hi :) this lesson is about 30-60-90 triangles.
I need a formula to find the long side. I dont need the actual length if the long side, I just need the equation to find it. help would be much appreciated​.

Sean reads 60 minutes on wednesday

Solution:

Given that,

Let "x" be the number of minutes read on monday

Let "y" be the number of minutes read on tuesday

Let "z" be the number of minutes read on wednesday

He reads 3 times as many minutes on Tuesday as he does on Monday

Number of minutes read on tuesday = 3 times the number of minutes read on monday

y = 3x --------- eqn 1

He reads 4 times as many minutes on Wednesday as he does on Monday

Number of minutes read on wednesday = 4 times the number of minutes read on monday

z = 4x ------- eqn 2

Sean reads 45 minutes on Tuesday

y = 45

Substitute y = 45 in eqn 1

45 = 3x

x = 15

Substitute x = 15 in eqn 2

z = 4(15)

z = 60

Thus he reads 60 minutes on wednesday

Final answer:

Sean reads for 60 minutes on Wednesday, calculated by knowing he reads four times as many minutes on Wednesday as on Monday, and he reads 45 minutes on Tuesday which is three times his Monday reading time.

Explanation:

Since Sean reads 3 times as many minutes on Tuesday as he does on Monday, and he reads 45 minutes on Tuesday, we can determine that he reads 45 minutes ÷ 3 = 15 minutes on Monday. Sean then reads 4 times as many minutes on Wednesday as he does on Monday. So, he must read 15 minutes × 4 = 60 minutes on Wednesday.

Answer: d. Infinitely many solutions

Step-by-step explanation:

The given equation is expressed as

10-3x +10x-7 = 5x-5+2x+8

The first step is to make all the terms containing the variable to be on the left hand side of the equation and the constants to be on the right hand side of the equation.

10-3x +10x-7=5x-5+2x+8

10 - 7 + 10x - 3x = 5x + 2x - 5 + 8

7x + 3 = 7x + 3

Subtracting 7x and 3 from the left hand side and the right hand side of the equation, it becomes.

7x - 7x + 3 - 3 = 7x - 7x + 3 - 3

0 = 0

It has infinitely many solutions because as any value of x would satisfy both sides of the equation.

Answer:

Part 1:- option first is correct

[tex]-\frac{1}{2}ab^{12}[/tex]

Part 1:- option third is correct

[tex]\frac{w^{10}}{3y^{4}}[/tex]

Step-by-step explanation:

Given:

The given ration expressions are.

1. [tex]\frac{-2a^{2}b^{4}}{4ab^{-8}}[/tex]

2. [tex]\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}[/tex]

We need to simplify the given expressions.

Solution:

Part 1:-

Given expression is

[tex]=\frac{-2a^{2}b^{4}}{4ab^{-8}}[/tex]

Using law of exponents [tex]\frac{x^{m} }{x^{n} } = x^{(m-n)}[/tex]

[tex]=-\frac{a^{2-1}b^{4-(-8)}}{2}[/tex]

[tex]=-\frac{a^{1}b^{4+8}}{2}[/tex]

[tex]=-\frac{ab^{12}}{2}[/tex]

[tex]=-\frac{1}{2}ab^{12}[/tex]

Therefore, option first [tex]-\frac{1}{2}ab^{12}[/tex] is correct.

Part 2:-

Given expression is.

[tex]=\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}[/tex]

Using law of exponents [tex]\frac{x^{m} }{x^{n} } = x^{(m-n)}[/tex]

[tex]=\frac{w^{4-(-6)}y^{-2-2}}{3}[/tex]

[tex]=\frac{w^{4+6}y^{-4}}{3}[/tex]

[tex]=\frac{w^{10}y^{-4}}{3}[/tex]

[tex]=\frac{w^{10}}{3y^{4}}[/tex]

Therefore, third option [tex]\frac{w^{10}}{3y^{4}}[/tex] is correct.

Answer:

Therefore, we use the  linear depreciation and we get is 17222.22 .

Step-by-step explanation:

From Exercise we have that  is boat  $250,000.

The straight line depreciation for a boat  would be calculated as follows:

Cost  boat is $250,000.  

For  $95,000 Deep Blue plans to sell it after 9 years.

