How do exponential functions differ from regular functions? In exponential functions the variable is: a. always negative c. representing the power b. representing the base d. always t Please select the best answer from the choices provided A B C D

Answer:

1.5 mi

Step-by-step explanation:

Billy speed = 3 mi/hr

Arnold speed = 1/2(3 mi/hr) = 1.5 mi/hr

distance = speed x time = (1.5 mi/hr)(1 hr) = 1.5 mi

The volume of the solid generated when region R is revolved about the x-axis = 0.1142 cubic units

Here, R is the region bounded by the following curves.

[tex]y= sin^{-1}(x)[/tex], y = [tex]\sqrt{\frac{\pi}{3} }[/tex], y = [tex]\sqrt{\frac{\pi}{4} }[/tex], x = 0

Using the shell method we need to find the volume of the solid generated when R is revolved about the x-axis.

Using shell method, the volume of the solid is given by,

V = [tex]\int\limits^b_a {xf(x)} \, dx[/tex]

First we find the limits.

when y = [tex]\sqrt{\frac{\pi}{3} }[/tex],

[tex]x=sin(y)\\\\x=sin(\frac{\pi}{3} )\\\\x=\frac{\sqrt{3} }{2}[/tex]

when y = [tex]\sqrt{\frac{\pi}{4} }[/tex],

[tex]x=sin(y)\\\\x=sin(\frac{\pi}{4} )\\\\x=\frac{1}{\sqrt{2} }[/tex]

Using shell method, the volume of the solid would be,

V = [tex]\int\limits^b_a {xf(x)} \, dx[/tex]

[tex]V=\int\limits^\frac{\sqrt{3} }{2} _\frac{1}{\sqrt{2} } {xsin^{-1}(x)} \, dx\\\\V=\int\limits^\frac{\sqrt{3} }{2} _\frac{1}{\sqrt{2} } {x\frac{x}{2\sqrt{1-x^2} } } \, dx\\\\V=\int\limits^\frac{\sqrt{3} }{2} _\frac{1}{\sqrt{2} } \frac{x^2}{2\sqrt{1-x^2} } } \, dxx^{2}[/tex]

V = 0.1142

Therefore, the volume is 0.1142 cubic units

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The complete question is:

Let r be the region bounded by the following curves. use the shell method to find the volume of the solid generated when r is revolved about the x-axis.  [tex]y= sin^{-1}(x)[/tex], y=sqrt(pi/3), y=sqrt(pi/4) , x=0

For given exponential function f(t), f(7)=24.7.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Growth

In Exponential Growth, the quantity increases very slowly at first, and then rapidly. The rate of change increases over time. The rate of growth becomes faster as time passes. The rapid growth is meant to be an “exponential increase”. The formula to define the exponential growth is:

y = a ( 1+ r )ˣ

Where r is the growth percentage.

Exponential Decay

In Exponential Decay, the quantity decreases very rapidly at first, and then slowly. The rate of change decreases over time. The rate of change becomes slower as time passes. The rapid growth meant to be an “exponential decrease”. The formula to define the exponential growth is:

y = a ( 1- r )ˣ

Where r is the decay percentage.

Now,

Given function f(t)=300(0.7)ᵗ

f(7)=300*0.7⁷

f(7)=300*0.0823

f(7)=24.7

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The line that passes through the given point and is parallel to the graph

y = -4x - 23.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Equation: y=-4x+3

As, we know that the slope of parallel line are same.

Now, using slope- intercept form

y = mx+ b

y = -4x+ b

Now, the line passes through (-4, -7).

So, y= -4x + b

-7 = -4(-4) + b

-7 = 16 + b

b = -23

So, the equation of parallel line is

y = -4x - 23

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For the given functions, the slope of f will be -1/2 and g will be -3/2, the respective y - intercepts will be -2 and 2.

The slope is m and the y-intercept is b in the slope-intercept equation (y=mx+b). It is also possible to rewrite some equations so that they appear to be in slope-intercept form. For instance, y=x can be written as y=1x+0, giving rise to a slope of 1 and a y-intercept of 0.

You can use the slope intercept formula y = mx + b if you know the slope of the line being studied and the given point is also the y intercept (0, b). In the formula, the term b stands in for the y value of the y-intercept point. In standard form, a quadratic equation is written as y=ax2+bx+c, where x and y are variables and a, b, and c are well-known constants.

