A rectangular prism with a square base has a height of 17. 2 cm and a volume of 24. 768 cm3. What is the side length of its base?

Chelsey is correct.

The equation of the tangent line is y = 8

Perimeter of BCDE is 28.28

Chelsey is correct. The tangent line at a point on a circle is perpendicular to the radius at that point.

Therefore, it has the same slope as the radius at the point of tangency.

To find the equation of the tangent line at point B(7,8), find the slope of the radius at B.

The radius at B passes through the center of the circle (7,3) and B(7,8), so its slope is:

m = (8 - 3) / (7 - 7) = undefined

This is because the radius is a vertical line. The slope of the tangent line at B is the negative reciprocal of the slope of the radius at B, which is 0.

The equation of the tangent line is:

y - 8 = 0(x - 7)

y = 8

Part B: To find the perimeter of BCDE, we need to find the length of one of its sides and then multiply by 4. Since the square is inscribed in the circle, its diagonal is equal to the diameter of the circle, which is 10 (twice the radius).

Therefore, the length of one side of the square is:

s = 10/√(2) ≈ 7.07

The perimeter of BCDE is:

4s = 4(7.07) ≈ 28.28

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Answer:

d

Step-by-step explanation:

so b = 4

and the slope is rise over run = 5/2

Answer:

D) [tex]y=\frac{5}{2}x+4[/tex]

Step-by-step explanation:

The line equation of a line is:

[tex]y=mx+b[/tex] with m being the slope and b being the y-intercept.

We can see from the graph that the y-intercept is 4, as that's where the line intercepts the y-axis, and when x=0.

To find the slope, we first need to pick 2 points: (0,4) and (2,9).

The formula for slope is:

[tex]\frac{rise}{run}[/tex]

The rise is how many units you go up/down from one point to another.  The run is how many units you go left/right from one point to another.
We can see that we go up 5 units and we go right 2 units.  This means our slope is 5/2.

The completed line equation is:

[tex]y=\frac{5}{2}x+4[/tex], which means D is the correct option.

Hope this helps! :)

The mechanic used 412 - 411.375 = 0.625 gallons of motor oil during the day.

To solve this problem, we need to convert both measurements to the same unit.

1 gallon = 8 pints (since there are 8 pints in a gallon)

So the mechanic started with:

412 gallons * 8 pints/gallon = 3,296 pints

And ended with:

5 pints

To find how much motor oil the mechanic used during the day, we can subtract the ending amount from the starting amount:

3,296 pints - 5 pints = 3,291 pints

To convert this back to gallons, we divide by 8:

3,291 pints / 8 pints/gallon = 411.375 gallons (rounded to three decimal places)

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The percent of sales that occurred in May is: 6.6%

If the sales in March were double the sales in May, and the central angle in the graph for March measured 47.5°, we can find the central angle for May as follows:

Let x be the central angle for May. Then we have:

2x = 47.5

Solving for x, we get:

x = 23.75

So the central angle for May is 23.75°.

To find the percent of sales that occurred in May, we need to calculate the ratio of the central angle for May to the total central angle of the circle graph, and then multiply by 100. The total central angle of a circle is always 360°.

So the percent of sales that occurred in May is:

(23.75/360) x 100 = 6.6%

Therefore, 6.6% of the sales occurred in May.

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Answer:

In a triangle, the side opposite to the largest angle is the longest side, and the side opposite to the smallest angle is the shortest side. In triangle XYZ, the length of side XY is m + 8, the length of side YZ is 2m + 3, and the length of side ZX is m - 3. Since m ≥ 6, we can determine that 2m + 3 is the largest value, m + 8 is the next largest value, and m - 3 is the smallest value. Therefore, side YZ is the longest side and side ZX is the shortest side.

Since side YZ is the longest side, angle X must be the largest angle. Since side ZX is the shortest side, angle Y must be the smallest angle. Therefore, the correct ordering of the angles from smallest to largest is ∠Y < ∠Z < ∠X.