We use the formula and we calculate :

(250000-95000)/9=155000/9=17222.22

Therefore, we use the  linear depreciation and we get is 17222.22 .

To calculate the annual depreciation expense for Deep Blue's boat using the straight-line method, subtract the salvage value from the purchase price and divide by the number of years of useful life, resulting in an annual depreciation expense of $17,222.22.

To determine the annual depreciation, subtract the salvage value from the purchase price and divide by the useful life of the asset in years:

Subtract the salvage value from the purchase price: $250,000 - $95,000 = $155,000.

Divide the result by the number of years of useful life: $155,000 / 9 years = $17,222.22.

Therefore, Deep Blue would record an annual depreciation expense of $17,222.22.

Answer:

 42 mph

Step-by-step explanation:

If you start with the assumption that the answer is an integer, you can solve a problem like this by looking at the factors of 294.

  294 = 2·3·7² = 6·49 = 7·42

At 42 mph, the 294-mile trip took ...

   time = distance/speed = 294 mi/(42 mi/h) = 7 h

At a speed 7 mph faster, the 294-mile trip took ...

   (294 mi)/(49 mi/h) = 6 h . . . . . 1 hour less

The average speed of Imogene's car for the 294-mile trip was 42 miles per hour.

_____

Alternative solution

If you let s represent Imogene's speed, you can use the above time and distance relationship to write an equation relating the trip times:

  294/s = 294/(s+7) +1

Multiplying by s(s+7), we get ...

  294(s+7) = 294s +s(s+7)

  2058 = s^2 +7s . . . . . . . . . . . subtract 294s

We can complete the square by adding (7/2)^2 = 12.25 to both sides

  2070.25 = s^2 +7s +12.25 = (s +3.5)^2

  ±45.5 = s +3.5 . . . . . take the square root; next subtract 3.5

  -3.5 +45.5 = s = 42 . . . . use the positive solution

Imogene's average speed was 42 mph.

Imogene's average speed was 294 mph. We solve this by using the relationship between distance, speed, and time, and applying it to the specific constraints of the problem. By setting s = speed, we use two equations representing each scenario and solve for s.

Let's assign 's' to Imogene's average speed for the trip. The time taken at this speed is the distance traveled (294 mi) divided by 's' (speed = distance/time), making the time = 294/s. If the car was faster by 7 mph, the speed would be s+7 mph, and the time taken would then be 294/(s+7). The problem states that the second scenario would take 1 hour less, so 294/s = 294/(s+7) + 1.

Cross-multiplication and simplification of this equation result in (294s + 2058) = 294(s +7) or 294s + 2058 = 294s + 2058, which simplifies to 2058 = 7s, or s = 294 mph. Therefore, Imogene's average speed was 294 mph.

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Answer:

B) 6 units

Step-by-step explanation:

The formula of the volume of the Pyramid is 1/3×area of the base×height

1/3×70×height=140

Dividing both sides by 70

1/3×height=2

Multiplying both sides by 3

Height = 6

Final answer:

The height of a right square pyramid with a rectangular base area of 70 square units and a volume of 140 cubic units is 6 units, by using the volume formula of the pyramid.

Explanation:

The question asks us to find the height of a right square pyramid with a given base area and volume. To find the height, we need to use the formula for the volume of a pyramid, which is given by the formula: Volume = (Base Area * Height) / 3. We are given the base area as 70 square units and the volume as 140 cubic units.

Using the formula to solve for the height we get:
Height = (Volume * 3) / Base Area = (140 * 3) / 70 = 6 units. Therefore, the height of the pyramid is 6 units.

Answer:

Step-by-step explanation:

area=4×22/7×14²=4×22×28=2464 units²

The surface area of a sphere with a radius of 14 is 2464 square units. When considering significant figures, this is rounded to 2500 square units to match the two significant digits of the given radius.

To find the surface area of a sphere with a radius of 14, using the given value of 22/7 for , the formula A = 4*pi*r2 is used. Plugging in the numbers:

A = 4 * (22/7) * (14)²

A = 4 * (22/7) * 196

A = 4 * 22 * 28

A = 88 * 28

A = 2464

Thus, the surface area of the sphere is 2464 square units.

Answer: Ballwin Bears

Step-by-step explanation:

Answer:

The Ballwin Bears are taller on average, and the Aviation Aces have players whose are more consistent.

