Given: f(x) = 4.1 42 4x-10 x-2 Determine the x- and y-intercepts of f. 4.3 a x=2² Write f(x) in the form: f(x)=- + q. Draw the graph of f, clearly show the intercepts with the axes and the asymptotes.: 15. 44 Give the equations of the asymptotes of f(x) + 3.​

a)The concentration will be 0.5 mg/L at approximately 1.18 hours.

c) [0, ∝) is a reasonable domain for this function.

d) The patient must receive the next intravenous dose of the drug between 0.75 and 1.35 hours after the initial dose.

e) The concentrations of the two drugs cannot be compared

A. To find when the concentration will be 0.5 mg/L, we can set the function equal to 0.5 and solve for t:

20t c(t)-20 2 +4 = 0.5

20t c(t)-20 2 = 3.5

20t c(t) = 2

3.5c(t) = 1.175

So the concentration will be 0.5 mg/L at approximately 1.18 hours.

B. Using the given formula, we can complete the table as follows:

| t    | c(t)         |

0    | 4            |

2    | 2.86        |

4    | 2.14         |

6    | 1.62         |

8    | 1.23         |

10   | 0.95         |

12   | 0.74         |

14   | 0.57         |

16   | 0.44         |

18   | 0.34         |

20   | 0.27        

C. Because time cannot be negative and the function has no imaginary values, the domain of the function is all non-negative real numbers.

As a result, [0,] is a reasonable domain for this function.

D. To maintain a concentration above 1 mg/L and below 8 mg/L, we need to solve the inequality:

1 < 20t

c(t)-20 2 +4 < 8

Simplifying this inequality, we get:

0.75 < t < 1.35

To maintain the desired concentration, the patient must receive the next intravenous dose of the drug between 0.75 and 1.35 hours after the initial dose.

E. Without additional information, we cannot compare the concentrations of the two drugs.

The information provided only allows us to analyze the intravenous drug concentration

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The theoretical probability of exactly 4 students from your school being selected as contestants out of 10 possible contestant spots is approximately 0.009.

Assuming that each member of the audience has an equal chance of being selected as a contestant, the total number of possible ways to select 10 contestants from the audience is:

[tex]150 $ choose 10 = 150! / (10! \times (150 - 10)!) = 2,535,316,699,000[/tex]

To calculate the probability of exactly 4 students from your school being selected as contestants, we need to count the number of ways this can happen and divide it by the total number of possible outcomes.

There are 30 students from your school and 120 students from other schools in the audience.

We need to choose 4 students from your school and 6 students from other schools for the contestant spots.

The number of ways to do this is:

[tex]30 $ choose 4 \times 120 $ choose 6 = (30! / (4! \times 26!)) \times (120! / (6! \times 114!)) = 23,400,140,040,000[/tex]

Therefore, the probability of exactly 4 students from your school being selected as contestants is:

P(4 students selected) = (number of ways to select 4 students from your school and 6 students from other schools) / (total number of ways to select 10 contestants from the audience)

P(4 students selected) = 23,400,140,040,000 / 2,535,316,699,000.

P(4 students selected) ≈ 0.00923 (rounded to 3 decimal places).

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Answer:

The equation of a line that is perpendicular to y = 3x + 3 is option A y equals negative one-third times x plus 1(-1/3x + 1)Given,The equation of line, y = 3x + 3The line passes through (-6, 3)We have to find the equation of the line that is perpendicular to y = 3x + 3Slope of the line, m = 3Here, in perpendicular case, slope is negative of its reciprocal.That is, m = -1/3Now, we can find the equationy - y₁ = m(x - x₁)

Here,

y₁ = 3x₁ = -6m = -1/3

So,y - 3 = -1/3(x - (-6))

y - 3 = -1/3(x + 6)

y - 3 = -1/3x + -1/3(6)

y - 3 = -1/3x - 6/3

y - 3 = -1/3

x - 2y = -1/3

x - 2 + 3

y = -1/3x + 1

That is, the equation of a line that is perpendicular to y = 3x + 3 is y equals negative one-third times x plus 1(y = -1/3x + 1)

Step-by-step explanation:

The required forms of the equation are;

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

Completing the square is a method used to rewrite a quadratic expression in standard form by adding and subtracting a constant to make it a perfect square trinomial. Completing the square is a useful method to solve quadratic equations and to rewrite quadratic expressions in standard form.