1. The given equation is f(x) = -1/2 x - 2

Slope of the equation = -1/2

y - intercept = -2

Let us consider 2 points from g function,

(-2,4) and (0,1)

The slope of the equation will be = y2 - y1 / x2 - x1

= 1 - 4 / 0 + 2

= -3/2

Equation of line will be = y - yo = m (x - xo)

= y - 4 = -3/2 (x + 2)

= 2y - 8 = -3x - 6

= 3x + 2y = 2

= y = 2 - 3/2x

y - intercept = 2

2. For the equation f(x) = 6x - 1

slope of the equation = 6

y intercept = -1

For the given graph,

let us consider 2 points, (-1, 3) and (-2, 6)

Slope of the graph = 6 - 3 / -2 + 1 = 3/-1 = -3

Equation of line will be -

y - 3 = -3 (x + 1)

y - 3 = -3x - 3

y = 3x

y intercept will be 0.

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If an algorithm is O(n), where n is the input size, then the execution time will scale linearly with the input size.

If an algorithm is O(n), where n is the input size, then the execution time will scale linearly with the input size. Therefore, if the input size is doubled, the execution time will also double. Mathematically, this can be expressed as:

Execution Time (With Doubled Input Size) = 2*Execution Time (With Original Input Size).

For example, if the execution time for an algorithm with an input size of 8 is 10 seconds, then the execution time for an input size of 16 will be 20 seconds. This is due to the fact that the algorithm's complexity is linear, and thus its runtime increases linearly with the input size.

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The measure of the third angle in Elise angle measurement is

The third angle of the triangle is solved with knowledge of sum of angles on a triangle being equal to 180 degrees and a triangle having three angles

say the third angle measure is x, so we have that

30 + 100 + x = 180

130 + x = 180

collecting like terms

x = 180 - 130

x = 50

we can therefore say that the third angle is 50 degrees

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Answer:

C

Step-by-step explanation:

43x=42Divided 42by 43

x=42/43

x=2/3

The value of x is 42/43.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

43x = 42

Divide both sides with 43.

x = 42/43

Thus,

x = 42/43.

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Answer:

The answer is 1548.99ft.

Step-by-step explanation:

To determine the length of the strip needed for waterproofing, you need to calculate the circumference of the circular floor. The formula for the circumference of a circle is 2π times the radius. If the floor of the treehouse has a radius of 490.625/2= 245.3125ft, then the circumference of the floor is:

2π x 245.3125ft = 1548.99ft

So, the length of the strip needed for waterproofing around the floor is approximately 1548.99ft.

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If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

We have a coefficient matrix of linear equations in the problem. If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. In light of this theorem, we conclude that the system is consistent.

If and only if a linear system's coefficient matrix and augmented matrix have the same rank, the system is said to be consistent.

If a pivot, or 1, appears in each column of the reduced row echelon form of the coefficient matrix of a linear system of equations involving four distinct variables, then the reduced row echelon form of the coefficient matrix is, let's say, A is an identity matrix, here 3, because there are four variables.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

Therefore,

If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

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If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

We have a coefficient matrix of linear equations in the problem. If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. In light of this theorem, we conclude that the system is consistent.

If and only if a linear system's coefficient matrix and augmented matrix have the same rank, the system is said to be consistent.

If a pivot, or 1, appears in each column of the reduced row echelon form of the coefficient matrix of a linear system of equations involving four distinct variables, then the reduced row echelon form of the coefficient matrix is, let's say, A is an identity matrix, here 3, because there are four variables.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

Therefore,

If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

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Answer:

20

Step-by-step explanation:

Ariana has 3 milk bones and she wants to give them to three of her 6 dogs, with each getting one bone. In 20 ways this can be done.

Ariana has 3 milk bones and she wants to give them to three of her 6 dogs, with each getting one bone.

We have to determine how many ways this can be done.

We have to distribute 3 milk bones to the 6 dogs.

Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

So the possibilities = [tex]^6C_{3}[/tex]

Using the formula; [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]

[tex]^6C_{3}=\frac{6!}{3!(6-3)!}[/tex]

[tex]^6C_{3}=\frac{6!}{3!3!}[/tex]

[tex]^6C_{3}=\frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]

[tex]^6C_{3}[/tex] = 5 × 4

[tex]^6C_{3}[/tex] = 20

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To find the OGF for the number of ternary sequences in which any occurrence of 2 has a 1 both immediately before and immediately after it, we can use a recursive approach.

Let A(x) be the OGF for sequences that start with a 1 and end with a 1. And let B(x) be the OGF for sequences that start with a 1, contain a 2, and end with a 1.

We have A(x) = x + [tex]x^{2}[/tex] + [tex]x^{3}[/tex] + [tex]x^{4}[/tex] + ...

And B(x) = x * [tex]A(x)^{2}[/tex], since a 2 can only appear after a 1 and must be immediately followed by another 1.

Finally, the OGF for the desired sequence is B(x) = x * x + [tex]x^{2}[/tex] + [tex]x^{3}[/tex] + [tex]x^{4}[/tex] + ...)^2 = x * [tex]A(x)^{2}[/tex]

So, the OGF for the number of ternary sequences in which any occurrence of 2 has a 1 both immediately before and immediately after it is x * ( x + [tex]x^{2}[/tex] + [tex]x^{3}[/tex]......)^2.

The ordinary generating function (OGF) for a sequence is a formal power series that encodes information about the sequence.

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A same day forecast of the temperature tends to be within 2.25°F of the actual temperature. The forecast for a particular day is 16°F Let be the actual temperature. Find the range of possible temperatures for the day when the forecast is 16°F, thus range becomes: {x| 16 < x < 18.25 }

The easiest way to assess data variability is range, which is the difference between the highest and smallest number. For instance, the range will be 12 - 2 = 10 if the provided data set is 2, 5, 8, 12, 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.

An integer type with a range restriction is one that can only take certain values. It is simply represented as a start value and an end value in numbers.

Let, x be the actual temperature

A same day forecast of the temperature tends to be within 2.25°F

The forecast for a particular day is 16°F

now, range becomes: {x| 16 < x < 18.25 }

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Answer: Third Option: The car was at -60 feet at one second after it passed the camera. When was the car 5 feet to the west of the camera?

Step-by-step explanation:

The negatives in the equation most match the the numbers in the third option and it also the one that makes the most sense.

Hope this helps!! :)

The mean () of the test is 150, while the standard deviation () is 25. In the case of a normal distribution, your z score would be: z = (x - ) / = (190 – 150) / 25 = 1.6.

A Z-score of 0 implies that the data point’s value is the same as the mean score. A Z-score of 1.0 indicates that the result is one standard deviation from the mean. The z-scores’ mean is always 0. The z-scores’ standard deviation is always 1. The z-score distribution graph always has the same form as the original sample value distribution graph. The total of the squared z-scores equals the number of z-score values.

z = (x – μ) / σ

z=[tex]\frac{(190-150}{25} = 1.6[/tex]

Take the raw data, remove the mean, then divide by the standard deviation to get the z-score. The data point of interest is represented by X. Mu and sigma reflect the population’s mean and standard deviation.

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We would have a graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100. Option A

We have to determine the nature of the graph that we have in the context of the question. In this case, we must recall that the function that we have would look something of the nature; y = 10x + 120 where y is the money raised and x is the number of students that attends the dance.

Here we can see that the nature of the equation just looks like the equation of the straight line graph that is given as; y = mx + c

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The length of the smaller of the two missing sides is; 24

The sides that make up a right angle triangle are;

Hypotenuse

Opposite

Adjacent

Now, the smallest side has a length of 10.

Let the hypotenuse be x + 2 while the other unknown side will be x since they are consecutive even integers.

Thus, using Pythagoras theorem we have;

(x + 2)² = 10² + x²

Expanding the bracket gives;

x² + 4x + 4 = 100 + x²

x² will cancel out to get;

4x + 4 = 100

4x = 96

x = 96/4

x = 24

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Answer:(x + 9)(x - 3)

Step-by-step explanation:

⇒x² + 6x - 27

breaking middle term

⇒x² + 9x - 3x - 27

⇒x (x + 9) - 3 (x + 9)

⇒(x + 9)(x - 3) ...answer

hope that helps ...

Answer:

1/3

Step-by-step explanation:

1/3 can be used as an expression that is exactly the same as 2/3x5.

