Find the volume of a pyramid with a square base, where the side length of the base is


11. 8 ft and the height of the pyramid is 5. 2 ft. Round your answer to the nearest


tenth of a cubic foot.

Answer: less than

Step-by-step explanation:

To evaluate the integral ∫(3/(√(x² + 8514))) dx, we can use the substitution u = x² + 8514 and du/dx = 2x, which gives us:

∫(3/(√(x² + 8514))) dx = (3/2)∫(1/√u) du
= (3/2) * 2√u + C
= 3√(x² + 8514) + C

Note that we absorbed the arbitrary constant into C as much as possible.
It seems that your question contains some typos and unclear expressions. However, I can help you evaluate a definite integral that includes fractions and an arbitrary constant.

Consider the integral:

∫(3√(x² + 8514) dx)

To solve this integral, let's perform a substitution:

u = x² + 8514
du = 2x dx

Now, we can rewrite the integral as:

(3/2) ∫(√u du)

Now, we can integrate:

(3/2) ∫(u^(1/2) du) = (3/2) * (2/3) * u^(3/2) + C

Now, substitute u back with the original expression:

(3/2) * (2/3) * (x² + 8514)^(3/2) + C = (x² + 8514)^(3/2) + C

So, the evaluated integral is:

(x^2 + 8514)^(3/2) + C

Where C is the arbitrary constant.

Visit here to learn more about integral brainly.com/question/18125359

#SPJ11

The fastest rate of growth that the foot experienced during the year is approximately 0.554 inches/year.

We can use the given relationship between foot length L and height h to determine the rate of change of foot length with respect to time. Taking the derivative of L with respect to time t, we have dL/dt = (3/4) * 0.5 * h^(-0.5) * dh/dt. We can then substitute the given values of L and h at the beginning and end of the growth spurt to find dh/dt.

At the start, h = 64 inches and L = (3/4) * 64^0.5 = 9 inches. At the end, h = 69 inches and L = (3/4) * 69^0.5 = 9.89 inches.

Solving for dh/dt, we have dh/dt = 2.4 inches/year. Substituting this value into the expression for dL/dt, we get dL/dt = (3/4) * 0.5 * 69^(-0.5) * 2.4 = 0.554 inches/year (rounded to three decimal places). Therefore, the fastest rate of growth that the foot experienced during the year is approximately 0.554 inches/year.

For more questions like Expression click the link below:

https://brainly.com/question/29583350

#SPJ11

A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, after using sampling distribution we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.

Based on the given information, we can assume that the population proportion of students who brought a can of food to contribute to the canned food drive is 0.45. Aiden picks a representative sample of 25 students, and he expects the percentage for this sample will be 45%.

We can use the sampling distribution formula to calculate the expected sample proportion:

SE = sqrt[p(1-p) / n]

where p is the population proportion, n is the sample size, and SE is the standard error.

Plugging in the values, we get:

SE = sqrt[0.45(1-0.45) / 25] = 0.0984

Next, we can use the normal distribution to find the z-score corresponding to a sample proportion of 0.45:

z = (0.45 - 0.45) / 0.0984 = 0

A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.

To know more about sampling distribution, visit:

https://brainly.com/question/29375938#

#SPJ11

The final step when solving the given math problem is:

Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5)[/tex]

To solve √19x^5 for x, follow these steps:

Isolate the square root term: [tex]\sqrt{19x^5}[/tex] = y (Let y be the other side of the equation)

Square both sides: [tex](y^2) = 19x^5[/tex]

Divide both sides by 19: [tex](y^2)/19 = x^5[/tex]

Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5^)[/tex]

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and can be found using mathematical operations.

Read more about square roots here:

https://brainly.com/question/428672

#SPJ1

The probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

Suppose the horses in a large stable have a mean weight of 807lbs and a variance of 5776. We want to find the probability that the mean weight of a sample of 41 horses would differ from the population mean by greater than 18lbs.

Step 1: Calculate the standard deviation of the population.
Standard deviation (σ) = √variance = √5776 = 76lbs.

Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 76 / √41 ≈ 11.88lbs, where n is the sample size (41 horses).

Step 3: Calculate the z-score for the difference of 18lbs.
z = (difference - 0) / SE = (18 - 0) / 11.88 ≈ 1.51

Step 4: Find the probability corresponding to the z-score.
Using a z-table, we find that the probability corresponding to a z-score of 1.51 is approximately 0.9345.

Step 5: Calculate the probability of the mean weight differing by more than 18lbs.
Since we are looking for the probability of the mean weight differing by more than 18lbs (in either direction), we need to consider both tails of the distribution.
P(z > 1.51) = 1 - 0.9345 = 0.0655
P(z < -1.51) = 0.0655 (since the distribution is symmetric)

Total probability = P(z > 1.51) + P(z < -1.51) = 0.0655 + 0.0655 = 0.1310

So, the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

To know more about probability, visit:

https://brainly.com/question/30034780#

#SPJ11

The possible amount of time for Dinah to drive 420 miles on the highway is between 6 & 7 hours.

To get the possible time, we need to consider the range of speeds she can drive at.

Because she must drive at least 60 miles per hour and at most 70 miles per hour, we can calculate the possible time ranges using "Time = Distance / Speed"

At 60 miles per hour:

= 420 miles / 60 miles per hour

= 7 hours

At 70 miles per hour:

= 420 miles / 70 miles per hour

= 6 hours.

Read more about time

brainly.com/question/26046491

#SPJ1

The cost to alter each dress is $25 and each suit is $30 based on the given set of relations.

Let us represent the dresses as x and suit as y. Forming the equation for both customers.

Cost of one dress × number of dress +

Cost of one suit × number of suit = total cost

2x + y = 80 : equation 1

x + 3y = 115 : equation 2

Multiply equation with 1

6x + 3y = 240 : equation 3

Subtract equation 2 from equation 3

6x + 3y = 240

- x + 3y = 115

5x = 125

x = 125/5

x = $25

Keep the value of x in equation 2 to find the value of y

25 + 3y = 115

3y = 115 - 25

3y = 90

y = 90/3

y = $30

Hence, the altering cost of each is $25 and $30.

Learn more about equation -

https://brainly.com/question/2972832

#SPJ4

The complete question is -

A tailor charges set amounts for alterations on dresses and suits. One customer has 2 dresses and 1 suit altered for a total of $80. Another customer has 1 dress and 3 suits altered for a total of $115. How much does it cost to alter each dress?

Answer: -12x + 16

Step-by-step explanation:

To find the difference between (−5x+6) and (7x−10), we need to subtract the second expression from the first. So we have:

(−5x+6) - (7x−10)

To subtract the second expression, we can distribute the negative sign to all the terms inside the parentheses:

-5x + 6 - 7x + 10

Then we can combine the like terms:

-12x + 16

Therefore, the difference between (−5x+6) and (7x−10) is -12x + 16.

The derivative of the given function is:

y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴

Find the derivative?

To find the derivative of the given function y= (4x² – 9x) e⁻⁴, we need to use the product rule of differentiation. The formula for the product rule is:

(fg)' = f'g + fg'

Where f and g are two differentiable functions. Applying this formula, we get:

y' = (4x² – 9x)' e⁻⁴ + (4x² – 9x) (e⁻⁴)'

The first term on the right-hand side can be simplified using the power rule and the constant multiple rule of differentiation:

(4x² – 9x)' = 8x – 9

The second term on the right-hand side requires the chain rule of differentiation. Let u = -4x, then we have:

(e⁻⁴)' = (e^u)' = e^u (-4) = -4e⁻⁴x

Substituting these results back into the expression for y', we get:

y' = (8x – 9) e⁻⁴ + (4x² – 9x) (-4e⁻⁴x)

Simplifying this expression, we get:

y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴

Therefore, the derivative of the given function is:

y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴

Learn more about chain rule of differentiation.

brainly.com/question/27072366

#SPJ11

The base of her ladder should be 12 feet from the house.