Step-by-step explanation:

The final answer to this question on vector is : - (v/2)/||v/2|| = -/sqrt((v1/2)^2 + (v2/2)^2 + (v3/2)^2).

To find a unit vector that is oppositely directed to v and half the length of v, we first need to find the length of v. Let's say v = . Then, the length of v, denoted as ||v||, is given by:

||v|| = sqrt(v1^2 + v2^2 + v3^2)

Now, since we want a vector that is half the length of v, we can simply divide v by 2: v/2

However, we also want this vector to be oppositely directed to v, which means we need to change the sign of each component.

Therefore, our final answer is:
- (v/2)/||v/2|| = -/sqrt((v1/2)^2 + (v2/2)^2 + (v3/2)^2)

This is the unit vector that is oppositely directed to v and half the length of v.

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The rate at which salt enters the tank at time t is constant & equal to 8 lb/min,

The rate at which salt enters the tank at time t is equal to the product of the concentration of the incoming brine & the rate at which it enters the tank

At time t, the amount of salt in the tank is y(t), & the volume of the brine in the tank is V(t)-

Therefore, the concentration of salt in the tank at time t is:-

c(t) = y(t) / V(t)

The rate at which brine enters the tank at time t is 4 gal/min, & the concentration of salt in the incoming brine is 2 lb/gal

So the rate at which salt enters the tank at time t is:-

2 lb/gal x 4 gal/min = 8 lb/min

Therefore, the rate at which salt enters the tank at time t is constant & equal to 8 lb/min, regardless of how much salt is already in the tank

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One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.

The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.

At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.

By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)[tex])^12[/tex] pounds, using the formula for compound interest. This simplifies to (1+1/12[tex])^12[/tex] pounds or (1.0833[tex])^12[/tex] pounds, which is approximately equal to 2.613 pounds.

Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)[tex])^12[/tex] pounds or approximately 2.613 pounds by the end of the year.

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Step-by-step explanation:

volume of a cylinder is pi × r² × height

r = 2.5

height= 4

volume = pi × 2.5² × 4

volume = 25 pi

The expected value of X is 2.33.

To find the expected value of the random variable X, we need to use the given probability function f(x) and the formula for expected value: E(X) = Σ[x * f(x)]. Here's a step-by-step explanation:

1. Identify the possible values of x: 1, 2, and 3.
2. Calculate f(x) for each x value using the given probability function f(x) = x/6:
  f(1) = 1/6
  f(2) = 2/6 = 1/3
  f(3) = 3/6 = 1/2
3. Apply the expected value formula by multiplying each x value by its corresponding f(x) and summing the results:
  E(X) = (1 * 1/6) + (2 * 1/3) + (3 * 1/2) = 1/6 + 2/3 + 3/2
4. Simplify the expression to find the expected value:
  E(X) = 1/6 + 4/6 + 9/6 = (1 + 4 + 9)/6 = 14/6 = 7/3

The expected value of the random variable X is 7/3 or 2.33.

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The solution to the system of linear equations is (x, y) = (13, -4).

To solve the system of linear equations using Gaussian elimination, we need to eliminate one variable from one of the equations. Here, we can eliminate x from the second equation by subtracting twice the first equation from the second equation:

x + 2y = 5    (equation 1)

2x + 3y = 6    (equation 2)

--------------

  -2x - 4y = -10   (2 * equation 1)

        y = -4

Now, we can substitute the value of y into the first equation to solve for x:

x + 2(-4) = 5

x - 8 = 5

x = 13

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ccabo de 25 años será la edad del padre tres veces mayor que la edad del hijo.El número es 36.Hay 8 hombres, 16 mujeres y 72 niños.Hay 27 cerdos y 8 pavos

Sea x el número de años transcurridos. La edad del padre será 35 + x y la edad del hijo será 5 + x. La ecuación que representa la situación es: 35 + x = 3(5 + x). Resolviendo la ecuación, tenemos:

35 + x = 15 + 3x

2x = 20

x = 10

Por lo tanto, después de 10 años, la edad del padre será tres veces mayor que la edad del hijo.

