If \( f(x)=5 x, g(x)=-2 x+1 \), and \( h(x)=x^{2}+6 x+8 \), find f(h \( (-3)] \).

The simplified expression is x^(454)y^(584) * 2^(109).

To simplify the given expression, we need to use the laws of exponents. The laws of exponents are:

- (a^m)^n = a^(mn)
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)

Using these laws, we can simplify the given expression as follows:

(x^3y^3)^31 * (32x^13y^18)^31 / (2xy^3)^2 * (2xy^3)^2 * (2x)^2 * (2x^3y^5)^3 * (4xy)^5 * (2x^3y^5)^3 * (4x)^5

= x^(3*31)y^(3*31) * 32^31x^(13*31)y^(18*31) / 2^2x^2y^(3*2) * 2^2x^2y^(3*2) * 2^2x^2 * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5y^(5*5) * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5

= x^(93)y^(93) * 32^31x^(403)y^(558) / 2^6x^6y^6 * 2^6x^6y^6 * 2^2x^2 * 2^6x^9y^15 * 4^5x^5y^25 * 2^6x^9y^15 * 4^5x^5

= x^(93+403)y^(93+558) * 32^31 / 2^6 * 2^6 * 2^2 * 2^6 * 4^5 * 2^6 * 4^5 * x^(6+6+2+9+5+9+5) * y^(6+6+15+25+15)

= x^(496)y^(651) * 32^31 / 2^(6+6+2+6+6) * 4^(5+5) * x^42 * y^67

= x^(496-42)y^(651-67) * 32^31 / 2^26 * 4^10

= x^(454)y^(584) * 32^31 / 2^26 * 4^10

= x^(454)y^(584) * 2^(5*31) / 2^26 * 2^(2*10)

= x^(454)y^(584) * 2^(155) / 2^(26+20)

= x^(454)y^(584) * 2^(155-46)

= x^(454)y^(584) * 2^(109)

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Answer:

6(n − 5) < 3(n + 4)

6n - 30 < 3n + 12 // Distribute the 6 and 3

3n < 42 // Add 30 to both sides

n < 14 // Divide both sides by 3

So the inequality is true for n < 14. This means that the only integer in the set S that satisfies the inequality is 11. Therefore, the solution is S:{11}.

The expected lifetime reproductive value for an individual in a population with an intrinsic rate of increase (r) of 0 is 1, the correct option is A.

The calculation for the expected lifetime reproductive value can be expressed as:

R₀ = ∑ lxmx

In a stable population with an intrinsic rate of increase of 0, the survival probability (lx) is constant across all age classes, and the average number of offspring produced by an individual (mx) is also constant.

R₀ = lxm

where l is the survival probability and m is the average number of offspring per individual.

Since the population is stable, each individual replaces itself with one offspring, so m = 1.

Therefore, the calculation for the expected lifetime reproductive value in a population with an intrinsic rate of increase of 0 is:

R₀ = lxm = 1 x 1 = 1, the correct option is A.

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Yes, it is better to use percentages to compare groups when making a graph. This is because percentages allow for a more accurate comparison of the data, as they take into account the relative size of each group. If we only use frequencies, we may get a skewed view of the data, as one group may be much larger than the other.

Here is the side by side bar graph showing the men's and women's responses to the question "Do you play sports?":

Gender Yes No

Male 9 7

Female 7 14

The graph indicates that a higher percentage of males play sports compared to females. However, it also shows that there are more females who do not play sports compared to males. This suggests that there may be a gender difference in the participation of sports among students.

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No function exists in this relation. No, since there isn't always a single output for every input.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.

We have to show the relation between a function.

The x-values are entered into the function machine. The function machine generates the y-values after its operations are complete. Any internal function is possible.

A mapping diagram with arrows pointing from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5, as well as two circles with the numbers 0, and labels for the x and y values, respectively

but according to the definition of y, it should give only one value

Hence, it is not a function.

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Answer: 7

Step-by-step explanation: The average rate of change of a function f(x) over an interval [a,b] is defined as the ratio of “change in the function values” to the "change in the endpoints of the interval"1. In other words, it is the slope of the line that passes through two points on the graph of f(x)2.