A Pythagorean theorem is a useful theorem which can be applied so as to determine the length of the missing side of a right angled triangle. It states that:

/Hyp/^2 = /Adj/^2 + /Opp/^2

So that from the information given in the question, let the distance from the base of her ladder and the house be represented by x;

/Hyp/^2 = /Adj/^2 + /Opp/^2

20^2 = x ^2 + 16^2

400 = x^2 + 256

x^2 = 400 - 256

      = 144

x = 144^1/2

  = 12

x = 12 feet

Thus, Allison should place the base of her ladder 12 feet to the house.

Learn more about Pythagorean theorem at https://brainly.com/question/15249087

#SPJ1

A reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.

Since the spinner has 8 congruent sections and is spun 24 times, we can use probability to make a reasonable prediction for the number of times it will land on the number 3.

1. Calculate the probability of landing on the number 3 for a single spin:
Since there are 8 congruent sections, the probability of landing on the number 3 is 1/8.

2. Determine the expected number of times the spinner will land on the number 3:
To do this, multiply the probability of landing on the number 3 (1/8) by the total number of spins (24).
Expected number of times = (1/8) * 24

3. Simplify the expression:
Expected number of times = 3

So, a reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.

Learn more about probability,

https://brainly.com/question/24756209

#SPJ11

Answer:

Therefore, the product of 23.5 and 2.3 is 54.05.

Step-by-step explanation:

To determine the product of 23.5 and 2.3, we can use the following steps:

Align the numbers vertically with the ones digit of the second factor (2.3) under the tenths digit of the first factor (3 in 23.5).

   23.5

 x 2.3

 -----

Multiply the ones digit of the second factor by the first factor and write the result below, shifted one place to the right.

   23.5

 x 2.3

 -----

    71

Multiply the tenths digit of the second factor by the first factor and write the result below, shifted two places to the right.

   23.5

 x 2.3

 -----

    71

   470

Add the two partial products together.

   23.5

 x 2.3

 -----

    71

   470

 -----

   54.05

Therefore, the product of 23.5 and 2.3 is 54.05.

Answer: 344cm²

Step-by-step explanation:

7x7=49

49x5=245

3x2=6

49-6=43

245+43=288

5x2=10 10x2=20

5x3=15 15x2=30

288+30+20+6=344

The correct arrangement of problem is explained below and their solution are as follows:

(1) Zaira will arrive at her grandmother's house at 9:00 am.

(2) The total distance covered by bus is 207.5 km.

(3) The average-speed of the train was 28 km/h.

Part (1) : The Problem is : Zaira goes to her grandmother's house. If she leaves home at 6:00 in the morning, she cycles 30 km at a steady speed of 10 km. What time will she arrive?

Solution:

Zaira cycles at a steady speed of 10 km, she will cover the distance of 30 km in 30/10 = 3 hours.

So, she will arrive at her grandmother's house at 6:00 + 3:00 = 9:00 am.

Part (2) : Problem : A bus had an average speed of 65 kph for 1.5 hours in the morning. It had average speed of 55 kph for 2 hours in afternoon. What was total distance covered by bus?

Solution:

The distance covered by the bus in the morning can be calculated as:

Distance = Speed × Time = 65 kph × 1.5 hours = 97.5 km,

The distance covered in the afternoon can be calculated as:

Distance = Speed × Time = 55 kph × 2 hours = 110 km

So, total-distance covered by bus is = 97.5 km + 110 km = 207.5 km.

Part (3) : Problem : A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. The distance between the two stations is 14 km. What was  average speed of train?

Solution:

The time taken by the train to cover the distance of 14 km can be calculated as:

Time = Arrival Time - Departure Time = 9:30 am - 9:00 am = 0.5 hours

The average speed of the train = Distance/Time = 14 km/0.5 hours = 28 km/h;

Therefore, the average speed of the train was 28 km/h.

