What the meaning of statement this?

1.)The length of the diagonal of the square would be = 5.7

2.) The perimeter of the equilateral triangle = 12.

To calculate the length of the diagonal of a given square, the Pythagorean formula should be used and it's given below as follows:

1.) C² = a² + b²

But the perimeter = 16

The length = 16/4 = 4

C² = 4²+4²

= 16+16

= 32

C = √32= 5.7

2.) The perimeter of the equilateral triangle = length×3 = 36.

The length = 36/3 = 12

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The equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, is:

5x + y - 3 = 0.

To determine the equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, we need to find the coordinates of point C.

Since triangle ABC is right-angled at point A, we know that the slope of line BC[tex](m_{BC})[/tex] multiplied by the slope of line AC [tex](m_{AC})[/tex]  is equal to -1 (because the two lines are perpendicular to each other).

The equation of line BC is given as 5y - x = 15.

By rearranging it in the form y = mx + b, we can determine its slope.

The slope of BC[tex](m_{BC})[/tex] is 5.

Using the perpendicularity condition, we have:

[tex]m_{BC} \times m_{AC} = -1[/tex]

[tex]5\times m_{AC} = -1[/tex]

[tex]m_{AC} = -1/5[/tex]

Now, let's find the coordinates of point C.

We have the coordinates of points A and B, so we can find the slope between points A and C using the formula:

[tex]m_{AC} = (N - (-2)) / (m - 1)[/tex]

-1/5 = (N + 2) / (m - 1)

Cross-multiplying, we get:

-5(m - 1) = N + 2

-5m + 5 = N + 2

-5m - N = -3

Rearranging this equation, we obtain:

5m + N = 3

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Describe the volatility of chloride across period 3

Answer:

[tex]f=\frac{N^2-H}{6}[/tex]

Step-by-step explanation:

[tex]N^2=6f+H\\\mathrm{or,\ }6f=N^2-H\\\mathrm{or,\ }f=\frac{N^2-H}{6}[/tex]

Answer:

12, 14, 16

Step-by-step explanation:

Let's say x is the lowest number:

x+x+2+x+4=42

Simplify the equation:

3x+6=42

Subtract 6 on each side to isolate 3x:

3x=36

x=12

So the lowest number is 12, which means the next number(x+2) would be 14, and the following number(12+4) would be 16.

Happy learning!

Step-by-step explanation:

A = 139°

B = 139°

You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.

The angle around a point always add up to 360°, so add the 41° angles.

41 + 41 = 82°

Then minus this by 360°.

360 - 82 = 278°

And to work out one angle, which gives you the angle for both, divide 278 by two.

278 ÷ 2 = 139°

Both A and B have an angle of 139°

Example:

To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:

3x - 5 = -2x + 7

5x = 12

x = 12/5

Then, plug x = 12/5 into either equation and solve for y:

y = 3(12/5) - 5

y = 36/5 - 25/5

y = 11/5

Therefore, the point of intersection is (12/5, 11/5).

If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:

slope = tan(41 degrees) ≈ 0.87

y = mx + b

y = 0.87x + 0

Then, you can use the same method as before to find the point of intersection with another line.

_______________________________________________________

The answer is 139 degrees, using the method I gave.

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Answer:

f * g)(x) = 8x^2 - 2x - 15

Step-by-step explanation:

Since we want to find (f * g)(x), we want to multiply the entire functions and leave the answer in terms of x (in terms of x simply means we do the multiplication and the simplified answer will be in terms of x):

Thus, we have (2x - 3)(4x + 5).  This is a binomial expression and we can multiply binomials using the FOIL method, where

We add all the terms and combine like terms to find (f * g)(x):

(2x * 4x) + (2x * 5) + (-3 * 4x) + (-3 * 5)

8x^2 + 10x - 12x - 15

8x^2 - 2x - 15

Thus, (f * g)(x) is 8x^2 - 2x - 15

The yearly installment that Thabo has to pay to the bank is c. R202.