Sea x el número desconocido. La ecuación que representa la situación es: 2x - (1/2)x = 54. Resolviendo la ecuación, tenemos:

(4/2)x - (1/2)x = 54

(3/2)x = 54

x = 36

Por lo tanto, el número desconocido es 36.

Sea x el número de hombres. Según la información dada, el número de mujeres es el doble, es decir, 2x, y el número de niños es el triple, es decir, 3(x + 2x) = 9x. La ecuación que representa la situación es: x + 2x + 9x = 96. Resolviendo la ecuación, tenemos:

12x = 96

x = 8

Por lo tanto, hay 8 hombres, 16 mujeres y 72 niños en la reunión.

Sea x el número de cerdos y y el número de pavos. Según la información dada, tenemos las siguientes ecuaciones: x + y = 35 (por el total de cabezas) y 4x + 2y = 116 (por el total de patas). Resolviendo este sistema de ecuaciones, obtenemos:

x + y = 35

4x + 2y = 116

Multiplicamos la primera ecuación por 2:

2x + 2y = 70

Restamos la segunda ecuación de la primera:

2x + 2y - (4x + 2y) = 70 - 116

-2x = -46

x = 23

Sustituyendo el valor de x en la primera ecuación, tenemos:

23 + y = 35

y = 12

Por lo tanto, hay 23 cerdos y 12 pavos en la granja.

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Answer:

E

Step-by-step explanation:

This figure contains a square and a quarter of a circle

The perimeter is the sum of all side lengths

Let's find the circumference of the quarter of a circle:

[tex]0.25c = 2\pi \times r[/tex]

The diameter is equal to a square's side length:

d = 8

hence, r = 0,5 × 8 = 4

[tex]0.25c = 2 \times 3.14 \times 4 = 25.12[/tex]

Now, we can find the perimeter:

P = 25,12 + 8 + 8 = 41,12

The dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.

We can use the following steps:

Step 1: Write the volume formula for the cylinder.
The volume (V) of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since the volume is given as 181 in³, we have:

181 = πr²h

Step 2: Solve for h in terms of r.
Divide both sides by πr²:

h = 181 / (πr²)

Step 3: Write the surface area formula for the cylinder without a top.
The surface area (S) of a cylinder without a top is given by the formula S = 2πrh + πr², where r is the radius and h is the height.

Step 4: Substitute h from step 2 into the surface area formula.
Replace h with 181 / (πr²) in the surface area formula:

S = 2πr(181 / (πr²)) + πr²

Step 5: Simplify the surface area formula.
After simplifying the surface area formula, we get:

S = (362 / r) + πr²

Step 6: Minimize the surface area.
To minimize the surface area, differentiate S with respect to r and set the derivative equal to 0:

dS/dr = -362/r² + 2πr = 0

Step 7: Solve for r.
To find the value of r that minimizes the surface area, solve the equation for r:

r³ = 181/π

r = (181/π)¹/³

Step 8: Find the height h.
Substitute the value of r back into the equation for h from step 2:

h = 181 / (π((181/π)¹/³)²)

Step 9: Calculate the dimensions.
Calculate the dimensions r and h using the values obtained in step 7 and step 8:

r ≈ 2.82 inches
h ≈ 7.10 inches

So, the dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.

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The equivalent expressions are p−3q=11 and 3p+q=3. Option A

It is important to note that equivalent equations are defined as equations that have the same solution but are different in the way with which the values are arranged.

From the information given, we have that;

3 times (p minus q) = 2 times p + 11

This equation is represented as;

3(p - q) = 2(p) + 11)

expand the bracket, we get;

3p - 3q = 2p + 11

collect the like terms

3p - 2p - 3q =11

Subtract the values

p - 3q = 11

Then,

4 times p + q = p + 3

4p + q = p + 3

collect like terms

4p - p + q = 3

3p = q = 3

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If both confidence intervals were correctly calculated (6. 53, 7. 95) is the 90 percent level. Therefore, the correct option is A.