Learn more about Speed here

https://brainly.com/question/25422377

#SPJ4

The given question is incomplete, the complete question is

Directions: Arrange the sentences in the box to form a problem. Then solve each problem.

(1) If she leaves home at 6:00 in the morning

What time will she arrive?

Zaira goes to her grandmother's house

She cycles 30 km at a steady speed of 10 km

(2) I had an average speed of 55 kph for 2 hours in the afternoon

What was the total distance covered by the bus

A bus had an average speed of 65 kph for 1. 5 hours in the morning.

(3) What was the average speed of the train?

The distance between the two stations is 14 km

A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. ​

V = ∫2πx f(y) dy volume of the solid

a. The integral of dz is simply z + C, where C is the constant of integration. So the result of integrating dz is:

∫ dz = z + C

b. To find the integral of (C^2 + I∫sin(x))/(1+cos(x)) dx, we can use the substitution u = 1 + cos(x), du/dx = -sin(x), and dx = du/(-sin(x)). Then we have:

∫(C^2 + I∫sin(x))/(1+cos(x)) dx = ∫(C^2 + I∫sin(x))/u (-du/sin(x))
= -I∫(C^2 + I∫sin(x))/u du
= -I(C^2ln|u| + I∫ln|u| sin(x) dx) + C'
= -I(C^2ln|1+cos(x)| - I∫ln|1+cos(x)| sin(x) dx) + C'

where C' is the constant of integration.

c. To find the volume of the solid obtained by rotating the shaded region about the x-axis or the y-axis, we need to use the method of cylindrical shells or disks, respectively.

If we rotate the region about the x-axis, we can use the formula:

V = ∫2πy f(x) dx

where f(x) is the distance from the x-axis to the function y(x) that defines the region. If we have a function y(x) = g(x) - h(x) that defines the region between two curves, then f(x) = g(x) - h(x) and the limits of integration are the x-values where the two curves intersect.

If we rotate the region about the y-axis, we can use the formula:

V = ∫2πx f(y) dy

where f(y) is the distance from the y-axis to the function x(y) that defines the region. If we have a function x(y) = g(y) - h(y) that defines the region between two curves, then f(y) = g(y) - h(y) and the limits of integration are the y-values where the two curves intersect.

To learn more about function click here

brainly.com/question/12431044

#SPJ11

Answer:

2 7/24 gallons

(sorry if its wrong)

The limiting frictional force depends only on:

The equation of the two straight lines through the origin making an angle of 45° with the line px + qy + r = 0 is (p²-q)(x² - y²) + 4pqxy = 0.

To prove that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0, we can use the concept of slopes and trigonometric identities.

Let's consider the line px + qy + r = 0. The slope of this line is given by -p/q.

Now, the lines making an angle of 45° with this line will have slopes equal to tan(45°), which is 1.

Using the formula for the tangent of the sum of angles, we have:

tan(45°) = (m - (-p/q))/(1 + m(-p/q)), where m represents the slope of one of the lines.

Simplifying the equation, we get:

1 = (mq + p)/(q - mp)

Cross-multiplying and rearranging the terms, we obtain:

(p² - q)(m² - 1) + 2pqm = 0

Since these lines pass through the origin (0,0), we can replace m with y/x. Substituting y/x for m in the equation above, we get:

(p² - q)(x² - y²) + 2pqxy = 0

Further simplifying the equation, we arrive at:

(p² - q)(x² - y²) + 4pqxy = 0

Hence, we have proven that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0.

Learn more about origin

brainly.com/question/28490920

#SPJ11

Part A: The mean of the data is approximately 5.79. Part B: The median is 6.5. Part C: The mode of the data is the set of values {5, 9}.

In statistics, mean is a measure of central tendency that represents the average of a set of numbers. The mean is calculated by adding up all the values in a data set and dividing by the total number of values.

The formula for calculating the mean of a set of n numbers is:

mean = (x1 + x2 + ... + xn) / n

where x1, x2, ..., xn are the individual values in the data set.