We shall use the formula for calculating the amortized loan payment to estimate the yearly installment that Thabo has to pay to the bank:

Installment = (Loan amount (L) * Interest rate (I)) / (1 - (1 + Interest rate)^(-Number of years (N))):

In short: Installment = (L * I) / (1 - (1 + I)⁽⁻ⁿ⁾)

Given:

L = R700

I = 6% = 0.06

N = 4

Plugging the values into the formula, we have the yearly installment:

Installment = (700 * 0.06) / (1 - (1 + 0.06)⁽⁻⁴⁾)

= 42/(1 - (1 + 0.06)⁽⁻⁴⁾ )

= 42/ (1 - (1.06)⁽⁻⁴⁾ )

= 42/(1 - 0.792)

= 42 / 0.2079 ≈ 202.01

Installment ≈ 202.01

Therefore, the yearly installment that Thabo has to pay to the bank is  R202.

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The answer is D) Smaller  Set B's standard deviation is expected to be smaller than Set A's due to its tighter range.

To determine whether Set A's standard deviation is smaller, larger, or about the same as Set B's, we can analyze the spread of the values in each set. The standard deviation measures the dispersion or variability of a data set.

Looking at Set A, we can see that the values range from 1 to 25, with a progression that is relatively spread out. On the other hand, Set B has values ranging from 9 to 18, with a more limited range.

Based on this observation, we can infer that Set B's values are more tightly grouped together compared to Set A. Consequently, Set B is expected to have a smaller standard deviation since the values are less dispersed around the mean.

Therefore, the answer is D) Smaller. Set B's standard deviation is likely to be smaller than Set A's. However, to precisely determine the standard deviations and compare them, it would be necessary to calculate the actual values using the formulas for standard deviation or use statistical software.

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Step-by-step explanation:

I'm assuming the sides can only be integers.

The most optimal area would be a square. We need to distribute 800 to 3 sides, which of course is not possible with integers. We will have to distribute the 800 as evenly as possible.

800/3 = 266.666666667.

We can let 2 sides be 267 and 1 side be 266. This will distribute it evenly. However, notices that the river side can be any length. Meaning that we can make one side be 268 and the other 2 sides be 266. This still satisfies our 800 feet of fencing, while being larger than 267 * 266.

Shorter side: 266 ft

Longer side: 268 ft

Greatest Possible Area: 71288

Por lo tanto, los primeros 10 términos de la sucesión son:

1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.

La sucesión que se describe tiene un primer término de 1/2 y aumenta constantemente en 1/3 en cada término subsiguiente. Podemos encontrar los primeros 10 términos de la sucesión calculando cada término de manera sucesiva.

El primer término es 1/2.

Para encontrar el segundo término, sumamos 1/3 al primer término:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

El segundo término es 5/6.

Para encontrar el tercer término, sumamos 1/3 al segundo término:

5/6 + 1/3 = 10/12 + 4/12 = 14/12 = 7/6

El tercer término es 7/6.

Podemos continuar este proceso para encontrar los siguientes términos:

4to término: 7/6 + 1/3 = 14/12 + 4/12 = 18/12 = 3/2

5to término: 3/2 + 1/3 = 9/6 + 2/6 = 11/6

6to término: 11/6 + 1/3 = 22/12 + 4/12 = 26/12 = 13/6

7mo término: 13/6 + 1/3 = 26/12 + 8/12 = 34/12 = 17/6

8vo término: 17/6 + 1/3 = 34/12 + 4/12 = 38/12 = 19/6

9no término: 19/6 + 1/3 = 38/12 + 8/12 = 46/12 = 23/6

10mo término: 23/6 + 1/3 = 46/12 + 4/12 = 50/12 = 25/6

Por lo tanto, los primeros 10 términos de la sucesión son:

1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.

Si tienes más preguntas, ¡no dudes en hacerlas!

