Find the GCF of each expression.
The GCF of 12y - 3 is_____.
The GFC of 4y + 10 is_____.
The GCF of 28 − 8 is _____.
The GCF of 30 + 18 is _____.

The equation in slope intercept for the given line is  y = -2/3x - 28/3.

What is Slope ?

The slope or gradient of a line in mathematics is a number that indicates the line's steepness and direction.

Given,  the line crosses the x-axis at 14 and is parallel to the line represented by y= -2/3x+6.

We know that two parallel lines always have the same slope.

We can say that the line has coordinate as (14,0) and slope (m) as -2/3.

We know that the slope-intercept form of the line is,

                    y= mx + b

Now, We put x=14, y=0 and m=-2/3 in equation above,

We get, 0 = -2/3 × 14 + b

             b = -28/3

So, the slope intercept form will be :

               y = -2/3x - 28/3

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There is a positive association between per capita chicken egg consumption and divorce rate is true.

A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity. A sentence can only be true or untrue and not both for it to be a statement.

A meaningful string of words that can be either true or incorrect makes up a mathematical statement. They are referred to simply as a statement. For instance, "ABC is an equilateral triangle" could be denoted by the letter "p." As a result, in an equilateral triangle, p = ABC.

There is a positive association between per capita chicken egg consumption and divorce rate is the correct and valid statement according to the given presented situation.

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Answer: 89

Step-by-step explanation:

1 hr of mowing = 8.20 dollars

1 hr of babysitting = 7.90 dollars

7 hrs of mowing = 8.20 x 7 = 57.4 dollars earned

4 hrs of babysitting = 7.90 x 4 = 31.6 dollars earned

Total amount she has earned = 57.4 + 31.6 + = 89 dollars

All the given three conditions are true for conducting a two proportion significance test.

To check the significance of two proportions, following conditions should be met

Hence, all the three conditions must be met to conduct a two-proportion significance test.

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Answer:

the mean (i.e. the average)

Step-by-step explanation:

There's no clear outlier or inconsistency therefore the mean should be used.

The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics.

Fill in blanks :

A point has no dimension. it is an abstract idea of a location in space.

A vertex is where two edges meet at a point

A line has edge dimension - length . An edge is a line segment where two faces meet.

A  flat plane figures has a 2 dimension - length and width

The 3 points of a 3D object is a plane.

Three dimensional objects have vertices, edges and faces unless they are the geometric solids like cylinders, cones and sphere.

when we talk about line we are looking at the measure of a one dimensional figure.

when we talk about area we are looking at the space inside of a two dimensional figure.

when we talk about volume we are looking at the total space enclosed by a three dimensional figure.

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The plane touches the runway with a speed of 65 m/s then the acceleration of the plane during its landing will be equal to 65 m/s².

The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.

Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.

As per the given information in the question,

Velocity, v = 65 m/s

Time, t = 1 sec.

Use the equation of acceleration,

a = v/t

a = 65/1

a = 65 m/s²

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The indefinite integral is - 1 / [5(6 + [tex]x^{5}[/tex])] + C.

An integral is considered to be indefinite if it has no upper or lower bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C. Without upper and lower bounds on the integrand, indefinite integrals are stated using the notation f(x), which represents the function as an antiderivative of F. Consequently, "f(x) dx=F" (x). As we observed in the same example with antiderivatives, the integral, x3 dx=14x4+C, is one example.

The area under the f(x) curve from x=a to x=b is represented by the definite integral of f(x), which is a NUMBER. Integral indefinite. An indefinite integral of a function f(x), also known as an antiderivative, is denoted by and its derivative is denoted by f. (x). The indefinite integral is not the only solution because the derivative of a constant is zero. Integration is the action of locating an indefinite integral.

Use a u-substitution with u = (6 + [tex]x^{5}[/tex])

du = 5[tex]x^{4}[/tex]dx

1/5 ∫ [tex]u^{-2}[/tex]du

= -1/5 [tex]u^{-1}[/tex] + C

= - 1 / [5(6 + [tex]x^{5}[/tex])] + C

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Correct Question:

Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)

[tex]\int\limits^ {} \frac{x^{4} }{(6+x^{5})^{2} } dx[/tex]

The solution is Option A.