Step-by-step explanation:

(This is the correct answer on Knewton-alta)

Answer:

(x + 1)² + (y − 3)² = 41

Step-by-step explanation:

The center of the circle is the midpoint of the diameter.

(h, k) = ((x₂ + x₁)/2, (y₂ + y₁)/2)

(h, k) = ((3 + -5)/2, (-2 + 8)/2)

(h, k) = (-1, 3)

The radius is half the length of the diameter.

r = ½ √((x₂ − x₁)² + (y₂ − y₁)²)

r = ½ √((3 − -5)² + (-2 − 8)²)

r = ½ √(8² + 10²)

r = √41

Therefore, the equation of the circle is:

(x − h)² + (y − k)² = r²

(x + 1)² + (y − 3)² = 41

The standard form of equation of the circle is (x + 1) + (y - 3) = (6.40)².

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}

Given is that the endpoints of a diameter of a circle are (3, -2) and (-5, 8).

The center: (3-5/2, -2+8/2) = (-1, 3)

The diameter d = √{(x₂-x₁)² + (y₂-y₁)²}

d = √{(-5-3)² + (8 + 2)²}

d = √{64 + 100}

d = √164

d = 12.81

The radius r = 6.40

The standard form of equation of the circle is,

(x + 1) + (y - 3) = (6.40)²

Therefore, the standard form of equation of the circle is,

(x + 1) + (y - 3) = (6.40)²

To learn more about the distance between two points;

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Answer:

  8/3

Step-by-step explanation:

The range of possible lengths for the third side is 16±9, or 7 to 25. For lengths of 7 and 25, the area of the triangle will be zero, so the ratio of altitudes will be infinite (actually, undefined, as division by 0 is involved).

For positive triangle area and integer side lengths, the range of side lengths can be from 8 to 24. For any given triangle, the ratio of maximum altitude to minimum altitude will be the same as the ratio of the maximum side length to the minimum side length.

For the triangles under consideration, the shortest side length we can have is 8. For that 8-9-16 triangle, the ratio of the maximum to minimum side lengths is 16/8 = 2.

The longest side length we can have is 24. For that 9-16-24 triangle, the ratio of maximum to minimum side lengths is 24/9 = 8/3 = 2 2/3. This is more than 2, so 8/3 is the largest possible ratio of any two altitudes.

_____

More explanation

The area of a triangle is given by the formula ...

  A = (1/2)bh

Then the altitude for a given base (b) is ...

  h = 2A/b

That is, the altitude is inversely proportional to the base length for a triangle of a given area. Once you choose the three sides of the triangle, the area is fixed, so the ratio of altitudes is the inverse of the ratio of base lengths. The ratio of maximum altitude to minimum altitude is the ratio of the inverse of the minimum base length to the inverse of the maximum base length, which is to say it is the same as the ratio of maximum to minimum base lengths.

Answer:

8/3

Step-by-step explanation:

Answer:

The answer to your question is 4x - 5

Step-by-step explanation:

                [tex](8x -10)\frac{1}{2}[/tex]

Distributive property, this property allows us to multiply two terms separately. That means that in this problem [tex]\frac{1}{2}[/tex]  will multiply the first term, and after that the second term. One half multiply 8x and also - 10.

                 [tex]\frac{8x}{2} - \frac{10}{2}[/tex]

Simplify and result

                [tex]4x - 5[/tex]

Using the distributive property on [tex](8x - 10) \times \frac{1}{2}[/tex], we get  [tex]4x-5[/tex]

Given: [tex](8x - 10) \times \frac{1}{2}[/tex]

To find: simplify using distributive property

Distributive property can be depicted by [tex]x(a+b) = xa + xb[/tex]

We can use this property and solve as follows:

[tex](8x - 10) \times \frac{1}{2} = [\frac{1}{2} \times 8x] - [10 \times \frac{1}{2}] = 4x -5[/tex]

We get the expression without parentheses [tex]4x-5[/tex]

The problem can be solved using combinatorics, specifically the permutation of a multiset. Using the formula P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is total number of operations and n1, n2,... are the number of each identical operation, the number of different possible sequences to complete the manufacturing operation are 35.

The number of sequences of the operations can be found by using the formula for permutations of multiset - a concept in combinatorics part of mathematics. Permutations of a multiset are the number of ways in which we can arrange all the elements of the multiset considering the repetition of elements. We have 7 operations in total: three identical notches (type A) and four identical bends (type B). The formula is:

P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is the total number of items(7 in this case), n1,n2,...,nk are the number of each type of item.

Therefore, the number of different possible sequences to complete the manufacturing is: P(7 ; 3, 4) = 7! / (3! * 4!). This evaluates to 35.

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Answer: a=6 b=9 c=8

Step-by-step explanation:

The problem consists of finding the roots of the quadratic equations:

[tex]x^2+15x+54=0\\[/tex]

[tex]x^2-17x+72=0\\[/tex]

The roots can be found with the following equation for solving quadratic equations:

[tex]x_{12}=\frac{-B\pm\sqrt{B^2-4AC}}{2A}[/tex]  for equation: [tex]Ax^2+Bx+C=0[/tex]

After solving the equations you can write the result as:

[tex]x^2+15x+54=(x+6)(x+9)\\[/tex]

[tex]x^2-17x+72=(x-9)(x-8)[/tex]

Answer:

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

Question:

The expression $x^2 - 15x - 54$ can be written as $(x-a)(x-b),$ and the expression $x^2 - 17x + 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?

Step-by-step explanation:

To determine the values of a,b and c.

We need factorize the two equations.

i) x^2 -15x +54

x^2 -6x -9x +54

x(x-6) -9(x-6)

=(x-6)(x-9)

ii) x^2 -17x +72

x^2 -9x -8x +72

x(x-9) -8(x-9)

=(x-9)(x-8)

From the question:

Comparing

(x-a)(x-b) to (x-6)(x-9)

And

(x-b)(x-c) to (x-9)(x-8)

We can see that b is common in the two cases and also 9 is common in the two factorised equations.

So,

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

Answer:The following states how confident are you? So Quadratic Functions are simple functions listen to this example Multiplying (x+4) and (x−1) together (called Expanding) gets x2 + 3x − 4 :

expand vs factor quadratic

So (x+4) and (x−1) are factors of x2 + 3x − 4

Just to be sure, let us check:

Step-by-step explanation:

Yes, (x+4) and (x−1) are definitely factors of x2 + 3x − 4

Answer:

Step-by-step explanation:

Answer: The equation that would help members to find how much they would pay per month is

40 + 12x = 460

Step-by-step explanation:

Let x represent the amount of money that members would pay per month.

Let y represent the number of months for which a member uses the gym.

There is a fee of $40 when you join, and the rest is paid monthly. This means that the cost of using the gym for x months would be

40 + xy

A one year membership to metro gym costs $460. Therefore are 12 months in a year. Therefore,

40 + 12x = 460

12x = 460 - 40 = 420

x = 420/12 = 35

The equation that would help members to find how much they would pay per month is

Answer:

Step-by-step explanation:

The kinetic energy for a given mass and velocity is ...

  KE = (1/2)mv^2 . . . . . m is mass

At its initial speed, the kinetic energy of the car is ...

  KEi = (1/2)(810 kg)(23.6 m/s)^2 ≈ 2.256×10^5 J . . . . . m is meters

At its final speed, the kinetic energy of the car is ...

  KEf = (1/2)(810 kg)(47.2 m/s)^2 ≈ 9.023×10^5 J

The ratio of final to initial kinetic energy is ...

  (9.023×10^5)/(2.256×10^5) = 4

4 times as much work must be done to stop the car.

_____

You know this without computing the kinetic energy. KE is proportional to the square of speed, so when the speed doubles, the KE is multiplied by 2^2 = 4.

Answer: to suggest or accept that a theory or idea is true as a starting point for reasoning or discussion.

Step-by-step explanation:

Here's an example: Astronomers postulate that the comet will reappear in 4000 years.

I'm not sure of whether or not you're aware of this, but you asked this question in the math section. Nevertheless, I remember in 5th grade I did a project on whether or not it is possible to use solar energy to heat up different colored bags filled with water, and to determine which one would heat up the quickest. If that one doesn't pique your interest, you can go to sciencebuddies.com and search through a variety of project ideas if you'd like. That's where I found mine.

Final answer:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. Students can collect cans with different types of food and predict which can will win a race down an inclined plane.

Explanation:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. In this experiment, students can collect several cans containing different types of food and predict which can will win the race down an inclined plane. They can then explain their prediction and see if it is correct. Another option is to collect empty cylindrical containers of the same size and fill them with different materials like wet or dry sand to see how it affects the race.

Answer:

Option D = Use a histogram with class width equal to 10

Step-by-step explanation:

A histogram will be better to represent the data. A histogram is a graphical representation of a frequency distribution, where you have rectangular bars placed side by side. the vertical axis represent the frequency while the horizontal axis represent the variable being represented which is the length of time worked by the employees.

One of the advantages of the histogram is that it has no gaps between the bars and it is mostly used for grouped data. This explains why the best representation ad the best option is to use the HISTOGRAM.

Final answer:

Option D, a histogram with class width equal to 10, would likely be the best representation for the data set of the length of time worked by employees, as it would facilitate easy viewing of data distribution and patterns.

Explanation:

The question asks for a better way to represent a data set of the length of time worked by employees at a local Honda plant. The provided options include a time plot, split stems, a pie chart, and a histogram with a class width of 10. Looking at the options:

In conclusion, option D, which suggests using a histogram with a class width equal to 10, would likely be the best graphical representation for this data set.

Answer:

Step-by-step explanation:

variance = 48,326.5, standard deviation = 219.8

Answer: variance = 48,326.5, standard deviation = 219.8

Step-by-step explanation: I completed the quiz, and option A. variance = 48,326.5, standard deviation = 219.8 was the correct answer!

Answer:

The answer to your question is width = 8ab³

Step-by-step explanation:

Data

Area = 32a³b⁴ u²

length = 4a²b   u

Formula

Area of a rectangle = width x length

Solve for width

                           width = [tex]\frac{Area}{length}[/tex]

Substitution

                          width = [tex]\frac{32a^{3}b^{4}}{4a^{2}b}[/tex]

Simplify using rules of exponents, just remember that in a division we subtract the exponents and divide the coefficients normally.

                          width = 8 a²b³

Answer:

Step-by-step explanation: 32a^3 is -8 < a < - 8 axis interceptions 32a^3            vertical asymphotes None Extreme points of a32a^3 0,0

Answer:

The standard deviation is 9.34

Step-by-step explanation:

First we need to find mean of the sample:

[tex]m=(23.9+15.3+40.2+30.3+12+22.8)/6=24.08[/tex]

Standard deviation will be like below:

[tex]d=\sqrt{(x-m^2)/6}=9.34[/tex]

Answer:he would arrive 0.2 miles faster.

Step-by-step explanation:

Distance = speed × time

Time = distance/speed

William cycles at a sped of 15 miles per hour. He cycles 12 miles from home to school. This means that the time it takes William to get to school from home would be

12/15 = 0.8 hours

If he increases his cycling speed by 5 miles per hour, his new speed becomes

15 + 5 = 20 miles per hour

Therefore, the new time it takes William to get to school from home would be

12/20 = 0.6 hours

The difference in both times is

0.8 - 0.6 = 0.2 hours

Therefore, he would arrive 0.2 miles faster.

Answer:

E.) 1

Step-by-step explanation:

Firstly we will solve for L.H.S.

L.H.S. =[tex]Csc^2\theta[/tex]

Since we know that [tex]Csc^2\theta[/tex] is the inverse of [tex]Sin^2\theta[/tex].

So we can say that;

[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]

Now For R.H.S.

[tex]Cot^2\theta+1[/tex]

Since we  can rewrite [tex]cot^2\theta[/tex] as [tex]\frac{cos^2\theta}{sin^2\theta}[/tex].

Now we can say that the R.H.S. is;

[tex]\frac{cos^2\theta}{sin^2\theta}+1[/tex]

Now we add the fraction and get;

[tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}[/tex]

Now according to trigonometric identity;

[tex]cos^2\theta+sin^2\theta=1[/tex]

So, [tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}[/tex]

Here,

[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]   and     [tex]Cot^2\theta+1[/tex] = [tex]\frac{1}{sin^2\theta}[/tex]  

L.H.S. = R.H.S.