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A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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The analysis above, graph (B) best represents the function g(x) = 3^(2x-1) as it demonstrates the expected exponential growth behavior as x increases.

The function g(x) = 3^(2x-1) is an exponential function with a base of 3. In this case, the base is raised to the power of (2x-1).

To determine the behavior of the function, we can analyze the exponent (2x-1).

When x is a positive number, 2x-1 will increase as x increases. This means that the function will experience exponential growth as x increases.

When x is a negative number, 2x-1 will decrease as x decreases. This indicates that the function will exhibit exponential decay as x decreases.

Now, let's analyze the options to identify the graph that best represents the function g(x).

Graph (A): This graph shows exponential decay. As x increases, the function decreases. However, the rate of decay seems to be slower than what we would expect for the given function g(x)=3^(2x-1). Therefore, graph (A) does not accurately represent the given function.

Graph (B): This graph shows exponential growth. As x increases, the function increases. The rate of growth appears to match the behavior we would expect for the function g(x)=3^(2x-1). Therefore, graph (B) is a potential candidate.

Graph (C): This graph shows exponential decay. As x increases, the function decreases. However, the rate of decay seems to be faster than what we would expect for the given function g(x)=3^(2x-1). Therefore, graph (C) does not accurately represent the given function.

Considering the analysis above, graph (B) best represents the function g(x) = 3^(2x-1) as it demonstrates the expected exponential growth behavior as x increases.

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Question

Which of the following graphs represents the function g(x)=3^2x-1

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

The value of a/b is 10/3.

We start by simplifying the expression under the square root:

√((4/5) * (5/4) * (6/5) * (x/a) * (b/x)) = 2

We can observe that the terms (4/5) and (5/4) cancel out, leaving us with:

√(6/5 * (x/a) * (b/x)) = 2

Next, we square both sides of the equation to eliminate the square root:

6/5 * (x/a) * (b/x) = 2²

Simplifying the right hand side, we get:

6/5 * (x/a) * (b/x) = 4

Multiplying both sides by 5/6, we get:

(x/a) * (b/x) = (5/6) * 4

x and b cancel out, and we are left with:

a = 10/3

Therefore, the value of a/b is:

a/b = (10/3) / 1

a/b = 10/3

So the value of a/b is 10/3.

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In terms of length, 218 inches is greater than 6 yards.

To determine which is more, 6 yards or 218 inches, we need to convert one or both of the measurements to a common unit of measurement. In this case, we can convert yards to inches or inches to yards for comparison.

Since there are 36 inches in a yard, we can convert 6 yards to inches by multiplying it by 36:

6 yards * 36 inches/yard = 216 inches.

Now, we can compare the converted measurements: 216 inches and 218 inches.

Since 218 inches is greater than 216 inches, we can conclude that 218 inches is more than 6 yards.

This comparison can also be verified by considering the conversion factors. 6 yards is equivalent to 216 inches, which is smaller than 218 inches.

It is important to note that when comparing measurements, it is crucial to ensure that both measurements are in the same unit for an accurate comparison. Converting them to a common unit helps provide a clear understanding of which value is greater or smaller.

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Work Shown:

A = 7 chilies + 9 beetroots = 16 items that aren't a carrot

B = 7 chilies + 9 beetroots + 11 carrots = 27 items total

P(not a carrot) = A/B = 16/27

The original number is -56/3. Let's assume the original number is represented by the variable "x."

According to the given information, "Five times a number is divided by $7$ more than that number," we can express this mathematically as:

5x / (x + 7) = 8

To find the original number, we need to solve this equation for x.

Cross-multiplying the equation gives us:

5x = 8(x + 7)

Expanding the equation:

5x = 8x + 56

Subtracting 8x from both sides:

-3x = 56

Dividing both sides by -3:

x = -56 / 3.

