The process of completing the square can be used to calculate the width, in feet, of the storage bin that gives a maximum area.

Jenny's average jogging speed in the distance covered is; 10 miles/hr

Let x miles/hr be the speed that Jenny walks at

Then, 2x miles/hr is the speed that Jenny runs at

She jogs for  9.5 miles

2x miles = 1 hours

9.5 miles = a hours

a = 9.5/2x hours

She walks for 2.5 miles

x miles = 1 hour

2.5 miles = b

b = 2.5/x hours

Thus;

(9.5/2x) + (2.5)/x = 1.45

Multiply through by 2x to get;

9.5 + 5 = 2.9x

14.5/2.9 = x

x = 5 miles/hr

Jogging speed = 2 * 5 = 10 miles/hr

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Answer: To verify the identity, we need to convert both sides into sines and cosines and see if they are equal.

Starting with the left side:

cotx = 1/tanx

So,

cotx - tanx = 1/tanx - tanx

Using the identity tan^2x = sec^2x - 1, we get

cotx - tanx = (sec^2x - 1) / tanx

Expanding the right side using the definition of cscx and sinx, we get:

cotx - tanx = secx(1/sinx - 2sinx)

So,

cotx - tanx = secx(cscx - 2sinx)

Since both sides are equal, we can conclude that the identity is verified.

Step-by-step explanation:

Answer: To find the height of the embankment, we need to first find the volume of the well and then the volume of the embankment.

Volume of the well = πr^2h = π * (d/2)^2 * h = π * (5/2)^2 * 24 = 157.08 cubic meters

Volume of the embankment = π * (R^2 - r^2) * h, where R is the outer radius of the embankment and r is the inner radius.

Outer radius of the embankment = (5 + 3)/2 = 4 m

Inner radius of the embankment = (5 - 3)/2 = 1 m

Volume of the embankment = π * (4^2 - 1^2) * h = π * 15 * h

We know that the volume of the well is equal to the volume of the embankment, so we can write:

157.08 = π * 15 * h

Solving for h, we get:

h = 157.08 / (π * 15) = 157.08 / 47.12 ≈ 3.32 m

So, the height of the embankment is approximately 3.32 meters.

Step-by-step explanation:

The mortgage of A is $110158.2.

The mortgage of B is $137494.8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Mortgage A:

15 years at 4.5% with monthly payments of $611.99.

15 years = 15 x 12 = 180 months

Total paycheck.

= 180 x 611.99

= $110158.2

Mortgage B:

30 years at 4% with monthly payments of $381.93

30 years = 360 months

Total paycheck.

= 360 x 381.93

= $137494.8

Thus,

Mortgage A = $110158.2

Mortgage B = $137494.8

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The mean of the sampling distribution (p) and The standard error of the mean (o)  are 56 and 2 respectively.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.

(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:

o = 12 / √36 = 2

(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.

This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.

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Answer:

8.6 m

Step-by-step explanation:

DE = 2 7/10 m

     = 2 + 7/10

     = 2 + 0.7

DE = 2.7 m

EF = 5 9/10 m

    = 5 + 9/10

    = 5 + 0.9

EF = 5.9 m

DF = DE + EF

     = 2.7 + 5.9

     = 8.6 m

Part A:

[tex]B\cap D[/tex] is asking for what the sets B and D have in common:

   [tex]B\cap D = \{4\}[/tex]

since B and D only have 4 in common.

Now [tex](B \cap D)'[/tex] is asking for all of the things in the universal set [tex]U[/tex] that are not in [tex]B\cap D[/tex].  That's what the little tick mark on the right side means.

   [tex](B \cap D)' = \{2, 3, 6, 7\}[/tex]

Part B:

[tex]B' = \{2, 3, 7\}[/tex] since those are the things not in B.

[tex]D=\{3, 4\}[/tex]

[tex]B'\cup D[/tex] is asking for all the things in either [tex]B'[/tex] or [tex]D[/tex].

    [tex]B'\cup D = \{2, 3, 4, 7\}[/tex]

(We don't need to list 3 twice, even though it was in both sets. )

Answer:

Step-by-step explanation:

To find the total number of seats in the theater, we can use the formula for the sum of an arithmetic series, which is given by:

S = n/2 * (a_1 + a_n)

where n is the number of terms in the series, a_1 is the first term, and a_n is the last term.