To determine which confidence interval corresponds to the 90 percent level and the 98 percent level, we can look at the width of the intervals. The interval with the larger width is the one with a higher confidence level because it accounts for more possible variation in the data.

The first interval (6.53, 7.95) has a width of 7.95 - 6.53 = 1.42.

The second interval (6.20, 8.28) has a width of 8.28 - 6.20 = 2.08.

Since the second interval has a larger width, it corresponds to the higher confidence level of 98 percent. Therefore, the first interval corresponds to the 90 percent confidence level. The correct answer is option A. (6.53, 7.95) is the 90 percent level.

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Answer: 2

sqrt 41

Step-by-step explanation:

distance formula is just d=√((x2 – x1)² + (y2 – y1)²)

√(-2+8)^2+(-5-3)^2

√(-10)^2+(-8)^2

√100+64

2√41

Answer:they cannot conclude the mean price

Step-by-step explanation:

khan

At the α=0.01 significance level, there is not enough evidence to conclude that the mean price of gasoline in your state is more than $3 per gallon on that day.

Here you collected a random sample of 40 gas stations and calculated the sample mean (bar x) and the sample standard deviation (sₓ).

In this case, you found that the test statistic t was approximately 0.65, and the P-value was approximately 0.260. The P-value is the probability of observing a test statistic as extreme as the one you calculated, assuming that the null hypothesis is true.

A P-value of 0.260 means that if the null hypothesis were true, there is a 26% chance of observing a sample mean as extreme or more extreme than the one you calculated.

To make a decision about the hypothesis, you need to compare the P-value to the significance level (α), which represents the maximum probability of rejecting the null hypothesis when it is actually true. In this case, the significance level is set to α=0.01, which means that you want to be 99% confident in your decision.

If the P-value is less than the significance level, you reject the null hypothesis in favor of the alternative hypothesis.

If the P-value is greater than the significance level, you fail to reject the null hypothesis.

In this case, the P-value is greater than the significance level, which means that you fail to reject the null hypothesis.

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Complete Question:

An economist studying fuel costs suspected that the mean price of gasoline in her state was more than $3 per gallon on a certain day. On that day, she sampled 40 gas stations to test H0:μ=$3

Ha​:μ>$3

where μ is the mean price of gasoline per gallon that day in her state.

The sample data had a mean of bar x=$3.04 and a standard deviation of sₓ=$0.39

These results produced a test statistic of t≈0.65 and a P-value of approximately 0.260

Assuming the conditions for inference were met, what is an appropriate conclusion at the α=0.01  significance level?

We estimate with 95% confidence that the number of cigarettes smoked per day in the United States is between 14.38 and 15.62 million.

To estimate the number of cigarettes smoked per day in the United States, we need to use the following formula for a confidence interval:

sample statistic +/- z* (standard error of the statistic)

where the sample statistic is the mean number of cigarettes smoked per day, z* is the critical value from the standard normal distribution for the desired confidence level, and the standard error of the mean is given by:

standard deviation / sqrt(sample size)

We do not have the sample mean or standard deviation directly, but we can estimate them from the sample of American adults who smoke.

Let's assume that the sample size is n = 1000, and that the sample mean and standard deviation of cigarettes smoked per day are 15 and 10, respectively. Then the standard error of the mean is:

standard error = 10 / sqrt(1000) = 0.316

To find the critical value of z* for a 95% confidence level, we look up the value in the standard normal distribution table or use a calculator. For a two-tailed test with alpha = 0.05, the critical value is approximately 1.96.

Thus, the 95% confidence interval for the mean number of cigarettes smoked per day in the United States is:

15 +/- 1.96*0.316 = (14.38, 15.62)

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The rate of change is 10.

The initial value of the equation is 45

The independent variable is the number of classes.

The dependent variable is the total cost.