The standard form of a quadratic equation  is ax² + bx + c = 0

We have that;

x²-8x+5=0

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

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The 6-digit number A is 419065.

To find the least 6-digit number A that is divisible by 495, we need to follow these steps:
Step 1: Find the prime factors of 495.
495 = 3 × 3 × 5 × 11 = 3^2 × 5 × 11
Step 2: Determine the lowest 6-digit number divisible by the prime factors.
The lowest 6-digit number is 100000, so we find the next multiple of 495 above 100000.
100000 ÷ 495 ≈ 202.02
The next integer value is 203, so:
203 × 495 = 100485
Step 3: Substitute the given digits (4, 9, and 6) into the 6-digit number.
The least 6-digit number divisible by 495 is 100485. To make A the smallest possible number, we will place the given digits in the following order: 4, 9, and 6. The missing digits in A are 1, 0, and 5.
So, the 6-digit number A is 419065.

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The inverse of the function f(x) = 1/x is B. f⁻¹(x) = 1/x

The inverse of a function f(x) written as f⁻¹(x) is such that ff⁻¹(x) = f⁻¹f(x)

Given the function f(x) = 1/x,we desire to find its inverse. We proceed as follows.

Since f(x) = 1/x

Let f(x) = y

So,we have that

y = 1/x

Now, multiplying both sides by x,we have that

x × y = 1/x × x

xy = 1

Dividing though by y, we have that

xy/y = 1/y

x = 1/y

Now, relacing y with x and x with f⁻¹(x), the inverse of f(x), we have that

x = 1/y

x = 1

f⁻¹(x) = 1/x

So, the inverse is B. f⁻¹(x) = 1/x

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The pythagorean theorem says a^2 + b^2 = c^2 when a and b are the sides of the right triangle and c is the hypotenuse (longest side, opposite the 90 degree angle).

so if  8^2 + 6^2 = 10^2, then it's a right triangle.

8^2 + 6^2 = 64 + 36 = 100 = 10^2, so yes, this is a right triangle.

The distance d between A and B is √(68), and the square of the distance in the y direction is 64.

To find the distance d between points A and B, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values of A and B, we get:
d = sqrt((4 - 2)^2 + (5 - (-3))^2)
d = sqrt(2^2 + 8^2)
d = sqrt(4 + 64)
d = sqrt(68)
Next, to calculate the square of the distance in the y direction, we need to find the difference between the y-coordinates of A and B and square it. So:
(y2 - y1)^2 = (5 - (-3))^2 = 8^2 = 64
Therefore, the square of the distance in the y direction is 64.
I'm here to help you with your question. To find the distance d between two points A(x1, y1) and B(x2, y2), we can use the distance formula:
d = √((x2-x1)² + (y2-y1)²)
Given the points A(2, -3) and B(4, 5), let's plug in the values:
d = √((4-2)² + (5-(-3))²)
Now, calculate the difference for each coordinate:
d = √((2)² + (8)²)
Next, square the differences:
d = √(4 + 64)
Finally, calculate the square root:
d = √(68)
ow, let's find the square of the distance in the y direction, which is (y2-y1)²:
(y2-y1)² = (5-(-3))²
Calculate the difference:
(y2-y1)² = (8)²
Square the difference:
(y2-y1)² = 64
So, the distance d between A and B is √(68), and the square of the distance in the y direction is 64.

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A) the average speed  of the journey from my home town to A is 30 miles per hour

B) the average speed of the journey from my home town to B is 40 miles per hours.

C) The average time is 36 miles per hours.