In this case, the first term is 25 seats and the last term is 25 + (38-1) * 4 seats (since the number of seats in each row increases by 4 each time). So, we have:

n = 38 (the number of rows)

a_1 = 25

a_n = 25 + (38-1) * 4 = 25 + 37 * 4 = 25 + 148 = 173

Now, we can substitute these values into the formula:

S = n/2 * (a_1 + a_n) = 38/2 * (25 + 173) = 19 * 198 = 3,762

So, the total number of seats in the theater is 3,762, which corresponds to option O3,762.

Answer:

Step-by-step explanation:

Answer:

The number is -10.4

Explanation:

Assume that the number we are looking for is x.

Now, we want to get 10 times te sum of half the number and 6 and equate this expression to 8. Then we can solve for x

Let's take this step by step:

half the number is 0.5x

the sum of half the number and 6 is 0.5x + 6

10 times the sum of half the number and 6 is 10(0.5x +6)

10 times the sum of half the number and 6 equals 8 is 10(0.5x+6) = 8

Now we can solve for x as follows:

10(0.5x + 6) = 8

5x + 60 = 8

5x = 8 - 60

5x = -52

x = -52/5

x = -10.4

Hope this helps :)

The mean number of hours the students spent listening to music is 31.25 hours.

In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.

Mean = (sum of all values) / (number of values)

For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:

Mean = 9

Therefore, the mean of this data set is 9.

The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.

We can find the mean number of hours spent listening to music using the formula:

mean = (sum of (midpoint of each class) * (frequency of each class)) / (sum of frequencies)

The midpoint of each class can be found by taking the average of the upper and lower class limits.

Using this formula, we get:

mean = ((1.25 + 3.75 + 6.25 + 8.75 + 11.25) * (22 + 15 + 3 + 3 + 1)) / (22 + 15 + 3 + 3 + 1)

mean = (31.25 * 44) / 44

mean = 31.25

Therefore, the mean number of hours the students spent listening to music is 31.25 hours.

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Answer:

26.it is all about thinking

The correct option is A {-5, 0, 3, 4}.

In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.

For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).

The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).

The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.

Therefore, the correct answer is A: {-5, 0, 3, 4}.

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The factors in the factored form represents the value of the function when x = 0.

Quadratic functions are defined as the polynomial functions consisting of variables and exponents with the degree of the variable being 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given is a quadratic function,

y = x² + 2x - 15

This can be factorized as (x + p)(x + q) such that p × q = -15 and p + q = 2.

Two such numbers are -3 and 5.

-3 × 5 = -15 and -3 + 5 = 2

y = x² + 2x - 15

y = (x - 3) (x + 5)

Factors are x - 3 and x + 5

Here, the numbers 3 and -5 represents the input values of the function when the output value or the value of the function equals 0 or they are the x intercepts of the function.

Hence the factors in the factored form are the x intercepts of the function.

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The complete question is as follows :

What do the factors in the factored form represent?

y = x² + 2x - 15

Answer:

A and C are the correct answers

Step-by-step explanation:

Answer:

And C is the answer to the question

Answer:

Add 3 and then multiply by 5.

Step-by-step explanation:

The problem looks like this to me:

[tex] \dfrac{m}{5} - 3 = 8 [/tex]

If this is correct, then the operations are:

Add 3 to both sides.

Multiply both sides by 5.

I don't see that answer. The picture is not very clear to me. What is the denominator of the fraction?

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

[tex]\frac{4x}{4} = \frac{64}{4}[/tex]

x = 16

Answer:

Step-by-step explanation:

a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:

     (1)

    /   \

 (H)     (T)

/   \   /   \

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

b) There are four stages in the tree diagram.

c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTTT

d) There are 2^4 = 16 outcomes in the sample space.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1)

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4)

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1).

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4).

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.

Answer:

The solution of the equation is B. 4

Step-by-step explanation:

√x + 2 = x

√x = x - 2

(√x)² = (x-2)²

x = (x-2) (x-2)

x = x² - 4x + 4

x moves to the right

0 = x² - 4x - x + 4

0 = x² - 5x + 4

0 = (x-1) and (x-4)

x-1 = 0 x-4 = 0

x = 1 (not) x = 4

So, the solution to the equation is B. 4

Answer:

Step-by-step explanation:

Step 1: Understanding the Problem

The problem involves finding an equation to approximate the amount of fuel in Jon's semitruck after he drives x miles. Jon started with 240 gallons of fuel and his truck uses 0.15 gallons of fuel for each mile he drives.