To find the average rate of change of f(x) = x² + x + 4 from x = 2 to x = 4, we can use this formula:

Average rate of change = [f(4) - f(2)] / (4 - 2)

First, we need to plug in x = 4 and x = 2 into f(x) and simplify:

f(4) = (4)² + (4) + 4 f(4) = 16 + 8 f(4) = 24

f(2) = (2)² + (2) + 4 f(2) = 4 + 6 f(2) = 10

Next, we need to subtract f(2) from f(4), and divide by (4 - 2):

Average rate of change = [24 - 10] / (4 - 2) Average rate of change = 14 / 2 Average rate of change = 7

The largest angle is [tex]\frac{7a}{4}[/tex] and the smallest angle is [tex]\frac{3a}{4}[/tex].

In this case, we have the angles [tex]\frac{5a}{2}, \frac{3a}{4}, and \frac{7a}{4}[/tex]. So we can set up the equation:

[tex]\frac{5a}{2} + \frac{3a}{4} + \frac{7a}{4} = 180[/tex]

To solve for "a", we can simplify the left side of the equation by finding a common denominator:

[tex]\frac{(10a + 3a + 7a)}{4} = 180[/tex]

Simplifying the left side gives:

[tex]\frac{20a}{4} = 180[/tex]

And further simplifying gives:

5a = 180

Dividing both sides by 5 gives:

a = 36

Now that we know the value of "a", we can substitute it back into each angle expression to find their actual values:

[tex]\frac{5a}{2} = \frac{5(36)}{2} = \frac{903a}{4} = \frac{3(36)}{4} = \frac{277a}{4} = \frac{7(36)}{4} = 63[/tex]

Therefore, [tex]\frac{7a}{4} = 63[/tex] is the largest angle and [tex]\frac{3a}{4} = 27[/tex] is the smallest angle.

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The length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

To find the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \), we can use the formula for arc length: \( s = r\theta \), where \( s \) is the arc length, \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians.

Plugging in the given values, we get:

\( s = (11 \mathrm{in})(\frac{\pi}{2}) \)

Simplifying, we get:

\( s = \frac{11\pi}{2} \mathrm{in} \)

Therefore, the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

Note: If the question asks for the answer to be rounded, you can use a calculator to find the approximate value of \( \frac{11\pi}{2} \) and round to the desired number of decimal places. For example, if the question asks for the answer to be rounded to the nearest tenth, the answer would be \( 17.3 \mathrm{in} \).

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The p-value for our test is 0.0120, accurate to 4 decimal places.

We are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. We are performing a two-tailed test and our sample data produce the test statistic z=2.517.

To find the p-value, we need to use a standard normal distribution table or calculator. We will use the table for this answer.

The first step is to find the area to the left of the test statistic z=2.517 in the standard normal distribution table. This gives us the probability of obtaining a z-score less than or equal to 2.517. The closest value in the table is 2.51, which gives us an area of 0.9940.

Since we are conducting a two-tailed test, we need to find the area in both tails of the distribution. To do this, we subtract the area to the left of the test statistic from 1: 1-0.9940 = 0.0060. This gives us the area in the right tail of the distribution.

Finally, we multiply this value by 2 to get the p-value for our two-tailed test: 0.0060 * 2 = 0.0120.

Therefore, the p-value for our test is 0.0120, accurate to 4 decimal places.

p-value = 0.0120

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Answer:

C

Step-by-step explanation:

6x° and 60° form a right angle and sum to 90° , that is

6x + 60 = 90 ( subtract 60 from both sides )

6x = 30 ( divide both sides by 6 )

x = 5

Answer:

100°

Step-by-step explanation:

∠A and ∠B are supplementary angles, which means:

∠A° + ∠B° = 180°

[tex](2x) + (2x + 20) = 180[/tex]

Expand the parenthesis and solve for x:

[tex]2x + 2x + 20 = 180[/tex]

[tex]4x + 20 = 180[/tex]

[tex]4x = 180 - 20[/tex]

[tex]4x = 160[/tex]

[tex]x = \frac{160}{40}[/tex]

∴[tex]x = 40[/tex]

Substitute the value of x to determine the measurement of ∠B:

[tex]2(40) + 20[/tex]

[tex]80 + 20[/tex]

= 100°

In response to the aforementioned query, we may say that D is equal to equation sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10. As a result, it takes 10 units to get from position X to point Y.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The distance formula may be used to determine the separation between two points:

Sqrt((x2 - x1) + (y2 - y1)) = sqrt(d)

where d is the distance between the two locations, and (x1, y1) and (x2, y2) are the coordinates of the two points.