Average speed = distance /   time

So the answers is

A) Average speed = 10 miles ÷ (1/3 hour) = 30 miles per hour

B) Average speed = 20 miles ÷ 0.5 hours = 40 miles per hour.

C) Average speed = 30 ÷ (50/ 60) = 30 ÷ 0.8333 = 36 miles per hour.

Average Speed is essential for understanding the rate at which a travel occurs.

The speed of a vehicle may change from time to time throughout a travel. In that instance, determining the average speed is critical in order to determine the pace at which the voyage will be completed.

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Full Question:

The diagram shows the distance between my home, H, and two towns, A and B. It also shows information about journey times. See same attached.

The actual side length of the house is 240 feet long.

The scale factor is 1 inch on the blueprint represents 60 actual feet.

The side of the house measures 4 inches on the blueprint. To find the actual length, we multiply the blueprint length by the scale factor:

Actual side length = 4 inches * 60 feet/inch = 240 feet

So, the actual side length of the house is 240 feet.

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The total payment required to pay off a promissory note issued for $400.00 is $412.

Using this formula

Total payment=Promissory note+(Promissory note× Ordinary interest× 90 day term/360)

Where:

Promissory note=$400

Ordinary interest=12%

Let plug in the formula

Total payment= $400 + ($400 × 12% × 90 days ÷ 360 days)

Total payment= $400 + $12

Total payment= $412

Hence, the total payment required to pay off a promissory note issued for $400.00 is $412.

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Answer: 15cm?

Step-by-step explanation: I am doing this assignment right now, after i submit it i will reply with the answer. Edit: 15cm is correct.

The distance from point A (tangent point on clock) to point B (the hanger) is approximately 10 cm, based on the principles of right-angle triangles and Pythagorean theorem.

In this geometry problem, we're looking at a situation where a circular clock is hung by wires connected to a tangential point on the clock. By using right-angle triangle principles and the given radius of 15 cm from E to D, it''s key to recognize that triangle AED is a right triangle (since a radius perpendicular to a tangent at its point of contact forms a right angle).

So, the distance from A to E (the radius) is 15 cm. The distance from E to D is also a radius, hence is 15 cm as well. Now, by Pythagoras theorem for right triangle AED, the distance AD (the hypotenuse) is square root of (15^2 + 15^2), which is approximately 21.21 cm.

The distance BD from the top of the clock at point D to the hanger at point B is given as 10 cm. Since the clock is hanging from point B, this creates another right triangle ADB. The length from point A to B is found by subtracting BD (10 cm) from the hypotenuse AD (21.21 cm), which is roughly 11.21 cm. However, this option is not offered in the question, meaning a rounding must be made, so the answer is approximately 10 cm.

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The measurement is the same for Charles and Jermod are lower quartile and upper quartile. Therefore, options C and D are the correct answer.

From the given dot plot.

The number of minutes Charles spent on homework.

15, 15, 20, 20, 25, 30, 30, 30, 30, 30, 45, 50, 55, 60, 60.

Here, lower quartile = 20

Upper quartile = 50

Median = 30

Range = 60-15

= 45

The number of minutes Jermod spent on homework.

15, 15, 15, 20, 20, 30, 35, 45, 45, 45, 50, 50, 55, 55.

Here, lower quartile = 20

Upper quartile = 50

Median = 45

Range = 55-15

= 40

Therefore, options C and D are the correct answer.

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"The correct answer is: g(x), f(x), h(x)."To determine the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4, we need to calculate the average rate of change for each function.

The average rate of change is calculated by finding the difference in the function's values at the endpoints of the interval (x = 4 and x = 0) and dividing it by the difference in the corresponding x-values.

For function f(x), we have:

Average rate of change = (f(4) - f(0))/(4 - 0) = (64 - 0)/(4 - 0) = 64/4 = 16

For function g(x), since it is a linear graph, the average rate of change is constant throughout. Therefore, the average rate of change for g(x) is the same as the slope of the line, which is determined by the ratio of the change in y to the change in x. In this case, it would be the slope between the given x-intercept (-2) and y-intercept (-1), which is -1/2.