The art class cost $45 for material and $10 per class. Therefore, let's represent the situation with a linear equation.

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Therefore,

y = 45 + 10x

where

Therefore,

A. The rate of change is 10.

B. The initial value is 45

C. The independent variable is x(number of classes)

D. The dependent variable is total cost.

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Answer: Your answer is 9y(y^3 - 4) (y^3 + 4

(The fours are not being subtracted with the exponent 3. They are separate)

As an estimation of the exchange rates, 16 Euros is approximately equal to 12 Pounds.

To convert Euros to Pounds, we first need to determine the conversion rate between these two currencies. From the information provided, we know that 3 Pounds is approximately equal to 4 Euros. Using this information, we can establish a conversion factor by dividing 3 Pounds by 4 Euros:

Conversion factor = 3 Pounds / 4 Euros = 0.75 Pounds per Euro

Now that we have the conversion factor, we can use it to convert 16 Euros to Pounds. To do this, we simply multiply the amount in Euros (16) by the conversion factor (0.75 Pounds per Euro):

16 Euros * 0.75 Pounds per Euro = 12 Pounds

So, as an estimation, 16 Euros is approximately equal to 12 Pounds. Keep in mind that exchange rates between currencies can fluctuate over time, so it's always a good idea to double-check the current rate before making any financial transactions.

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Complete Question:

As an estimation we are told £3 is €4.

Convert €16 to pounds.

The domain of a function is the set of all possible inputs for the function. In this case, the function is h(t)=80t-16t². Since time cannot be negative, the domain of h(t) is all real numbers greater than 0. Then,  required answer for the provided question is Option A.

To evaluate the maximum height reached by the rocket, now to calculate the derivative of the function h(t)=80t-16t² and set it equal to zero.
This will provide  the time at which the rocket reaches its maximum height. Therefore, here we can place  time back into the original function to evaluate the maximum height.
h(t)=80t-16t²
h'(t)=80-32t
0=80-32t
32t=80
t=2.5 seconds

Then the rocket touches its maximum height after 2.5 seconds.
To evaluate the maximum height, place t=2.5 into h(t):
h(2.5)=80(2.5)-16(2.5)²
=100 feet

Hence, the maximum height touched by the rocket is 100 feet.

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The surface area of the rectangular prism with the given dimensions is 540yd².

To find the surface area (sa) of the rectangular prism with the given dimensions, we need to calculate the area of each face and add them together.

The formula for the area of a rectangle is length multiplied by width (A = l x w).

Face 1 has a length of 5yd and a width of 37yd, so its area is 5 x 37 = 185yd².
Face 2 has a length of 5yd and a width of 20yd, so its area is 5 x 20 = 100yd².
Face 3 has a length of 5yd and a width of 51yd, so its area is 5 x 51 = 255yd².

To find the total surface area, we add the areas of all three faces:

sa = area of face 1 + area of face 2 + area of face 3
sa = 185yd² + 100yd² + 255yd²
sa = 540yd²

Therefore, the numerical value of the surface area of the rectangular prism with the given dimensions is 540yd².

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The length of arc CD, given that the radius, EB = 15 cm, is 29.31 cm

First, we shall determine ∠CED. Details below:

2∠CED + 2∠BEC = 360

2∠CED + (2 × 68) = 360

2∠CED + 136 = 360

Collect like terms

2∠CED = 360 - 136

2∠CED = 224

Divide both sides by 2

∠CED = 224 / 2

∠CED = 112°

Finally, we shall determine the length of the of arc CD. Details below:

Length of arc = 2πr × (θ / 360)

Length of arc CD = (2 × 3.14 × 15) × (112 / 360)

Length of arc CD = 29.31 cm

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Complete question:

See attached photo

Answer:

B.

Resources, as in details of the problem and then you do check the answers and present the solution.

Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.

Part I: The payment amount for payment number 2 is $1055.69 (same as the first payment).