We may get the separation between points X at (3, 2) and Y at (3, -8), using the following formula:

D is equal to sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10.

As a result, it takes 10 units to get from position X to point Y.

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Answer:A

Step-by-step explanation:

because

The solution to the equation 1/2 + 3y = y/5 is y = -3/14.

What is the linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form:

ax + b = 0

where x is the variable, a and b are constants, and a is not equal to zero. The solution to the equation is the value of x that makes the equation true.

To solve for y in the equation 1/2 + 3y = y/5, we need to isolate y on one side of the equation.

First, we can simplify the left side of the equation by combining the like terms:

1/2 + 3y = (6/10) + (30y/10) = (6 + 30y)/10

Now we can rewrite the equation as:

(6 + 30y)/10 = y/5

To solve for y, we can start by multiplying both sides of the equation by 10, to eliminate the denominators:

6 + 30y = 2y

Next, we can simplify by subtracting 2y from both sides:

6 + 28y = 0

Finally, we can solve for y by subtracting 6 from both sides and then dividing by 28:

28y = -6

y = -6/28

Simplifying the fraction, we get:

y = -3/14

Therefore, the solution to the equation 1/2 + 3y = y/5 is y = -3/14.

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The contractor has 5.95 hours for the job if  $930 is spent by him.

The total cost for the job can be modeled by C = 42H + 680, where C is the total cost of the job, H is the number of hours of labor, and 680 is the cost of materials.

If the owner wants to spend $930 for the job, then the number of hours that the contractor has for the job can be found by solving the equation C = 42H + 680 for H.

Thus, 42H + 680 = 930. Subtracting 680 from both sides gives 42H = 250. Dividing both sides by 42 gives H = 250/42 = 5.95 hours.

Therefore, the contractor has 5.95 hours for the job if the owner wants to spend $930.

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The answer tο the pοsed questiοn using equatiοns is that hence, it will take 500 bacteria apprοximately 9.7 days frοm the day Sandy put her sandwich in her lοcker tο thοrοughly cοver it.

The equals sign (=) denοtes equality when twο statements are jοined by a mathematical equatiοn. A mathematical statement that establishes the equality οf twο mathematical expressiοns is knοwn as an equatiοn in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign divides the numbers. A mathematical fοrmula can be used tο identify the link between the twο sentences οn either side οf a letter.

The expοnential equatiοn fοr this prοblem is as fοllοws:

[tex]N(t) = e(kt) \times N_0 (kt)[/tex]

The data mentiοned above can be used to calculate the values of [tex]N_0[/tex] and k:

=>[tex]N (4) = \frac{71}{sN(7)} = 185[/tex]

These numbers are entered intο the formula as follows:

[tex]71 = N_0\times e^{(4k) (4k) (4k)}\\185 = N_0 \times e^{(7k) (7k) (7k)}\\185/71 = e^{(3k) (3k) (3k)}[/tex]

Hence, the equation for this prοblem is:

[tex]N(t) = 23.77 \times e^ {(0.3056t) (0.3056t) (0.3056t)}[/tex]

To determine hοw many days, it will take for 500 germs to prοliferate, we can set N(t) equal to 500 and solve for t:

[tex]500 = 23.77 \times e^ {(0.3056t) (0.3056t) (0.3056t)}[/tex]

Based οn t = ln (500/23.77) / 0.3056, 9.7 days.

Hence, it will take 500 bacteria rοughly 9.7 days from the day Sandy put her sandwich in her lοcker to thoroughly cοver it.

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Answer:

The answer is c 180 miles

Step-by-step explanation:

the exact is 179.8 miles rounded up is 180 mark brainliest pls and your welcome

The correct statement regarding whether there are two parallel lines is given as follows:

C. Yes, lines n and p are parallel because corresponding angles are congruent.

When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and the transversal. Corresponding angles are always congruent, which means that they have the same measure.

The angles in the same position for this problem are given as follows:

1 and 2.

The parallel lines relative to which these two angles are at the same position are given as follows:

n and p.

Hence the correct option is given by option c.

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For Michael to pay cash for the tractor priced at R160,000 with the exchange rate as US$1 = R17.96, the amount he must change is US$8,908. 69.