For function h(x), we need to find the average rate of change between x = 0 and x = 4. Substituting the values, we get:

Average rate of change = (h(4) - h(0))/(4 - 0) = (36 - 6)/(4 - 0) = 30/4 = 7.5

Now, let's compare the average rates of change for each function:

f(x): 16

g(x): -1/2

h(x): 7.5

From least to greatest, the correct order according to the average rate of change is:

g(x), f(x), h(x).

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The mean absolute deviation for the data-set in the table is given as follows:

1.52 million.

The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.

Hence the mean for the data-set in this problem is given as follows:

(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.

The deviations are given as follows:

Hence the mean absolute deviation is given as the sum of the deviations divided by the number of observations, hence:

(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.

The table is given by the image presented at the end of the answer.

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The measure of the angle ∠S is 95°

Let's call angle Q as x. Then we can express the other angles in terms of x as follows:

Angle R = x + 25 (since angle R is 25° more than angle Q)

Angle S = x + 65 (since angle S is 65° more than angle Q)

We know that the sum of the angles in a triangle is always 180°, so we can write:

x + (x + 25) + (x + 65) = 180

Simplifying this equation, we get:

3x + 90 = 180

Subtracting 90 from both sides, we get:

3x = 90

Dividing both sides by 3, we get:

x = 30

Therefore, angle S is:

x + 65 = 30 + 65 = 95 degrees

So the measure of angle S is 95 degrees.

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The area of the triangle in the shaded region is derived to be 12.5 square units.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

For the triangle in the shaded region;

base = 5 units

height = 5 units

area of the triangle = 1/2 × 5 units × 5 units

area of the triangle = 25/2

area of the triangle = 12.5 square units

Therefore, the area of the triangle in the shaded region is derived to be 12.5 square units.

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A(5,0), B(3,2), C(0,5), and D(-6,1) are all located in the first quadrant. D(-6,1) is located within the second quadrant.

A coordinate system within geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points and other geometrical objects over a manifold, such Euclidean space. The order of the coordinates is crucial, and they are frequently identified by their position within an arranged tuple or through a letter, such as "the x-coordinate."  Within the first quadrant is A(5,0). The first quadrant is occupied by B(3,2), followed by C(0,5) with the first quadrant, D(-6,1) with the second quadrant, E(-4,4) from the second quadrant, and F(2,-3) with the fourth quadrant.

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The approximate length of the diagonal to the nearest tenth of an inch is 32.52 inches.

To find the length of the diagonal, we can use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides.

In this case, since the sides of the square television screen are 23 inches, we can calculate the length of the diagonal using the following formula

So, if the sides of the square television screen are 23 inches, then:

[tex]Diagonal^2 = Side^2 + Side^2[/tex]

[tex]Diagonal^2 = 23^2 + 23^2[/tex]

[tex]Diagonal^2[/tex]= 529 + 529

[tex]Diagonal^2[/tex] = 1058

Diagonal = √1058

Diagonal ≈ 32.52 inches

Rounding to the nearest tenth of an inch, the approximate length of the diagonal is 32.52 inches.

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The trinomial expression when factored is (3x - 3)² & A = 3 and B = 3

From the question, we have the following parameters that can be used in our computation:

9x² - 18x + 9 = (Ax − B)²

Factor out 9 in the expression

So we have

9(x² - 2x + 1) = (Ax − B)²

When the above expression is factored

We have

9(x - 1)² = (Ax − B)²

Express 9 as 3²

3²(x - 1)² = (Ax − B)²

So, we have

(3x - 3)² = (Ax − B)²

This means that

A = 3 and B = 3

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The expression simplifies to |2x| = -2x, when x<0 by definition of absolute value

If x<0, then the expression |2x| simplifies to -2x.

The absolute value of a number is the distance of the number from zero on the number line.

