1

Answer:

equilateral triangle

Step-by-step explanation:

B. equilateral triangle

One theme of the poem Dream variations is the desire to live freely and expressively (option A).

In poems and other literary texts, themes are deep ideas about life that are indirectly expressed by the author. In the case of the poem "Dream variations", the author Langhtons Hughes refers to life and death.

About life, Hughes expresses the importance of living life at its fullest before death occurs. This desire to live freely and expressively is shown in verses such as:

         In the face of the sun"

or in

Learn more about poem in: https://brainly.com/question/9527212

Answer:

Step-by-step explanation:

I took the quiz :)

Answer:

That seems a little hard-

Step-by-step explanation:

Answer:

$220

Step-by-step explanation:

If seven tickets cost 385, then 1 ticket costs one-seventh of that amount, so we divide it by 7 to see how much one ticket costs.

385/7 = 55

One ticket is $55. To find out how much 4 tickets cost, multiply 55, the price of one ticket, by 4.

55 * 4 = 220

$ tickets cost $220

Answer:

405

Step-by-step explanation:

divide 270 by 6 the multiply what you got with 9

:)

If your looking for Standard Form Rewrite it as... [tex]7x^5+7x^3[/tex]

Answer:

160.93

Step-by-step explanation:

I'm not that great at math so forgive me if I'm wrong, but from my knowledge the answer would be 160.93 since you're multiplying 16.093 to 10.

hope this helped! :)

Step-by-step explanation:

Since the first coordinates are both (0,0) it implies that the line passes through the origin.

The slope of the line is therefore 5/8

The equation:

y-0=5/8(x-0)

y=5/8x

Answer:

The slopes are equal

Step-by-step explanation:

Calculate the slope m of f(x) using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m = [tex]\frac{2-5}{0-(-1)}[/tex] = [tex]\frac{-3}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

g(x) = - 3x - 6 ← is in slope- intercept form

with slope m = - 3

Then the slopes of f(x) and g(x) are equal, meaning the lines are parallel

Answer:

Thats one heck of a whole lot nuts

Step-by-step explanation:

Answer: a 15y=18 and c 5y+4=10

Step-by-step explanation:

1. -2 + 15 = 13

If the temperature is -2 and it rises 15 degrees, the new temperature is 13 degrees.

2. The temperature rose 15 degrees

-6 + 9 = 15

Answer:

1 a) 13 degrees Celsius

b) By fifteen degrees

Step-by-step explanation:

a ticket for 3 days cost = 35968

cost of 1 ticket = 35967÷3= 11989.33

therefore, 500 tickets cost= 500 x 11989.33

= 5994666.666, approximately 5994667

Answer: A = 15 + 0.5(w)

Step-by-step explanation: The above equation represents the amount of dollars after selling w cups of water. Remember: we also have 15 in advance, so we add that to the total amount of cups sold. We multiply 0.5 (the amount earned per water cup) by w (the number of water cups sold) and we will get our answer.

To check this, let's say we sold 10 water cups. So w = 10. Therefore, we write A = 15 + 0.5(10). That = A = 15 + 5 which A = 20. We can use any number in place of w now and we will know it is correct using this formula

Answer:  Graph is below

=============================================================

Explanation:

We divide both sides by -4 to isolate p. This will flip the inequality sign.

-16 > -4p

-16/(-4) < -4p/(-4)

4 < p

p > 4

The graph has an open hole at 4 and shading to the right. See below.

The solution of the inequality - 16 > - 4p is shown in number line as given below in figure.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

The inequality is,

⇒ - 16 > - 4p

Now, Solve the inequality as;

⇒ - 16 > - 4p

Multiply by -1;

⇒ 16 < 4p

Divide by 4;

⇒ 4 < p

Thus, The solution of the inequality is,

⇒ 4 < p

And, This is shown in number line.

Learn more about the number line visit:

https://brainly.com/question/28223520

#SPJ2

Answer:

  D.  f(x) = -6x^3 -5x^2 +21x

Step-by-step explanation:

The given zeros mean the function has factors ...

  (x -(-7/3))(x -3/2)(x -0)

Multiplying by 6, we can write this as ...

  (3x +7)(2x -3)(x) = 6x^3 +5x^2 -21x

And multiplying by -1 gives ...

  -6x^3 -5x^2 +21x . . . . . matches choice D

__

Additional comment

The product of factors will be zero when f(x) = 0. This means we can multiply or divide by any convenient factor and the product will remain zero. Effectively, we have multiplied our original factorization by -6 to make the expression match one of the given forms. When we write this final expression as the function f(x), it remains true that the given zeros are zeros (x-intercepts) of f(x).

Answer:

PROOF FOR THE "PROVE" SECTION:

As linear pairs, angle 2 and 3 are supplementary to each other. Angle 1 is equal to angle 2, as they are both same-side interior angles. Therefore, angle 1 and angle 3 are also supplementary.

Filling in the missing blanks:

S1. Angle 1, Angle 2, Angle 3

S2. Angle 1 and Angle 2

R3. Congruent (___)

R5. supplementary angles

S7. Angle 1 = Angle 2, so Angle 1 can be substitued in for Angle 2 in any equation, and Angle 2 can be substitued for Angle 1 in any equation as well (they can replace each other, like x=y & y=x or a=b & b=a)

Hope this helped! Have a great day (pls mark brainliest)!!