The exponential growth model for the number of bacteria in the sample after x hours is    [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the equation for the number of bacteria in the sample after x hours = P

The value of the equation P ( x ) is given by

After 4 hours , the sample contained 400 bacteria

So ,

when x = 4

[tex]P ( 4 ) = ae ^{4b }=400[/tex]   be equation (1)

After 12 hours , the sample contained 1600 bacteria

And , when x = 12

[tex]P ( 12 ) = ae ^{12b }=1600[/tex]   be equation (2)

Divide equation (2) by equation (1) , we get

[tex]\frac{P ( 12 )}{P ( 4 )} = \frac{ae ^{12b }}{ae ^{4b }} = \frac{1600}{400}[/tex]

On simplifying the equation , we get

e¹²ᵇ⁻⁴ᵇ = 4

e⁸ᵇ = 4

Taking logarithm on both sides of the equation , we get

8b = ln (4)

Divide by 8 on both sides , we get

b = ln (4) / 8

Substituting the value for b in equation (1) , we get

[tex]ae ^{4*ln (4) / 8 }=400[/tex]

[tex]ae ^{ln (4) / 2}=400[/tex]

On simplifying the equation , we get

a x 2 = 400

Divide by 2 on both sides of the equation , we get

a = 200

Therefore , the exponential growth equation is given by

Substitute the values of a and b in the equation , we get

[tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]

Hence , The exponential growth model for the number of bacteria in the sample after x hours is    [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]

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according to question,

given data.

h(x)=8x-3/4+5

then,

Answer:

Step-by-step explanation:

To solve this problem, we need to calculate Martha's out-of-pocket expenses, and the total amount of money she had to pay for her medical bills.

First, we need to calculate the amount of money Martha had to pay toward her deductible. Since her deductible is $200, this is the amount she had to pay out of pocket.

Next, we need to calculate the amount of money Martha had to pay toward her co-payment. Since her co-payment is 20%, we can calculate this by multiplying her medical bills by the co-payment rate: $6,500 x 0.2 = $1,300.

To find Martha's total out-of-pocket expense, we can add the amount she paid towards her deductible ($200) and the amount she paid towards her co-payment ($1,300):

$200 + $1,300 = $1,500

Therefore, Martha's out-of-pocket expense was $1,500.

Martha's insurance required her to pay a $200 deductible and a 20% co-payment on the remaining balance of her medical bills. After paying the deductible, she pays 20% of the remaining $6,300 which is $1,260. So, Martha's total out-of-pocket expense was $1,460.

Martha's health insurance plan includes a $200 deductible and a 20% co-payment. The deductible is the amount Martha has to pay before the insurance company starts to pay. In this case, Martha first pays a $200 deductible from her $6,500 medical bills, which leaves her with $6,300 to be covered by insurance and her co-payment. The 20% co-payment means Martha is responsible for paying 20% of the remaining $6,300. To calculate this, we multiply $6,300 by 0.20 (20%), which equals $1,260. Therefore, Martha's total out-of-pocket expense for her medical bills last year was the $200 deductible plus the $1,260 co-payment, equalling $1,460.

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Division followed by simplification of mentioned rational function gives:

(x + 1)/(x + 4)

Factoring an algebraic expression specifically means writing a given expression as the product of its factors. These factors may be numbers, variables, or algebraic expressions.

1, 2, 6, and 12 are all divisors of 12 because they divide 12 equally. This is an important algebraic operation, which is used to simplify expressions, simplify fractions, and solve equations. This is also called algebraic factorization.

Factorization of x² + 2x - 3

x² + 3x - x - 3

(x² + 3x) - (x + 3)

x(x + 3) - 1(x + 3)

(x + 3)(x - 1)

Factorization of x² + 3x - 4

x² + 4x - x - 4

(x² + 4x) - (x + 4)

x(x + 4) - 1(x + 4)

(x + 4)(x - 1)

Factorization of x² - 2x - 3

x² - 3x + x - 3

(x² - 3x) + (x - 3)

x(x - 3) + 1(x - 3)

(x - 3)(x + 1)

Using identity, a² - b² = (a + b)(a - b)

x² - 9 = x² - 3²

x² - 3² = (x + 3)(x - 3)

Now, for the division:

(x² + 2x - 3)/(x² - 9) ÷ (x² + 3x - 4)/(x² - 2x - 3)

[(x + 3)(x - 1)/(x + 3)(x - 3)] ÷ [(x + 4)(x - 1)/(x - 3)(x + 1)]

By reciprocal of (x + 4)(x - 1)/(x - 3)(x + 1)

[(x + 3)(x - 1)/(x + 3)(x - 3)] × [(x - 3)(x + 1)/(x + 4)(x - 1)]

= (x + 1)/(x + 4)

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Answer:

Step-by-step explanation:

40k

Answer:

$16,000

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Let investment 1 be the bond that pays 5.75% simple interest.