Since x is negative in this case, 2x will be negative as well.

Taking the absolute value of -2x will give us the opposite of -2x, which is 2x.

However, since we know that x<0, this means that -2x will always be a positive number.

Hence, the expression simplifies to |2x| = -2x, when x<0.

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Complete question

Simplify the expression |2x|  when x is less than 0, x<0

To use the substitution method to solve the system, we need to solve one of the equations for x or y in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable that we can solve.

Let's solve the first equation for x in terms of y:

x + 4y = -9

x = -4y - 9

Now we substitute this expression for x into the second equation:

2x + 5y = -6

2(-4y - 9) + 5y = -6

Simplifying this expression, we get:

-8y - 18 + 5y = -6

-3y = 12

y = -4

Now we can substitute this value of y into either of the original equations to find x. Let's use the first equation:

x + 4y = -9

x + 4(-4) = -9

x - 16 = -9

x = 7

Therefore, the solution to the system is x = 7, y = -4.

Now let's look at the answer choices and see which one matches the equation we got by substituting x = -4y - 9 into the second equation:

A) 2(4-9)+ 5y-6 = -10 + 5y - 6 = 5y - 16

B) 21-4y-9)+5% -6 = -4y + 6

C) 2x+5(4-9)=-6 = 2x - 25 = -6

D) 2x+5(-4y-9)=-6 = 2x - 20y - 45 = -6

The answer choice that matches our equation is D), 2x + 5(-4y - 9) = -6.

Answer:

midsegment = 23

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = [tex]\frac{18+28}{2}[/tex] = [tex]\frac{46}{2}[/tex] = 23

Angle 1 and angle 2 are corresponding angles since they are in the same relative position. Corresponding angles are congruent. So, to solve, we will need to set the given expressions equal to each other and then solve for the value of x algebraically.

80 - 2x = 93 - 3x

80 + x = 93

x = 13

Answer: x = 13

Hope this helps!

Answer:

x = 10

Step-by-step explanation:

m<1 = m<2

(80-2x) = (90-3x)

80 - 2x = 90 - 3x

80 = 90 - x

-10 = -x, x = 10

If the temperature of a chemical mixture is tan√x degree celsius after x hours then the rate of change of temperature after π /4 hours is 0.141099

We are given that the temperature of the chemical mixture after x hours is given by:

T(x) = tan(√x)

To find the rate of change of temperature after π/4 hours, we need to find the derivative of T(x) with respect to x and evaluate it at x = π/4.

T'(x) = sec²(√x)/2√x

So, the rate of change of temperature after π/4 hours is given by:

T'(π/4) = sec²(√(π/4))/2√(π/4)

= sec²(π/2)/2√(π/4)

= 1/2√(π/4)

We can simplify this expression as:

T'(π/4) = 1/2(π/2)⁰⁵

= 0.141099

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Answer:

f(- 5) = 10

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

given

f(x) = 5 + | x |

to find f(- 5) substitute x = - 5 into f)x)

f(- 5) = 5 + | - 5| = 5 + | 5 | = 5 + 5 = 10

The segment lengths are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering the geometric mean theorem, the triangle has bases of 7 and 14 - 7 = 7, hence the altitude BD is given as follows:

BD² = 7 x 7

BD² = 7²

BD = 7.

The segment BC is the hypotenuse of a right triangle of two sides with length 7, hence:

(BC)² = 7² + 7²

[tex]BC = \sqrt{2 \times 49}[/tex]

[tex]BC = 7\sqrt{2}[/tex]

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The derivative of the inverse trigonometric function is equal to f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ). (Correct choice: D)

In this problem we find the case of the inverse trigonometric function, whose derivative must be found. This can be done by means of derivative rules and chain rules. First, write the entire function:

f(x) = sin⁻¹ (e²ˣ)

Second, find the derivative of the inverse trigonometric function:

f'(x) = [1 / √[1 - (e²ˣ)²]] · (2 · e²ˣ)

f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ)

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