When you multiply 2/3 x 5-

Look here if you need help solving 2/3 X 5: (2/3 x 5/1.is the simplest way to

multiply the two, make sure to multiply 2 by 5 and 3 by 1 to get your answer.)

(5x2=10…..3x1=3)

-you get 10/3. This answer simplified is 1/3. So in the end, 1/3 is a great

expression or answer to use as an equivalent to the equation 2/3 x 5

Hoped this helped! :)

2x:3y=4:8 is correct because it states that for every 2 units of x, there are 3 units of y, so the ratio of x to y is 4:8.

A. 2x:4y=4:8

B. 4x:2y=2:4

C. 4x:2y=4:8

D. 2x:4y=2:4

E. 3x:2y=2:4

F. 2x:3y=4:8

B, C, F

B. 4x:2y=2:4 is correct because it states that for every 4 units of x, there are 2 units of y, so the ratio of x to y is 2:4.

C. 4x:2y=4:8 is correct because it states that for every 4 units of x, there are 2 units of y, so the ratio of x to y is 4:8.

F. 2x:3y=4:8 is correct because it states that for every 2 units of x, there are 3 units of y, so the ratio of x to y is 4:8.

the complete question is :

Kiesha and her classmates wrote proportions for the reduction of a triangle. Which proportions are set up correctly? select three options.

A. 1/2:2/3:3/4

B. 3/2:2/3:1/4

C. 1/2:2/4:3/6

D. 1/4:2/3:4/5

E. 2/3:3/4:4/5

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2x:4y=4:8

B. 4x:2y=2:4

C. 4x:2y=4:8

D. 2x:4y=2:4

E. 3x:2y=2:4

F. 2x:3y=4:8

B, C, F

B. The formula 4x:2y=2:4 is accurate because it says that there are 2 units of y for every 4 units of x, making the x:y ratio 2:4.

C. 4x:2y=4:8 is true because it says that there are 2 units of y for every 4 units of x, making the x:y ratio 4:8.

F. 2x:3y=4:8 is true because it says that there are 3 units of y for every 2 units of x, making the x to y ratio 4:8.

Shelton needs a minimum of 46 ft of molding to go around the perimeter of the ceiling.

The minimum amount of molding Shelton needs can be calculated by finding the length of the perimeter of the square ceiling. To do this, we first need to find the length of a side of the square.

We can use the Pythagorean theorem to find the length of a side of the square. The theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the length of the hypotenuse (in this case, the diagonal of the square).

Thus, we have the equation: side^2 + side^2 = diagonal^2.

Solving for the side length, we have side = sqrt(diagonal^2/2).

So, the side length is sqrt(23^2/2) = 11.5 ft.

Therefore, the perimeter of the square is 4 * 11.5 = 46 ft.

Therefore, Shelton needs a minimum of 46 ft of molding to go around the perimeter of the ceiling.

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Complete question:

A square ceiling ha a diagonal of 23 ft. Shelton wants to put molding around the perimeter of the ceiling. The molding is old by the foot. What i the minimum amount of molding he needs?

The function f(x) = -9 + 4x - x³ is increasing on the intervals (-∞, -√(4/3)) and (√(4/3), +∞), and decreasing on the interval (-√(4/3), √(4/3)).

The relative minima occur at x = ±√(4/3).

A function is a mathematical mapping from one set of values to another set of values.

To find the first derivative of the function, we need to take the derivative of each term in the function. The derivative of -9 is 0, the derivative of 4x is 4, and the derivative of -x³ is -3x². So the first derivative of the function f(x) is:

f'(x) = 4 - 3x²

We want to find the values of x where f'(x) = 0 (because this will tell us where the function changes from increasing to decreasing, or vice versa). Solving for x, we get:

=> 0 = 4 - 3x²

=> 3x² = 4

=> x² = 4/3

=> x = ±√(4/3)

The first derivative of the function f(x) is positive for x values less than -√(4/3) and for x values greater than √(4/3), so the function f(x) is increasing on those intervals.

The first derivative of the function is negative for x values between -√(4/3) and √(4/3), so the function f(x) is decreasing on that interval.