An exchange rate is the unit rate at which one country's currency is exchanged for another.

Exchange rates are based on a country's economic performance or indices in comparison to other countries.

The price of the tractor = R160,000

Exchange Rate: US$ = R17.96

R160,000 = US$8,908. 69 (R160,000/R17.96)

Thus, Michael needs to exchange US$8,908. 69 to purchase the tractor costing R160,000.

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The point E' will have a y-value of -1 instead of 3 and x-value of 6 instead of -6.

A polygon is a two-dimensional shape composed of straight line segments that close in a loop to form a single shape. Generally, polygons have three or more sides and angles. Depending on the number of sides, polygons can be classified as triangles, quadrilaterals, pentagons, hexagons, and so on.

A reflection across the x-axis of the graph of polygon ABCDE with point E at (-6,3) would result in the creation of a second polygon A'B'C'D'E' with E' at (-6,-1). This is because the reflection flips the points across the x-axis, meaning all of the y-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have a y-value of -1 instead of 3. This is because the reflection across the x-axis will cause the y-values of each point to flip signs, with the y-value of E increasing from -3 to -1.

Similarly, a reflection across the y-axis of polygon ABCDE with point E at (-6,3) would result in the creation of polygon A'B'C'D'E' with E' at (6,1). This is because the reflection flips the points across the y-axis, meaning all of the x-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have an x-value of 6 instead of -6. This is because the reflection across the y-axis will cause the x-values of each point to flip signs, with the x-value of E increasing from -6 to 6.

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Answer:

Reflection across y = 1

Step-by-step explanation:

i got this right on the flvs test!

Answer: 200

Step-by-step explanation:

40% of y = 100

40/100 of y = 100

40y/100 = 100

40y = 100 multiplied by 100

40y/40 = 10000

y = 250.

40% of 2 multiplied by 250

40/100 of 500

40 multiplied by 5

answer = 200.

By answering the above question, we may infer that So Kendra's water equation bottle holds 64 fluid ounces.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The volume of a quart is 32 fluid ounces. Kendra's water bottle, which holds 2 quarts of water, therefore has:

64 fluid ounces are equal to 2 quarts when each is 32 fluid ounces.

So Kendra's water bottle holds 64 fluid ounces.

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Natural numbers are squared to get the succession of square numbers. These sequence's initial terms  includes 1, 4, 9,16, 25, so on and so forth.

We must square the fifth natural integer, which is five, in order to determine the fifth term in this series. As a result, 25 is the fifth term in the square number series.

In a more general sense, n2 represents the nth phrase in the series of square numbers. This is so that the nth term, which is n, equals the rectangle of the nth arbitrary integer.

Tn = n2 is the formulae for the nth term. The chain of square integers is a direct example of the more generic order of degrees.

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Correct statements are m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z

Similar triangles are triangles that have the same shape but can be of different sizes. All equilateral triangles and squares of any length are examples of similar objects. That is, if two triangles are similar,  their corresponding angles are congruent and their corresponding sides have the same proportions. Here, triangle similarity is indicated by the symbol '~'.

Given,

two triangles ABC and DEF

m∠A = m∠D = 40°

m∠B = m∠E = 60°

Sum of all interior angles of a triangle is equal to 180°

m∠A + m∠B + m∠C = m∠D + m∠E + m∠F = 180°

40 + 60 + m∠C = 40 + 60 + m∠F

m∠C = m∠F

All three angles are congruent

By A-A-A rule

ΔABC ~ ΔDEF

ratio of corresponding sides will be equal

6/10 = y/z

3/5 = y/z

Hence, m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z are the correct statement.

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5. The expression fοr the area of a rectangle with length l and width w is l × w.

What is a rectangle?

In Euclidean plane geοmetry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all οf its angles are equal.

5. The area of a rectangle is given by the prοduct of its length and width. Therefore, the expressiοn for the area of a rectangle with length l and width w is:

Area = l x w

6. Imagine dilating the rectangle with length & and width w by a factοr of k.

⇒ (l × k) × (w × k)

7. An expression fοr the area of the dilated rectangle.

⇒ l × w × k²

⇒ k²lw

8. Vοlume = l × w

Volume' = k²lw

Then we have

Volume/Volume'  = (l × w)/k²lw

Vk²lw = V'lw

Divide bοth sides by lw

Vk² = V'

Thus, The area ο a rectangle when it's dilated by a scale factor of k will be dilated k² times

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Based on the calculation we know that

The value of x as 7− is 35.