Let investment 2 be the bond that pays 7.25% simple interest.

Given:

Create two equations for the interest from both investments.

Interest from Investment 1

[tex]\implies \sf I_1=P_1 \cdot 0.0575 \cdot 1[/tex]

[tex]\implies \sf I_1=0.0575\:P_1[/tex]

Interest from Investment 2

[tex]\implies \sf I_2=P_2 \cdot 0.0725 \cdot 1[/tex]

[tex]\implies \sf I_2=(28000-P_1)0.0725[/tex]

[tex]\implies \sf I_2=2030-0.0725\:P_1[/tex]

Given that the sum of the interest from both investments is $1,790:

[tex]\implies \sf I_1+I_2=1790[/tex]

[tex]\implies \sf 0.0575\:P_1+2030-0.0725\:P_1=1790[/tex]

[tex]\implies \sf -0.015\:P_1=-240[/tex]

[tex]\implies \sf P_1=16000[/tex]

Therefore, $16,000 should be invested in the 5.75% bond.

Check:

[tex]\implies \sf I_1=16000 \cdot 0.0575 \cdot 1 = 920[/tex]

[tex]\implies \sf I_2=12000 \cdot 0.0725 \cdot 1 = 870[/tex]

[tex]\implies \sf I_1+I_2=920+870=1790[/tex]

Step-by-step explanation:

0 hours -> $500 total cost

1 hour -> $575 total cost (500 + 1×75)

2 hours -> $650 total cost (500 + 2×75)

3 hours -> $725 total cost (500 + 3×75)

P(t) = 75t + 500

a.The formula that describe the sequence or progression is a+(7-7n)

b. 2nd term = -10 , 3rd term = 10, 4th term = -10 and 5th term = 10

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

The nth term of an arithmetic progression is given as a(n)= a + (n − 1) × d

In geometric progression the nth term is given as a(n)= ar^(n-1)

where a is the first term

therefore if a = 12 and d is - 7

the formula for the arithmetic progression =

a(n) = 12+(n-1) -7 = 12+( 7-7n)

If the first term of a GP is 10 with common ratio of -1

then the second term = 10×-1 = -10

third term = -10×-1 = 10

fourth term = 10×-1 = -10

fifth term = -10× -1 = 10

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Answer:

10°

Step-by-step explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is 360°.

x + 3x + 4x + 5x + 6x + 8x + 9x = 360

36x = 360

x = 10

In a polygon, an exterior angle is supplementary to its adjacent interior angle.

The smallest exterior angle is x, and x = 10.

Answer: 10°

Answer:

p = -8 6/35

Step-by-step explanation:

p/(1 6/7)=−4.4

To solve for p, multiply each side by 1 6/7

p/(1 6/7) * ( 1 6/7)=−4.4 *  (1 6/7)

p = - 4.4 * ( 1 6/7)

Change each number to fractions

p = -44/10 * 13/7

p = -286/35

Change to a mixed number

p = -8 6/35

The rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.

Given is the expression as follows -

f(x) = 4/(x - 3)

[A] -

{x - 3/x + 2} • {x + 2/4} = {x - 3/4}

[B] -

{x - 3}/{x + 2} / {4/x + 2} = {x - 3}/{x + 2} × {x + 2/4} = {x - 3/4}

[C] -

{x + 2/x - 3} • {4/x + 2} = {4/x - 3}

[D] -

{x + 2/x - 3} / {4/x + 2} = {(x + 2)²/ 4x - 3}

Therefore, the rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.

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Answer: the first one is 7/9 and the second one is option 2

Step-by-step explanation:

4+7 = 11

< or> = open dot

The critical value is -2.70

What is a null hypothesis?

Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.

Here, we have

The objective of this experiment is to compare two compounds, designed to reduce braking distance, used in tire manufacturing to prove if the braking distance of SUVs equipped with tires made with compound 1 is shorter than the braking distance of SUVs equipped with tires made with compound 2.