Step 2: Writing the Equation

We know that the amount of fuel in Jon's tank decreases as he drives. So, we can write the equation as:

f(x) = 240 - 0.15x

This equation says that the amount of fuel in Jon's tank after he drives x miles is equal to 240 gallons (the amount of fuel he started with), minus 0.15 gallons for each mile he drives.

Step 3: Interpreting the Equation

The function f(x) = 240 - 0.15x is a linear equation, which means that it is a straight line on a graph. The value 240 is the y-intercept, which means that when x = 0, the y-value of the function is 240 (the amount of fuel in Jon's tank when he starts driving). The value -0.15 is the slope of the line, which tells us how much the y-value decreases for each unit increase in x (in this case, how much the fuel decreases for each mile Jon drives).

Step 4: Conclusion

So, the equation f(x) = 240 - 0.15x can be used to approximate the amount of fuel in Jon's semitruck after he drives x miles. The equation is linear and can be written in the form f(x) = mx + b, where m = -0.15 (the slope of the line) and b = 240 (the y-intercept).

The numeric value of the marginal revenue at 33 units will be $336.

The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.

Revenue function is R(q) = - 8q ^ 2 + 600q

Differentiate with respect to q

R^ prime (q) = - 8(2q) + 600(1)

R' (q)=-16q+600 ...(1)

substitute q = 33 in equation

MR(113) = - 8(33) + 600

=-264 + 600

MR (113)= $336 per unit

The marginal revenue is $336.

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A more accurate value would be 13.8271643518519

Round it however you need to.

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

Explanation:

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Let's see how many seconds there are in a day.

[tex]1 \text{ day} = (1 \text{ day})*\frac{24 \text{ hrs}}{1 \text{ day}}*\frac{60 \text{ min}}{1 \text{ hr}}*\frac{60 \text{ sec}}{1 \text{ min}}\\\\=\frac{24*60*60}{1*1*1}\text{ sec}\\\\=86,400\text{ sec}\\[/tex]

I set up those fractions so that the units "day", "hours", "minutes" cancel out. The only unit left over is "seconds".

There are exactly 86,400 seconds in 1 day.

This leads to the fact the sink fills up at a rate of 86,400 drops per day, since the leak rate is 1 drop per second.

----------

1 drop = 0.003 cubic inches approximately

x of those drops give a volume of 0.003x cubic inches, where x is some positive whole number. Set this equal to the volume of the sink and solve for x.

0.003x = 3584

x = 3584/0.003

x = 1,194,666.66666667 approximately

Round up to the nearest whole number to get 1,194,667

The sink starts to overflow when we have 1,194,667 drops of water in it.

Divide this over 86,400 mentioned earlier.

(1,194,667)/(86,400) = 13.8271643518519 approximately.

Round that however you need to. If for instance you round to 3 decimal places, then it would be 13.827

Answer:

4x + 42

Step-by-step explanation:

[tex]\text{Perimeter}=(x+15)+(2x+15)+(x+12)=4x+42[/tex]

After all the spending costs, Tino's weekly salary is approximately $60.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Let's call Tino's weekly salary "x".

Each week, Tino sets aside half of his salary for rent, so:

0.5x = rent

He also sets aside half of his salary for credit card payments, so

0.5x = credit card payments

And he sets aside a quarter of his salary for groceries and utilities, so:

0.25x = groceries and utilities

And he has approximately $15 left for entertainment, so:

x - 0.5x - 0.5x - 0.25x = 15

We can simplify this equation by combining the terms on the left side:

x - 1.25x = 15

And then solving for x:

-0.25x = 15

x = 60

Therefore, Tino's weekly salary is approximately $60.

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Answer:

Step-by-step explanation:

(1/3) x 81=27 people

The specified radical expressions in the questions are evaluated and presented in the simplest form as follows;

(2) [tex]\sqrt[3]{x^2\cdot y^2} \cdot \sqrt[4]{x^5\cdot y^3} = \sqrt[12]{x^{23}\cdot y^{17}}[/tex]

(3) f(g(x)) = √(6·x + 1) - 5

(4) x = (15 ± √(33))/2

(5) x = 126

A radical is a mathematical expression which contains the radical expression, '√', which represent a fractional indices of the form 1/n.