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The slope-intercept form of the function described by this line is y = x + 1

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

x   y

0   1

From the above table of values, we can see that

The difference between the x and the y value is 1

Mathematicallly, this can be represeted as

y - x = 1

Add x to both sides

y - x + x = x + 1

Evaluate the like terms

So, we have the following representation

y = x + 1

The above equation is in the slope intercept form, y = mx + c

Hence, the equation is y = x + 1

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Complete question

Can you find the slope-intercept equation of each line and type the correct code? Please remember to type in ALL CAPS with no spaces. *

x   y

0   1

Solving the problem using basic algebra, the total number of hamburgers that were sold on Saturday can be obtained as 108 hamburgers.

The word problem that has been formulated in the question falls under the basic discipline of mathematics known as algebra.

Algebra is a branch of mathematics that deals with mathematical variables and the rules for manipulating these variables to solve diverse mathematical problems.

Let the total number of hamburgers sold be x.

In the question, it is given that the total number of cheeseburgers sold would be 3 times the number of hamburgers sold. Then the number of cheeseburgers sold would be 3x.

It is also given that the total number of hamburgers and cheeseburgers sold together is 432.

Using these data, the equation can be formulated as x + 3x = 432.

As x and 3x are variables of the same nature, which is x, they can be added to obtain the answer as 4x, hence the equation becomes

4x = 432. Solving for x, we get

x = 432 ÷ 4

x = 108.

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Frequency and wavelength are related by the equation f=cλ, where c is the speed of light in a vacuum. The speed of light in a vacuum is 2.9979×108 m/s. Wavelength must be converted from kilometers to meters, then the values can be plugged into the equation. f=2.9979×108 m/s5,700 m=52,594 Hz. The resulting frequency is 52,594 Hz or 5.3×104 Hz when rounded to the correct number of significant figures.

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Answer:

  3(x-8)(x+5)

Step-by-step explanation:

You want to factor the quadratic 3x² -9x -120.

Each of the coefficients is divisible by 3, so that is the first thing we can factor out:

  = 3(x² -3x -40)

To factor the quadratic, we need factors of -40 that have a sum of -3.

  -40 = -40(1) = -20(2) = -10(4) = -8(5)

The last of these factor pairs have a sum of -3, so the factorization is ...

  = 3(x -8)(x +5)

__

Additional comment

The product of factors (x+a) and (x+b) is ...

  (x +a)(x +b) = x² +ax +bx +ab = x² +(a+b)x +ab

This is why we're looking for factors of -40 = ab, that have the sum (a+b) = -3.

The radius r of the circle is  28 m

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.

Arc length,

   S = rθ

=> 16 = r (4/7)

=> r=(16*7)/4 =  28 m

The radius r of the circle is  28 m

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Answer:

9.2

Step-by-step explanation:

If an angle measures 69° then measure of its complementary angle is

90° - 69° = 21°. thus option a is answer.

In geometry, two angles are considered complementary if their sum is equal to 90 degrees. If an angle has a measure of 69 degrees, its complementary angle would be the angle that produces 90 degrees when 69 degrees are added to it. We simply deduct the given angle's measure from 90 degrees to determine the measure of the complementary angle:

90° - 69° = 21°

This is because the sum of complementary angles is always equal to 90 degrees.

Therefore, a 69° angle's complementary angle is a 21° angle.

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The measure of the complementary angle of 69° is 21°.

The complementary angle of an angle is the angle that adds up to 90°. To find the measure of a complementary angle, you can subtract the given angle from 90°. In this case, the given angle is 69° so the complementary angle would be 90° - 69° = 21°. Therefore the measure of the complementary angle of 69° is 21°.

To calculate the measure of the complementary angle, you can use the following formula: Complementary Angle = 90° - Given Angle. The complementary angle of an angle is the angle that completes a right angle (90°). The complementary angle of an angle can be found by subtracting the given angle from 90°. If an angle measures 69°, then the measure of its complementary angle is 21°.

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The decimal approximation for the solution is

x = -9.8635

The exponential equation can be written as

e^x = 1/41219

Taking the natural logarithm of both sides, we have:

x = ln(1/41219)

Using a calculator to evaluate the natural logarithm, we get:

x = -9.8635

So the solution set expressed in terms of natural logarithms is

x = ln(1/41219) = -9.8635

And the decimal approximation for the solution is

x = -9.8635

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