So you have 2 independent populations, SUV's equipped with tires made using compound 1 and SUVs equipped with tires made using compound 2.

Two samples of 66 braking tests are made and the braking distance was measured each time, the study variables are determined as:

X₁: Braking distance of an SUV equipped with tires made with compound one.

Its sample mean is X[bar]₁= 41 feet

And the Standard deviation S₁= 12.1 feet

X₂: Braking distance of an SUV equipped with tires made with compound two.

Its sample mean is X[bar]₂= 46 feet

And the Standard deviation S₂= 9.0 feet

We don't have any information on the distribution of the study variables, nor the sample data to test it, but since both sample sizes are large enough n₁ and n₂ ≥ 30 we can apply the central limit theorem and approximate the distribution of both variables sample means to normal.

The researcher's hypothesis, as mentioned before, is that the braking distance using compound one is less than the distance obtained using compound 2, symbolically: μ₁ < μ₂

The statistical hypotheses are:

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

α: 0.05

The statistic to use to compare these two populations is a pooled Z test

Z= {(X[bar]₁-X[bar]₂) - (μ₁ - μ₂)}/√S₁²/n₁+S₂²/n₂ ≈ N(0;1)

Z = {(41-46)-0}/√146.41/66+81/66

Z = -5/1.85

Z = -2.70

The rejection region of this hypothesis test is one-tailed to the right, so you'll reject the null hypothesis to small values of the statistic. The critical value for this test is:

Z(α) = Z(0.05) = -1.645

Decision rule:

If Z(H₀) ≥  -1.645, then you do not reject the null hypothesis.

If Z(H₀) < -1.645, then you reject the null hypothesis.

Since the statistic value is greater than the critical value, the decision is to not reject the null hypothesis.

At a 5% significance level, you can conclude that the average braking distance of SUVs equipped with tires manufactured used compound 1 is greater than the average braking distance of SUVs equipped with tires manufactured used compound 2.

Hence, the critical value is -2.70.

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You can successfully use nominal GDP, real GDP, and other economic indicators to draw conclusions because they health of the country's economy.

GDP stands for Gross Domestic Product. This is a very common economic indicator that shows the value of the services and products produced by a country usually in a one year period.

In general real GDP is considered to be more accurate as nominal GDP is influenced by factors such as inflation that can distort the general idea you can get about a country's economy and the total output of it.

Both real, nominal GDP and other indicators show the health of the economy in a country, which makes it useful to draw conclusions about the economy.

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The line segment of length 3 1/2 is sketched with mid pint at -1 and attached

A line segment in geometry has two different points on it that define its boundaries.

A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

The endpoints is important before a line can be defined as a line segment, however the midpoint will be essential in calculating for the endpoints

The mid point of the line is given to be -1

the other ends will be 3 1/2 /2

1.75

from -1 add and subtract 1.75 to get the endpoint's

-1 + 1.75 = 0.75

-1 - 1.75 = 2.75

each unit on the number line is 0.3333

to get 0.75 from 0 count two units to give 0.6667 then a bit more to get to 0.75

to get 2.75 from 2 count two strokes to get to 2.6667, then add a little more to get 2.75

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Answer:

I believe if I just believe that you can work this out then you can do it thank you You are intelligent you can do this

Answer:

Step-by-step explanation:

-2 * -10 = 20

Answer:

30×2×(-10)-5+2

=60×(-10)-3

=-60-3

=-63

Answer:

x < - 3

Step-by-step explanation:

4x + 6 < 3x + 3 ( subtract 3x from both sides )

x + 6 < 3 ( subtract 6 from both sides )

x < - 3

Answer:

x < -3

Step-by-step explanation:

4x+6<3x+3

= 4x+6-3x<3

= 4x-3x<3-6

4x-3x<3-6

=x<3-6

x<-3

The cost of a 25-minute rental will be $92.00.