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Answer:

y - 3 = 1(x - 6)  or y - 4 = 1(x - 7)

Step-by-step explanation:

to find the slope: m = (3-4) / (6-7) = -1 / -1 = 1

next, substitute the values into the equation: y2 - y1 = m(x2 - x1)

you can use any x or y value from the given.

y - 3 = 1(x - 6)

or

y - 4 = 1(x - 7)

Step-by-step explanation:

This is a law of sines problem.

Law of sines states that

A / sin (a) = B(sin b) = C (sin c)

5 / sin (60) = 9 / sin (x)

Simplifying this equation gives us sin (x) = (9 * sin (60)) / 5. Now we take the arc sin of both sides, to get that x = arc sin ((9 * sin (60)) / 5). Plugging this into a calculator gives us..... no solutions

I think thats the right solution as I plugged it into a law of sines calculator as well.

If each bus holds ten students and there are three buses, then the total number of students going to the show is 10 x 3 = 30 students.

The mass of the bus, 1900, is most likely measured in kilograms (kg) because kilograms are a commonly used unit for measuring the mass of large objects like vehicles.

If there are five rows in the theatre and Mr. Murray wants an equal number of students to sit in each row, then the number of students in each row would be the total number of students (30) divided by the number of rows (5), which is 30 / 5 = 6 students per row.

If Mrs. Stewart has two times as many students as Mr. Murray, and Mr. Murray has 30 students, then Mrs. Stewart would have 2 x 30 = 60 high school students in the theatre for the show.

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The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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5) The measures of central tendency for the monthly rainfall (in inches) are as follows:

Mean = 1 inch

Median = 0.5 inches

Modes = 0.25 inches.

6) The measures of central tendency for the July 4th Temperatures (°F) are as follows:

Mean = 94.75°F

Median = 95.5°F

Modes = 96°F

7) The measures of central tendency for the Baby Sleep Log (in hours) are as follows:

Mean = 8.7 hours

Median = 8.5 hours

Modes = 8 hours

8) The measures of central tendency for the Daily running log (in kilometers) are as follows:

Mean = 3 km

Median = 3 km

Modes = 2.5 km

9) The measures of central tendency for the Reading log (in pages) are as follows:

Mean = 33.4 pages

Median = 34 pages

Modes = None

10) The measures of central tendency for the Monthly snowfall (in inches) are as follows:

Mean = 1.75 inches

Median = 1

Modes = None

The measures of central tendency are summary statistics of a data set which present the typical values about the data set.

Generally, the measures of central tendency are as follows:

1, 0, 2, 0.5, 0.25, 3, 0.25

Arranged data: 0, 0.25, 0.25, 0.5, 1, 2, 3

Total value = 7 (0 + 0.25 + 0.25 + 0.5 + 1 + 2 + 3)

Number of items = 7

Mean = 1 inch (7 ÷ 7)

Median = 0.5 inches

Modes = 0.25 inches

89, 94, 96, 99, 96, 97, 95, 92

Arranged data: 89, 92, 94, 95, 96, 96, 97, 99

Total value = 758°F (89 + 92 + 94 + 95 + 96 + 96 + 97 + 99)

Number of items = 8

Mean = 94.75°F (758 ÷ 8)

Median = 95.5°F (95 + 96)

Modes = 96°F

10, 8, 9, 8, 8.25, 9.25, 8.5

Arranged data: 8, 8, 8.25, 8.5, 9, 9.25, 10

Total value = 61 (8 + 8 + 8.25 + 8.5 + 9 + 9.25 + 10)

Number of items = 7

Mean = 8.7 hours (61  ÷ 7)

Median = 8.5 hours

Modes = 8 hours

3.5, 0, 2.5, 5, 2.5, 3, 4.5

Arranged data: 0, 2.5, 2.5, 3, 3.5, 4.5, 5

Total value = 21 (0 + 2.5 + 2.5 + 3 + 3.5 + 4.5 + 5)