The value of x as 7+ is 35.

Suppose that f( x ) = 7 x − 7. We can complete the following statements by plugging in the values of x and evaluating the function.

As x → 7 − , f ( x ) → 42 − 7 = 35
As x approaches 7 from the left, the function f(x) approaches 35.

As x → 7 + , f ( x ) → 42 − 7 = 35
As x approaches 7 from the right, the function f(x) also approaches 35.

Therefore, the function f(x) = 7x - 7 has a horizontal asymptote at y = 35 as x approaches 7 from both the left and the right.

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Answer: 2,640 yards

Step-by-step explanation:

2,640 yards. Two and three-fourths miles is equal to 14,400 yards. 14,400 yards divided by 5, which is the number of yards in a mile, is equal to 2,640 yards.

Answer: 4,840 yards

Step-by-step explanation:

The cumulative distribution function for N when a coin is flipped 3 times with  P[H]=0. 3 is given by ,

F(N≤ 0) = 0.343 , F(N≤1) = 0.784 , F(N≤2) = 0.973 , F(N≤3) = 1.000.

Cumulative distribution function (CDF) of N,

Probability of getting n or fewer heads in three coin flips,

(All values of n from 0 to 3)

Probability of getting exactly n heads in three flips.

Apply binomial distribution,

P(N = n) = ³Cₙ ×(0.3)ⁿ × (0.7)³⁻ⁿ

For cumulative distribution function, add up the probabilities of getting 0, 1, 2, or 3 heads in three flips,

F(N≤ 0)

=P(N=0)

=³C₀ × (0.3)⁰ × (0.7)³

= 1 × 1 × 0.343

= 0.343

For F(N≤1) is equal to,

⇒F(N≤1)

= P(N=0) + P(N=1)

 =  ³C₀ × (0.3)⁰ × (0.7)³ + ³C₁ × (0.3)¹ × (0.7)²

= 0.343 + 0.441

= 0.784

F(N ≤ 2)

= P(N=0) + P(N=1) + P(N=2)

= ³C₀ × (0.3)⁰ × (0.7)³

+ ³C₁ × (0.3)¹ × (0.7)²

+³C₂ × (0.3)² × (0.7)¹

= 0.343 + 0.441 + 0.189

= 0.973

This implies CDF for N is equal to,

F(N ≤n) = [tex]\sum_{0}^{x}[/tex]³Cₓ × (0.3)ˣ × (0.7)³⁻ˣ

And F(N≤3) is equal to,

⇒F(N≤3)

= P(N=0) + P(N=1) + P(N=2) + P(N=3)

=  ³C₀ × (0.3)⁰ × (0.7)³

+ ³C₁ × (0.3)¹ × (0.7)²

+ ³C₂ × (0.3)² × (0.7)¹

+ ³C₃× (0.3)³ × (0.7)⁰

= 0.343 + 0.441 + 0.189 + 0.027

= 1.000

Therefore, the cumulative distribution function for N is equal to,

F(N≤ 0) = 0.343

F(N≤1) = 0.784

F(N≤2) = 0.973

F(N≤3) = 1.000

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Answer:

  BD = 5√3

  AD = 10

  CD = 10√3

Step-by-step explanation:

You want the missing side lengths in a right-triangle geometry that shows the hypotenuse divided into lengths 5 and 15 by the altitude.

In this geometry, all of the right triangles are similar. The similarity proportions can be solved to give three geometric mean relationships:

  BD = √(AB·CB) = √(5·15) = 5√3

  AD = √(AB·AC) = √(5·20) = 10

  CD = √(CB·CA) = √(15·20) = 10√3

__

Additional comment

It can be handy to remember the geometric mean relations. They can be thought of as "each side is equal to the geometric mean of the hypotenuse segments it touches." (Note that touching the end is interpreted as touching the nearest part and the whole.)

For example, the similarity proportion for AD is ...

  hypotenuse/(short side)

  AD/AB = AC/AD   ⇒    AD² = AB·AC   ⇒   AD = √(AB·AC)

These are called "geometric mean" relations because the geometric mean of two numbers is the square root of their product.