To find the amount a 25-minute rental would cost, we need to first determine the rate per minute and the flat fee. We can do this by setting up the following system of equations:

30 minutes x rate + flat fee = $110.50

40 minutes x rate + flat fee = $145

To solve this system of equations, we can multiply the first equation by 2 and subtract the second equation from it to eliminate the rate:

(30 minutes x 2) x rate + flat fee x 2 = 2 x $110.50

80 minutes x rate + flat fee x 2 = 2 x $110.50

Subtracting the second equation from the first equation, we get:

flat fee x 2 - flat fee x 2 = 2 x $110.50 - 2 x $145

flat fee x 2 - flat fee x 2 = -$34.50

Since the left side of the equation is equal to zero, we can divide both sides by 2 to solve for the flat fee:

flat fee - flat fee = -$34.50 / 2

flat fee - flat fee = -$17.25

Since the left side of the equation is also equal to zero, the flat fee must be zero.

We can now use either of the original equations to solve for the rate per minute. Using the first equation, we get:

30 minutes x rate + flat fee = $110.50

30 minutes x rate = $110.50

rate = $3.68

We can now use this rate to find the cost of a 25-minute rental:

25 minutes x $3.68 + flat fee = $92.00 (Since the flat fee is zero)

Thus, a rental of 25 minutes costs $92.00.

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A. By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.

What is a logarithm function?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, its logarithm in base 10 is 3, or log₁₀ 10³= 3.

Given function are

f(x) = log x and g(x) = log₃ x.

The rate of raise of the graph g(x) is more than that of the graph f(x).

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To find a Riemann sum that gives an upper estimate of the double integral, we need to divide the region of integration into small subregions (in this case, squares) and take the maximum value of f(x, y) over each subregion.

The Riemann sum will then be the sum of the areas of the subregions times the maximum value of f(x, y) over each subregion.

For example, if we divide the region of integration into four squares, the Riemann sum would be given by:

Riemann sum = (area of first square) * (maximum value of f(x, y) in first

                           square) + (area of second square) * (maximum value of

                           f(x, y) in second square) + (area of third square) *

                           (maximum value of f(x, y) in third square) + (area of fourth

                           square) * (maximum value of f(x, y) in fourth square)

We can then fill in the specific values of the areas and maximum values of f(x, y) for each square based on the given values of f(x, y).

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Answer:

AB = 45.688 metres

Step-by-step explanation:

* i used a scientific calculator for my working. i am not sure if calculators are permitted for your exam on Wednesday *

⭐AB = AD + DB

⭐AB = 16.5 + DB

Thus, we need to find DB in order to solve for AB.

First, I utilized the triangle sum theorem to find ∠BDC:

[tex]< BDC + < DCB + < B = 180\\ < BDC + 59 + 90 = 180\\ < BDC + 149 = 180\\ < BDC = 31[/tex]

Then, I utilized the linear pair sum to find ∠ADC:

[tex]< ADC + < BDC = 180\\ < ADC + 31 = 180\\ < ADC = 149[/tex]

Next, I utilized the triangle sum theorem to find ∠DAC:

[tex]< DAC + < ADC + < ACD = 180[/tex]

[tex]< DAC + 149 + 10 = 180[/tex]

[tex]< DAC + 159 = 180[/tex]

[tex]< DAC = 21[/tex]

After, I utilized the law of sines to find DC:

[tex]\frac{sin10}{16.5} = \frac{sin21}{DC}[/tex]

[tex]DCsin10 = 16.5sin21[/tex]

[tex]DC = \frac{16.5sin21}{sin10}[/tex]

[tex]DC = 34.052[/tex]

Then, I utilized the sine function to find DB for ΔBDC:

[tex]sin(59) = \frac{DB}{34.052}[/tex]

[tex]34.052sin(59) = DB[/tex]

[tex]29.188 = DB[/tex]

Finally, I substituted DB into our original equation for AB:

[tex]AB = AD + DB[/tex]

[tex]AB = 16.5 + 29.188[/tex]

[tex]AB = 45.688 metres[/tex]

Good luck on your exam on Wednesday! :-)

The height of the pole will be equal to 45 meters.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Given that the angle BCD is 59 and the angle BCA is 69. The height will be calculated as,

tan(59) = BD / BC

BC = BD / tan(59)

BC = 0.6BD

tan(69) = AB / BC

tan(69) = ( 16.5 + BD ) / BC

BC = 0.38( 16.5 + BD )

Equate the values of BC,

0.6BD = 0.38 ( 16.5 + BD )

0.6BD = 6.27 + 0.38BD

0.22BD =6.27

BD = 28.5 meters

The height of the pole is,

AB = AD + DB

AB = 16.5 + 28.5

AB = 45 meters

The height is 45 meters.

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