Number of items = 7

Mean = 3 km (21  ÷ 7)

Median = 3 km

Modes = 2.5 km

21, 42, 25, 45, 37, 34, 30

Arranged data: 21, 25, 30, 34, 37, 42, 45

Total value = 234 (21 + 25 + 30 + 34 + 37 + 42 + 45)

Number of items = 7

Mean = 33.4 pages (234 ÷ 7)

Median = 34 pages

Modes = None

0.5, 2, 5, 0.25, 1

Arranged data: 0.25, 0.5, 1, 2, 5

Total values = 8.75 inches(0.25 + 0.5 + 1 + 2 + 5)

Number of items = 5

Mean = 1.75 inches (8.75÷ 5)

Median = 1

Modes = None

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Answer:

[tex]6,10[/tex]

Step-by-step explanation:

Method 1:

[tex]\mathrm{Let\ two\ numbers\ be\ x\ and\ y\ such\ that:}\\\mathrm{x:y=3:5\ \ \ \ and\ \ \ \ x+y=16}\\\mathrm{or,\ \frac{x}{y}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3y..........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{x+y=16}\\\mathrm{or,\ 5(x+y)=5(16)}\\\mathrm{or,\ 5x+5y=80}\\\mathrm{or,\ 3y+5y=80\ [From\ equation\ 1]}\\\mathrm{or,\ 8y=80}\\\mathrm{or,\ y=10}\\\mathrm{From\ equation\ 1,}\\\mathrm{5x=3y}\\\mathrm{or,\ 5x=3(10)=30}\\\mathrm{\therefore x=6}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Alternative method 1:

[tex]\mathrm{Let\ the\ two\ numbers\ be\ x\ and\ 16-x.}\\\mathrm{Then,\ we\ have}\\\mathrm{x:(16-x)=3:5}\\\\\mathrm{or,\ \frac{x}{16-x}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3(16-x)=48-3x}\\\mathrm{or,\ 5x+3x=48}\\\mathrm{or,\ 8x=48}\\\mathrm{\therefore x=6}\\\mathrm{So,\ the\ other\ number=16-x=16-6=10}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Alternative method 2:

[tex]\mathrm{Let\ the\ two\ numbers\ be\ 3x\ and\ 5x.}\\\mathrm{Then,}\\\mathrm{3x+5x=16}\\\mathrm{or,\ 8x=16}\\\mathrm{or,\ x=2}\\\mathrm{So,\ first\ number=3x=3(2)=6}\\\mathrm{Second\ number=5x=5(2)=10}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Answer:

x-2 and y(-1) -1

Step-by-step explanation:

Explained
it made a reflection of the y-axis (-1) and lowered it by 1 unit (-1)

It moved to the left by two units so x-2

X-2 and y(-1) -1

When the scale factor is 1, the triangle is a 30-60-90 triangle. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 1:√3.

When the scale factor is 3, the triangle is still a 30-60-90 triangle. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 3:√3.

The ratio of the side length of the side opposite any 30° angle and the length of the hypotenuse is always 1:√3. This is because the side opposite the 30° angle is always the shorter leg of the triangle, and the hypotenuse is always twice the length of the shorter leg.

30-60-90 triangle with a scale factor of 3

The side opposite ∠A is 3 units long, and the hypotenuse is √3 units long. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 3:√3.

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Answer:  Choice C

Condition 1 fails. [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] does not exist

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

Explanation:

Use a table or a graph to determine that [tex]\ln(\text{x}^2)[/tex] approaches negative infinity as x gets closer to 0.

Symbolically [tex]\displaystyle \lim_{\text{x} \to 0}\ln(\text{x}^2) = -\infty[/tex]. Since this result is not a finite number, we consider the limit to not exist. Write "DNE" as shorthand for "does not exist".

Therefore, [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x}) = -\infty[/tex] making [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] not exist as well.

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Hello!

8 x 10⁵

= 8 x 100000

= 800000