(2) The specified radical expression is presented as follows;

∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex]

Expressing the above radical expression in index form, we get;

∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}}[/tex]

Adding the index of like variable terms, we get;

[tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}} = x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} }[/tex]

(2/3) + (5/4) = (2×4 + 5×3)/12 = 23/12 = 1 11/12

Therefore; [tex]x^{\frac{2}{3} + \frac{5}{4} } = x^{\frac{23}{12} }[/tex]

2/3 + 3/4 = (2 × 4 + 3 × 3)/(12) = 17/12 = 1 5/12

Therefore; [tex]y^{\frac{2}{3} + \frac{3}{4} } = y^{\frac{17}{12} }[/tex]

Which indicates that we get; [tex]x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} } = x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]

Therefore; ∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]

(3) The functions, f(x) = √(3·x + 4) - 5, g(x) = (2·x - 1)

The composite function, f(g(x)) can be found as follows;

f(g(x)) = √(3·g(x) + 4) - 5 = √(3·(2·x - 1) + 4) - 5

f(g(x)) = √(3·(2·x - 1) + 4) - 5 = √((6·x - 3) + 4) - 5 = √(6·x + 1) - 5

(4) (√(x - 1)) = x - 7

Squaring both sides, we get;

(√(x - 1))² = (x - 7)²

Therefore;

(√(x - 1))² = x - 1 = (x - 7)² = x² - 14·x + 49

x - 1 = x² - 14·x + 49

x² - 14·x + 49 - (x - 1) = 0

x² - 15·x + 48 = 0

The quadratic formula can be used to solve the above equation to get;

x = (-(-15) ± √((-15)² - 4×1×48))/(2 × 1) = (15 ± √(33))/2

(5) 2·∛(x - 1) + 6 = 16

2·∛(x - 1) + 6 = 16

Subtracting 6 from both sides, we get;

2·∛(x - 1) + 6 - 6 = 16 - 6 = 10

2·∛(x - 1) = 10

∛(x - 1) = 10/2 = 5

∛(x - 1) = 5

∛(x - 1)^3 = 5^3

∛(x - 1)^3 = x - 1

5^3 = 125

∛(x - 1)^3 = x - 1 = 125

x = 125 + 1 = 126

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Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]

Solve:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]        Since 2y - 2y = 0 we take that away now we have;

[tex]4x=-6\\3x=13[/tex]        Add 4x + 3x = 7x

[tex]\frac{7x}{7} =\frac{7}{7}[/tex] Divide both sides by 7.

[tex]x=1[/tex]

Now substitute x to find y.

[tex]4(1)+2y=-6[/tex]

[tex]4 + 2y =-6[/tex]  Add 6 to the other side.

[tex]10 = 2y[/tex] Divide both sides by 2.

[tex]\frac{10}{2} =\frac{2y}{2}[/tex]

[tex]y = 5[/tex]

Hence, the answer is [B]. (1,-5)

RevyBreeze

Answer:

Step-by-step explanation:

Using the ratio of corresponding side lengths, we have:

x/42 = 9/35

y/21 = 9/35

z/35 = 9/35

Solving for x, y, and z:

x = (9/35) * 42 = 14

y = (9/35) * 21 = 7

z = 9

So the other two sides of the smaller triangle are 14 and 7 units.

Answer:

y=b+5+k/2

Step-by-step explanation:

2y-k=b+5

2y=b+5+k

2y/2=b+5+k/2

y=b+5+k/2

Answer:

y = b+ 5 + k/2.

Step-by-step explanation:

2y - k = b + 5

the subject for y

[tex]2y - k = b + 5 \\ 2y = b + 5 + k \\ \frac{2y}{2} = \frac{b + 5 + k}{2} \\ y = \frac{b + 5 + k}{2}. [/tex]

Answer: To find the distance between the tops of two buildings, we first need to find the horizontal distance between the two buildings. This distance can be found using the Pythagorean theorem.

Let's call the horizontal distance between the two buildings "d".

d^2 = 12^2 + (34 - 29)^2

d^2 = 144 + 25

d^2 = 169

d = 13

So, the horizontal distance between the two buildings is 13 meters.

To find the distance between their tops, we simply add the height of each building:

distance = 34 + 29 = 63 meters

So, the distance between the tops of the two buildings is 63 meters.

Step-by-step explanation: