Find [fog](x) and [gof](x), if they exist. State the domain and range for each.
5.f(x) = -3x
g(x) = x +8

6. f(x) = 2x²-x + 1
g(x) = 4x + 3

The value of the indicated trigonometric ratio.

cosβ is equal to 0.9167

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

the side CA = 22 is adjacent to the angle β while BA = 24 is the hypotenuse, so:

cosβ = 22/24 {adjacent/hypotenuse}

cosβ = 11/12

cosβ = 0.9167

Therefore, the cosine of the angle β is equal to 0.9167 using the trigonometric ratio.

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The difference of the fractions 42¾ - 34⅛ is equal to 8⅝.

The given fractions are expressed as mixed numbers, so we shall first rewrite them as improper fractions, find the lowest common multiple of their denominators to have a single fraction, before then subtracting the resulting numerators to have their difference.

42¾ = 171/4

34⅛ = 273/8

42¾ - 34⅛ = 171/4 - 273/8

LCM of 4 and 8 is 8, so;

42¾ - 34⅛ = (171 ×2 - 273 × 1)/8 {simplifying to a single fraction}

42¾ - 34⅛ = (342 - 273)/8

42¾ - 34⅛ = 69/8

42¾ - 34⅛ = 8⅝

Therefore, difference of the fractions 42¾ - 34⅛ is equal to 8⅝.

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Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

The conditional probability that a randomly chosen student studies every day, given that the student passes a math test is O P(M|S). The correct option is A.

P(M|S) is the probability that a randomly chosen student passes a math test given that the student studies every day. But, the question is asking for the probability that a student studies every day given that the student passes a math test.

Considering an P(M|S) situation,
Option D: P(SM) is incorrect because it means the probability that both events S and M occur simultaneously.
Option C: P(S) and P(M) is incorrect because it shows the probabilities of two individual events, not the probability of one event given that the other event has occurred.
Option B: P(M AND S) is incorrect because it means the probability that both events M and S occur simultaneously.

The given problem is based on Conditional Probability Notation to Describe Events. The notation used for conditional probability is P(A|B). Where A and B are two events, the notation represents the probability of event A occurring, given that event B has occurred. Conditional probability can be described as the probability of one event happening given that another event has already happened.

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Answer:

Roughly 10 oz, exact amount is 10.58219

Equation for the total cost of paint job 'y' with number of hours spent on paining 'x' is formed as:

y = 50 + 3x

y = 50 + 5x

Let the total cost of paint job be' 'y'.

Let 'x' be the number of hours spent on paining.

Then,

Total cost = supplies + hourly fee* number of hours.

Let the supplies cost be 'z'

140 = z + 3x

200 = z + 5x

Solving both equation.

2x = 60

x = 30

z = 50

Thus, equation for the  total cost of paint job 'y' with number of hours spent on paining 'x' is formed as:

y = 50 + 3x

y = 50 + 5x

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For XY and BD are parallel lines,

a) Complete sentence: Angle XBC = 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.

b) The angle XBC is 55 degrees due to the equal sides XB = XC, and angle BXC is 125 degrees as the sum of angles in a straight line is 180 degrees.

Working out angle BXC:

Angle XBC = 55 degrees (given)

Angles XBC and BXC form a straight line, so:

Angle BXC = 180 - 55 = 125 degrees (sum of angles in a straight line)

Reasoning for each angle:

Angle XBC is given as 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.

Angle BXC is found by subtracting the given angle XBC from the sum of angles in a straight line (180 degrees).

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The question is -

XY and BD are parallel lines.

X is a point on AB and C is a point on BD.

XB = XC.

a) complete this sentence.

Angle XBC = 55 Degrees Because . . .

b) Work out angle BXC.

give a reason for each angle you work out.

Answer:

Step-by-step explanation:

Correct option is B)

Center is the point of intersection of diagonals.

⇒2x−3y=5

⇒3x−4y=7

Solving simultaneous equation, x=1,y=−1

Center =(1,−1)

For radius r ( let )

⇒r=

π

154

​

​

  ⇒

22

154

​

×7

​

=7

Equation -

⇒(x−1)

2

+(y+1)

2

=7

2

⇒x

2

+1−2x+y

2

+1+2y=49

⇒x

2

+y

2

−2x+2y=49−2

⇒x

2

+y

2

−2x+2y=47

Hence, the answer is x

2

+y

2

−2x+2y=47.

The amount repaid in the three months of the loan amount $24,000 with a condition of 20% repayment is equal to $11,712.

Percent of amount Maricarmen has to pay = 20% of the loan each month.

This implies  Maricarmen pay 0.2 times the loan amount each month.

Amount Maricarmen will pay in the first month is equal to,

0.2 x $24,000 = $4,800

Amount left after the first payment,

$24,000 - $4,800 = $19,200

In the second month, Maricarmen will pay,

0.2 x $19,200 = $3,840

Amount left after the second payment,

$19,200 - $3,840 = $15,360

In the third month, Maricarmen will pay,

0.2 x $15,360 = $3,072

Amount left after the third payment,

$15,360 - $3,072 = $12,288

total amount paid in three months,

$4,800 + $3,840 + $3,072 = $11,712

Therefore, after three months Maricarmen will have repaid a total of  $11,712 of the loan.

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Answer: 59%

Step-by-step explanation:

To find the percentage of youths who prefer reading electronic books, we need to divide the number of youths who prefer electronic books by the total number of youths surveyed and then multiply by 100.

The total number of youths surveyed is:

28 + 40 = 68

The number of youths who prefer electronic books is:

40

Dividing the number of youths who prefer electronic books by the total number of youths surveyed and multiplying by 100, we get:

(40/68) x 100% = 58.82%

Rounding to the nearest whole number percent, we get:

59%

Therefore, approximately 59% of the youths surveyed prefer reading electronic books.

Answer:

59%

Step-by-step explanation:

Answer:

Angie is 20, Mandy is 42.

Step-by-step explanation:

Angie's current age = x

Mandy's current age = y, also x + 22

Mandy's age in 2 years = 2x+2

2x + 2 = x + 22

x + 2 = 22

x = 20

y = x + 22

y = 20 + 22

y = 42

A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.

A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).

A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria:

Linearity: The graph must shοw a straight line passing thrοugh the οrigin (0,0). This means that as οne variable increases, the οther variable increases in prοpοrtiοn.

Cοnstant ratiο: The slοpe οf the line (i.e., the change in the y-variable divided by the change in the x-variable) must be cοnstant thrοughοut the entire graph.

This cοnstant ratiο represents the prοpοrtiοnality cοnstant between the twο variables.

Hence,  A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.

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Therefore , the solution of the given problem of speed comes out to be train is moving at 60 miles per hour while the freight train is moving at 20 miles per hour.

By keeping an eye on something from a distance, we can gauge its speed. An object's speed determines how far it can travel in a given period of time. Utilizing the equation velocity = distance/time, velocity is determined. Kilometers per hour (mileage), kilometres per hour (km/h), and metres per second (m/s) are the three most widely used measures of speed (mph).

Here,

The freight train would cover the following distance in three hours at the speed of "x" miles per hour:

=> Distance = speed x duration = x miles/hour x 3 hours = 3x miles.

The passenger train would cover the following distance in three hours at "3x" kilometres per hour:

Distance is calculated as follows: 3 kilometres per hour times 3 hours equals 9 miles.

We can now determine the 240-mile overall distance between the two trains at 6 o'clock:

Overall distance equals the sum of the routes taken by the passenger and freight trains.

=> 240 miles = 3x miles + 9x miles

=> 240 miles = 12x miles

Therefore,

=> x=20 kilometres per hour

=> 3x = 60 mph 

As a result, the passenger train is moving at 60 miles per hour while the freight train is moving at 20 miles per hour.

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Answer:

Number C shows to be first image being reflected across.

The answer of the given question based on finding roots are  roots of the equation are -3, 3/2, and 1.

Synthetic division is  shortcut method used to divide  polynomial by  linear factor of  form (x-a), where "a" is a constant. It is  simplified method of polynomial long division, and it is especially useful when dividing by linear factor, as it avoids the need to write out all  powers of x.

We list the factors of the leading coefficient 2 and the constant term 9:

Factors of 2: ±1, ±2

Factors of 9: ±1, ±3, ±9

Possible rational roots are: ±1, ±2, ±3, ±9

Using synthetic division with x = -1, we get:

-1 | 2 1 -12 9

-2 1 11

2  -1    -1  20

The remainder is not zero, so x = -1 is not a root of the equation.

Using synthetic division with x = -2, we get:

-2 | 2 1 -12 9

-4 6 -88

2  -3    -6 -79

The remainder is not zero, so x = -2 is not a root of the equation.

Using synthetic division with x = -3, we get:

-3 | 2 1 -12 9

-6 15 -9

2  -5     3  0

The remainder is zero, so x = -3 is a root of the equation. This means that (x + 3) is a factor of the equation.

Using polynomial long division, we get:

2x³ + x² - 12x + 9 = (x + 3)(2x² - 5x + 3)

quadratic factor can  factored further we get:

2x² - 5x + 3 = (2x - 3)(x - 1)

Therefore, roots of  given equation is:

x = -3 (root obtained earlier)

x = 3/2 (from 2x - 3 = 0)

x = 1(from x -1=0)

For the given equation 2x³ + x² - 12x + 9 = 0, the factors of the leading coefficient 2 are ±1, ±2, and the factors of the constant term 9 are ±1, ±3, ±9. Therefore,  possible rational roots of  equation are:

±1/1, ±3/1, ±1/2, ±3/2, ±9/2, ±1/9, ±3/9, ±9/9

Using synthetic division or other methods, we can check that the real rational roots of the equation are -3, 3/2, and 1.which we found in part (a).

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The probability that this whole shipment will be accepted is 0.000133. The probability that this whole shipment will be accepted can be found using the binomial probability formula, where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.[tex]P(x) = (n! / (x! * (n - x)!)) * (p^x) * (q^(n - x))[/tex]


In this case, n = 17, p = 0.97 (the probability of a tablet meeting the required specifications), and q = 0.03 (the probability of a tablet not meeting the required specifications).

We want to find the probability of either 0 or 1 defects, so we will calculate the probabilities for both and add them together.
[tex]P(0) = (17! / (0! * (17 - 0)!)) * (0.97^0) * (0.03^(17 - 0)) = 0.00000497P(1) = (17! / (1! * (17 - 1)!)) * (0.97^1) * (0.03^(17 - 1)) = 0.000128P(0 or 1) = P(0) + P(1) = 0.00000497 + 0.000128 = 0.000133[/tex]

Therefore, the probability that this whole shipment will be accepted is 0.000133.

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Answer: $384

Step-by-step explanation: 480 - 20% = 384

Answer:

2

Step-by-step explanation:

Answer:

A and C : cones and pyramids

Step-by-step explanation:

only cones, pyramids and isosceles triangles have apexes

The shapes that have at least 1 apex are:

Right circular cone

Right pyramid

Therefore, the answer is C and D.

As the table shows the estimated water depth in feet, y, after x days of drought. The function that represents the data is y = -0,5x + 100. The Option A is correct.

A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output.

Based on the given table, it appears that the water depth is decreasing by 0.5 feet every day due to the drought. Additionally, the initial depth of the lake was 100 feet.

Therefore, the function that represents the data is y = -0.5x + 100 where y represents the water depth in feet and x represents the number of days of drought.

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Answer:

To find the Maclaurin series for $f(x) = xe^x$, we can use the formula for the Maclaurin series of $e^x$ and differentiate the product term by term:

$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$

$$xe^x = x \sum_{n=0}^\infty \frac{x^n}{n!} = \sum_{n=0}^\infty \frac{x^{n+1}}{n!}$$

So the first few terms of the Maclaurin series for $f(x)$ are:

$$f(x) = xe^x = x + x^2 + \frac{x^3}{2} + \frac{x^4}{3} + \frac{x^5}{24} + \cdots$$

To find the radius of convergence, we can use the ratio test:

$$\lim_{n\to\infty} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{n\to\infty} \left| \frac{x^{n+2}/(n+1)!}{x^{n+1}/n!} \right| = \lim_{n\to\infty} \frac{|x|}{n+1} = 0$$

Since the limit is less than 1 for all values of $x$, the Maclaurin series converges for all values of $x$, and the radius of convergence is infinite.

Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. His total moving cost including tax charges equals to the $2,053.8375.

We have to calculate Jay's moving cost if the service also charges 7.25% tax on the total. Here, Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. Now, first we determine the NuHome Movers charges,

Rate of NuHome Movers charges for loading/unloading services = $95 per hour and NuHome Movers charges for 9 hours of loading/unloading services = Multiplication of number of hours by rate of service = 9× $95 = $855 --(1)

Rate of NuHome Movers charges for packing/unpacking services = $80 per hour land NuHome Movers charges for 7 hours of packing/unpacking services = Multiplication of number of hours by rate of service = 7× $80 = $560--(2)

Now, determine charge for truck rental,

Rate of NuHome Movers charges for truck rental = $2.50 per mile

and NuHome Movers charges for 200 miles truck rental = number of miles × rate of each mile = $2.50 × 200

= $500--(3)

Thus, total cost of charges which Jay will pay = charges cost for packing/unpacking services + charges cost for loading/unloading services + charges for truck rental

= $855 + $560 + $500 ( from (1), (2),(3))

= $1,915

Tax charges on total = 7.25%

Determine the Jay's total moving cost including taxes = $1,915 + $1915(7.25/100)

= $1,915 + $1915( 0.0725)

= $1,915 + $138.8375

= $2,053.8375

Hence, required cost value is $2,053.8375.

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Complete question :

NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?

The correct answers are x³ + 19 x² + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0.

Given:

A box with dimensions 3 cm × 5 cm × 11 cm

Current volume of given box = 3×5×11 = 165 cm^3

New volume of box = (3+x) × (5+x) × (11+x)

= (15 + 8 x + x²) × (11+x)

= 165 + 103 x + 19 x^2 + x³

For volume to be 300 cm³

=> x³+ 19 x² + 103 x + 165 = 300

=> x³ + 19 x² + 103 x - 135 = 0

For volume to be 900 cm³ -

=> x³ + 19 x² + 103 x + 165 = 900

=> x³ + 19 x²+ 103 x - 735 = 0

Therefore, x^3 + 19 x^2 + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0 are the solution.

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The variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is 3657.6.

What is Variance?

Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.

First, we can calculate the mean of the original dataset:

Mean = (a + b + c + ta + e) / 5

Then, we can calculate the variance using the formula:

Variance = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5

Given that the variance of the original dataset is 2032, we can substitute this value in the formula and solve for the mean:

2032 = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5

Simplifying this equation, we get:

(a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)² = 10160

Now, we can apply the transformation to the dataset by adding 2 and multiplying by 3:

New dataset: 3a + 2, 3b + 2, 3c + 2, 3d + 2, 3e + 2

To find the variance of the new dataset, we follow the same steps as before:

Mean = (3a + 2 + 3b + 2 + 3c + 2 + 3d + 2 + 3e + 2) / 5 = 3Mean + 2

Variance = ((3a + 2 - Mean)² + (3b + 2 - Mean)² + (3c + 2 - Mean)² + (3d + 2 - Mean)² + (3e + 2 - Mean)²) / 5

Simplifying this equation, we get:

Variance = ((3a - 3Mean)² + (3b - 3Mean)² + (3c - 3Mean)² + (3d - 3Mean)² + (3e - 3Mean)²) / 5

Variance = 9((a - Mean)² + (b - Mean)² + (c - Mean)² + (d - Mean)² + (e - Mean)²) / 5

Variance = 9(2032) / 5

Variance = 3657.6

Therefore, the variance of the new dataset is 3657.6.

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Answer: 1456 square yds

Step-by-step explanation: Please mark brainliest and give thanks!

Answer:728

Step-by-step explanation:

V=abc=19*14*c=266c=3724

c=14

S=(19c+14c+14*19)=33c+266=33*14+266=728

Santina drive 14 miles more than Carole. The owner needs to buy 8 bags this week. John bought 48 individual can of cola.

Mile is measurement unit of land or any surface. We use it to calculate the distance.

Now we have to calculate these questions,

a. Santina drive 203 miles and Carole drive 189 Miles.

Santina drive 14 miles more than Carole.

b. A restaurant uses 80 pounds of potatoes per week and the owner buys the potatoes in 10 pound bags.

So, Number of bags, 80/10 = 8 bags.

The owner needs to buy 8 bags this week.

c. Six-packs of cola were on sale at a grocery store (i.e. 6 cola in pack) and he buy 8 six-packs of cola.

Total number of cola can = 8 X 6 = 48 cola can

John bought 48 individual can of cola.

d. Lori read 85 pages last weekend, 135 pages during the week, and 98 pages this weekend.

So, total number of pages read by Lori = 85 + 135 + 98

= 318

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Apart from each other 3.33 hours

To determine at what time the freight and express trains will be 600 km apart from each other, we must first determine the distance covered by each train. We can then use these distances to determine the total distance between the two trains at any given time.In this problem, we are given the following information:A freight train leaves the main station heading east at an average speed of 100 km/h.An hour later, an express train leaves the same station heading west at an average speed of 170 km/h.We are asked to determine the time at which they will be 600 km apart from each other.We can use the following formula to determine the distance covered by each train:D = RTwhere:D is the distance coveredR is the average speedT is the time takenTo find the distance covered by the freight train, we can use the following formula:D1 = RT1where:D1 is the distance covered by the freight trainR is the average speed of the freight trainT1 is the time taken by the freight trainTo find the distance covered by the express train, we can use the following formula:D2 = RT2where:D2 is the distance covered by the express trainR is the average speed of the express trainT2 is the time taken by the express trainNow, let's determine the distances covered by each train:D1 = 100(T1+1)D2 = 170T2We know that the total distance between the two trains is 600 km, so we can use the following equation to solve for the time at which they will be 600 km apart:D1 + D2 = 600100(T1+1) + 170T2 = 600100T1 + 170T2 + 100 = 600100T1 + 170T2 = 500(100/170)T1 + T2 = 5.9 hoursThe time taken by the freight train is T1 + 1, so we can substitute T1 + 1 for T1 in the equation above to solve for T1:T1 + T2 = 5.9100(T1+1)/170 + T2 = 5.9T1 + 1 + 1.7T2 = 5.9T1 + 1.7T2 = 4.9T1 = (4.9 - 1.7T2)/1.9Now, we can substitute this value of T1 into the equation we used earlier to solve for T2:100T1 + 170T2 = 500100((4.9 - 1.7T2)/1.9) + 170T2 = 500T2 ≈ 2.33Therefore, the time at which the two trains will be 600 km apart from each other is approximately 2.33 hours after the express train leaves the main station. To find the exact time, we need to add this value to the time at which the express train left the main station:Time = 1 + 2.33 = 3.33 hoursTherefore, the two trains will be 600 km apart from each other 3.33 hours after the express train leaves the main station.

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Answer:

30 degrees and 70 degrees

Step-by-step explanation:

A triangle has 180 degrees, and if you take away the known 80, you are left with 100 degrees to be split in a 3:7 ratio.

The frequency of all the five intervals is 9 + 13 + 12 + 7 + 15 = 56.

The cumulative frequency distribution table from the given frequency table:Class IntervalFrequencyCumulative Frequency0 − 89 89 + 1312 25 + 12 + 7 32 + 1515 47 + 15 62It is clear that the frequency of the first interval is 9. Therefore, the frequency of the first interval is 9.Next, the frequency of the second interval is 13. Therefore, the frequency of the first and second intervals is 9 + 13 = 22.Next, the frequency of the third interval is 12. Therefore, the frequency of the first, second and third intervals is 9 + 13 + 12 = 34.Then, the frequency of the fourth interval is 7. Therefore, the frequency of the first, second, third, and fourth intervals is 9 + 13 + 12 + 7 = 41.Finally, the frequency of the fifth interval is 15. Therefore, the frequency of all the five intervals is 9 + 13 + 12 + 7 + 15 = 56.

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Answer:

Adian would pick 396 apples in 36 minutes.

Step-by-step explanation:

Therefore, in 1 minute, Adian picks 11 apples.

In 36 minutes, he will pick:

11 apples/minute x 36 minutes = 396 apples.

Therefore, Adian would pick 396 apples in 36 minutes.

Answer:

396 apples

Step-by-step explanation:

adian picks apples at the rate of 11 apples every minute

So in order to find out how many he picks in 36 minutes we just multiply 36 by 11

36 x 11 = 396 apples in 36 minutes

Hope this helps!

Brainliest and a like is much appreciated.

The product in diagram A is: (3x)*(2x + 3y)

And the product in diagram B is: 5a*(8a + 3)

Let's start with the diagram A, we can define the long stripe as x and the short one as y.

On the top side we can see 3x.

On the left side we can se 2x + 3y

Then the product modeled is just:

(3x)*(2x + 3y)

Now let's go to diagram B.

Here we can see that the left side has a length 5a, and then we have two top sides, so this can be written as a sum:

8a + 3

The product between these two quantities is:

p = 5a*(8a + 3)

These are the two products.

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