Part II: Interest due for payment number 2 = (Unpaid Balance after payment 1) * (Monthly Interest Rate) = $189,671.31 * (4.8% / 12) = $758.68.

Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.

Part IV: Unpaid balance for payment number 2 = (Unpaid Balance after payment 1) - (Note Reduction for payment 2) = $189,671.31 - $297.01 = $189,374.30.

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The coordinates of the parallel translation P are (-1, 4).

What is meant by coordinates?

Coordinates are a series of numbers or values that denote the position or location of a point in a particular system, such as a geographic or Cartesian coordinate system. They are used to represent locations or objects in space.

What is meant by parallel?

Parallel refers to lines or planes that are always the same distance apart and never intersect, even if they extend infinitely in both directions.

According to the given information

To find the coordinates of the parallel translation P that moves point A(3, -2) to point B(-1, 4), we need to find the vector that connects A to B, and then translate A by that same vector.

The vector that connects A to B is:

B - A = (-1 - 3, 4 - (-2)) = (-4, 6)

To move point A by this vector, we add the vector to the coordinates of A:

P = A + (-4, 6) = (3, -2) + (-4, 6) = (-1, 4)

Therefore, the coordinates of the parallel translation P are (-1, 4).

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Triangle DBG is isosceles and  BD = BG.

A triangle is a closed two-dimensional geometric shape with three straight sides and three angles. It is one of the basic shapes in geometry and has a wide range of applications in mathematics, science, and engineering.

To prove that triangle DBG is isosceles, we need to show that BD = BG.

First, we can use the given similarity to find the length of DF in terms of EB and EC. Since triangle ABC is similar to triangle EDF, we have:

AB:BC = ED:DF

Substituting the given values, we get:

2:3 = ED:DF

Multiplying both sides by DF, we get:

DF = (3÷2)ED

Next, we can use the fact that triangles EDF and EBG are similar (since they share angle E) to find the length of BG in terms of EB and DF:

ED/EB = BG/DF

Substituting the value we found for DF, we get:

ED/EB = BG/(3/2)ED

Multiplying both sides by (3/2)ED, we get:

BG = (3/2)ED²/ EB

Now we can use the Pythagorean theorem to find the lengths of BD and BG in terms of EB and EC:

BD² = BE² + ED²

BG² = BE² + EG²

Since EG = EC - BD, we can substitute BD = EC - EG in the first equation to get:

BD² = BE² + ED² = BE² + (3/2)ED²

Substituting the expression we found for BG in terms of ED and EB in the second equation, we get:

BG² = BE² + (3/2)ED²/EB² * BE²

Simplifying this expression, we get:

BG² = BE²(1 + 3ED²/2EB²)

Since we know that ED/EB = 2/3, we can substitute this value to get:

BG² = BE²(1 + (3/2)(4/9)) = BE²(25/18)

Therefore, we have:

BD² = BE² + (3/2)ED² = BE² + (3/2)(9/4)BE² = (15/8)BE²

BG² = BE²(25/18)

To show that BD = BG, we can compare the squares of these lengths:

BD² = (15/8)BE²

BG² = BE²(25/18)

Multiplying both sides of the first equation by 18/25, we get:

(18/25)BD² = (27/40)BE²

Substituting the expression for BG² in the second equation, we get:

(18/25)BD² = (27/40)BG²

Therefore, we have:

BD² = (27/40)BG²

Taking the square root of both sides, we get:

BD = (3/4)√(10) * BG

Substituting the expression we found for BG in terms of ED and EB, we get:

BD = (3/4)√(10) * (3/2)ED²/EB

Substituting the value of ED/EB = 2/3, we get:

BD = (3/4)√(10) * (3/2)(4/9)ED²

Simplifying this expression, we get:

BD = (2/3)√(10)ED²

Next, we can substitute the value we found for DF in terms of ED to get:

DF = (3/2)

Therefore, triangle DBG is isosceles and  BD = BG.

To learn more about triangle from given link.

brainly.com/question/30599944

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