Hence [tex]csc^2\theta=cot^2\theta+1[/tex]

Answer:

Pan is closest to Paris when she gets to Florence when she is 35 miles away

Step-by-step explanation:

With Paris at (0,0), Rome is 40miles west which is on the negative x axis.

Florence is 35 miles closer (east to Paris) so we have -45 + 35 = -10

and 55 mikes north of Rome which is on the positive y-axis. So Florence is at point (-10,55)

The distance between the two points Florence and Paris is √(x2 - x1)^2 + (y2 - y1)^2

x1 = 0, y1 = 0

x2 = -10, y2 = 55

So we have

√(-10-0)^2 + (55-0)^2

= √(-10)^2 + (55)^2

= √ 100 + 3025

= √3125

= 55.9 mikes from Paris

Pam is closest to Paris when she gets to Florence when she is 35 miles away

Pam gets closest to Paris when she is 5 miles away, which occurs when she travels directly east from Rome before heading north to Florence.

Pam is taking a train from Rome to Florence, and we need to find out how close she gets to Paris along the way. Rome is 40 miles due west of Paris, and Florence is 35 miles east and 55 miles north of Rome. While traveling from Rome to Florence, Pam would initially get closer to Paris as she travels east, but as she moves north, the closest point to Paris would be directly east from Rome before moving north.

Answer:

A prison administration wants to know whether the prisoners think the guards treat them fairly. The explanation, of each component could be used to produce biased and unbiased results, is as follow  

A) Component 2:

B) Component 4:

Bias in research on prisoner-guard dynamics can result from the involvement of researchers and the phrasing of questions. To ensure unbiased results, neutral interactions and carefully worded questions are vital.

Biased Research Components in Prisoner-Guard Dynamics

In research, it is crucial to mitigate factors that can lead to bias. Two such components in the study of prisoner-guard dynamics are researcher involvement and the phrasing of measurements and questions. If the researcher has direct contact with participants, they can unknowingly influence responses based on their body language, tone, or preconceived notions.

To produce unbiased results, researchers should maintain a neutral demeanor and minimize unnecessary interaction. The exact nature of measurements and questions can also introduce bias. Leading or emotional language in survey questions can skew results towards a specific answer. To avoid this, questions must be neutrally worded and designed to reflect the respondent's true perspective without influence.

Answer:

Population : all the steaks Tessa can cook

Parameter : minimum internal temperature of 160 degrees Fahrenheit

Sample : two random thermometer readings

Statistic : minimum sample reading of 165 degrees Fahrenheit

Step-by-step explanation:

Let's recall the definitions of these statistical concepts and match it with the information that were provided to us:

Answer:

Step-by-step explanation:

The function is given by [tex]g(x) = 3x^{2} - 12x - 3[/tex].

Differentiating the function, we get [tex]\frac{d g(x)}{dx} = 6x - 12[/tex].

Now, at x = 2, 6x - 12 will be 0.

Hence, at x = 2, either the function will have maximum or minimum value.

g(2) = 12 - 24 -3 = -15.

g(1) = 3 -12 -3 = -12.

g(0) = -3.

Hence, the given function passes through (2, -15), (1, -12) and (0, -3).

Answer:

33 hearts sold, 48 roses sold

Step-by-step explanation:

x- number of roses sold

y- number of hearts sold

x=15+y <- " The number of bouquets sold was 15 more than the number of hearts sold"

5x+3y=339

5(15+y)+3y=339

75+5y+3y=339

8y=339-75

8y=264

y=33

x=15+33=48

The number of chocolate hearts sold was 33, and the number of bouquets sold was 48 for a total revenue of $339.

Let's assume the number of chocolate hearts sold was 'x'. Since the number of bouquets sold was 15 more than the number of hearts sold, the number of bouquets sold would be 'x + 15'.

The price of each rose bouquet is $5, so the total revenue from selling bouquets would be '5(x + 15)'.

Similarly, the price of each chocolate heart is $3, so the total revenue from selling hearts would be '3x'.

Since the total revenue collected was $339, we can set up an equation: '5(x + 15) + 3x = 339'.

Simplifying the equation, we get '8x + 75 = 339'.

Subtracting 75 from both sides of the equation, we get '8x = 264'.

Dividing both sides of the equation by 8, we get 'x = 33'.

Therefore, 33 chocolate hearts were sold, and the number of bouquets sold would be '33 + 15 = 48'.