Part A:

To find the mean of the data, we need to add up all the values and divide by the total number of values:

3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 9 = 81

There are 14 values in the data set, so we divide the sum by 14 to get:

81/14 ≈ 5.79

Therefore, the mean of the data is approximately 5.79.

Part B:

To find the median of the data, we need to arrange the values in order from lowest to highest:

3, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9, 9

There are 14 values, so the median is the middle value. Since there is an even number of values, we need to find the average of the two middle values, which are 6 and 7. Thus, the median is:

(6 + 7)/2 = 6.5

Therefore, the median of the data is 6.5.

Part C:

To find the mode of the data, we need to look for the value(s) that occur most frequently. From the stem plot, we can see that the values 5 and 9 occur three times each, while all other values occur either once or twice. Therefore, the mode of the data is:

5 and 9

Thus, the mode of the data is the set of values {5, 9}.

To know more about mode visit:

https://brainly.com/question/27827306

#SPJ1

Answer: 8

Step-by-step explanation:

CF looks like the radius of the circle.

ED looks like the diameter.

.: ED = 2 x CF = 2 x 4 = 8

.: ED = 8

Answer:

The length of ED, or the diameter, is 8

Step-by-step explanation:

As the other person explained, CF is the radius, as the radius is from the centermost point to the edge.  I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point.  Therefore, since the diameter is double the radius, we can solve this with the following equation:

2 * r = d, where r is radius and d is diameter.

2 * 4 = d

8 = d

The statements is true of this categorical proposition is: It is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p option A.

A proposition or statement that is categorically affirmed or denied of all or part of the topic is known as a categorical proposition in syllogistic or classical logic. Hence, there are four fundamental types of categorical propositions: "Every S is P," "No S is P," "Some S is P," and "Some S is not P."

Every man is mortal, for instance, is an A-proposition since these forms are denoted by the letters A, E, I, and O, respectively. In particular, being declarations of reality rather than logical connections, they contrast significantly with hypothetical propositions, such as "If every man is mortal, then Socrates is mortal," which categorical propositions are to be differentiated from and enter into as integral words.

Learn more about categorical proposition:

https://brainly.com/question/30874385

#SPJ4

The simplest radical form of the given expression (∛(8x⁴y⁵))² is 4x²y³∛(x²y). So, correct option is A.

To simplify the expression (∛(8x⁴y⁵))², we can first simplify the cube root of 8x⁴y⁵. Since 8 is equal to 2³, and we have three factors of x and five factors of y, we can simplify the cube root as 2[tex]x^{(4/3)}y^{(5/3)[/tex].

Substituting this into the original expression, we get:

(2[tex]x^{(4/3)}y^{(5/3)[/tex])²

Squaring each term inside the parentheses, we get:

4[tex]x^{(8/3)[/tex][tex]y^{(10/3)[/tex]

To express this in radical form, we can rewrite [tex]x^{(8/3)[/tex] and [tex]y^{(10/3)[/tex] as cube roots:

4∛(x²)⁴ ∛(y³)³

Simplifying the cube roots, we get:

4x²y³∛(x²y)

So, correct option is A.

To learn more about radical form click on,

https://brainly.com/question/30949226

#SPJ1

There are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.  When the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.

To answer this question, we need to use the normal distribution formula.

a. To find how many units to the right of 1000 is 1009, we need to calculate the z-score:

z = (X - μ) / σ

where X = 1009, μ = 1000, and σ = 25.

z = (1009 - 1000) / 25 = 0.36

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.36 or higher is 0.3520.

To convert this probability to units to the right of the mean, we subtract it from 0.5 (which represents the area to the left of the mean):

units to the right = 0.5 - 0.3520 = 0.1480

Therefore, there are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.

b. To find the X value that is 2.6 units to the left of the mean, we can rearrange the formula:

X = μ - zσ

where z = -2.6 (since we want units to the left of the mean) and μ and σ are the same as before.

X = 1000 - (-2.6) * 25 = 1065

Therefore, when the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.

To know more about standard deviations refer here:

https://brainly.com/question/23907081

#SPJ11

Using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions, one on the left side and one on the right side, which are connected by an equals sign (=). Equations are fundamental to mathematics, and are used to solve many problems. In addition, equations can also be used to describe physical laws, such as Newton's law of gravity.

10 + 2(20) + 3(30) + 4(100)

= 10 + 40 + 90 + 400

= 540 mmHg

The linear model suggests that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg. This can be seen by using the linear equation 10 + 2x + 3x + 4x. Here, the first coefficient of 10 represents the change in blood pressure for a 10 mg dose, the second coefficient of 2 represents the change in blood pressure for each additional 10 mg dose, the third coefficient of 3 represents the change in blood pressure for each additional 20 mg dose, and the fourth coefficient of 4 represents the change in blood pressure for each additional 30 mg dose.

For example, if the patient was given a 40 mg dose, the equation would be 10 + 2(20) + 3(30), which would yield a change in blood pressure of 140 mmHg. Similarly, if the patient was given a 50 mg dose, the equation would be 10 + 2(20) + 3(30) + 4(10), which would yield a change in blood pressure of 190 mmHg.

Therefore, using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.

To know more about equation click-

http://brainly.com/question/2972832

#SPJ1

The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.

A mathematical statement that expresses the equality of two expressions is known as an equation. It comprises of two expressions that are joined together by the equals sign (=), one on the left side and one on the right. Equations are essential to mathematics and are frequently used to resolve issues. Moreover, equations can be utilised to explain natural laws like Newton's law of gravity.

10 + 2(20) + 3(30) + 4(100)

= 10 + 40 + 90 + 400

= 540 mmHg

The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.

Using the linear equation 10 + 2x + 3x + 4x, this may be observed. In this case, the first coefficient of 10 denotes the change in blood pressure for a dose of 10 mg, the second coefficient of 2, the change for each additional dose of 10 mg, the third coefficient of 3, the change for each additional dose of 20 mg, and the fourth coefficient, the change for each additional dose of 30 mg.

For instance, if the patient received a dose of 40 mg, the equation would be 10 + 2(20) + 3(30), resulting in a 140 mmHg change in blood pressure. The calculation would be 10 + 2(20) + 3(30) + 4(10) if the patient received a 50 mg dose, which would result in a 190 mmHg change in blood pressure.

As a result, we can infer from the linear model that a 100 mg dose of the experimental medication would result in a 540 mmHg change in the patient's blood pressure.

To know more about equation, click-

brainly.com/question/2972832

#SPJ9

The total area of the given figure is 12 units²

In the given figure, we have 3 shapes. One is rectangle and the other two are triangles. We can find areas of all three shapes and add to find the total area.

Finding area of the triangle ABC,

base of the triangle ABC = 4 units

height of the triangle ABC = 4 units

Area of the triangle ABC = 1/2 x base x height = 1/2 x 4 x 4 = 8 units²

Finding area of the triangle CDE,

base of the triangle CDE = 2 units

height of the triangle CDE = 2 units

Area of the triangle CDE = 1/2 x base x height = 1/2 x 2 x 2 = 2 units²

Finding area of the rectangle,

length of the rectangle = 2 units

breadth of the rectangle = 1 unit

Area of the rectangle = length x breadth = 2 x 1 = 2 units²

So, total area of the given figure = 8 units² + 2 units² + 2 units² = 12 units²

To know more about area,

https://brainly.com/question/21735282

#SPJ1

Among rectangles, rhombuses, and squares, all three of these shapes are parallelograms that have specific properties.

A rectangle is a parallelogram with four right angles. Its opposite sides are equal and parallel, and it has diagonals that are equal in length and bisect each other.

A rhombus, on the other hand, is a parallelogram with all four sides being equal in length. Like a rectangle, its opposite sides are parallel, but it does not necessarily have right angles. The diagonals of a rhombus are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other into two equal parts.

Finally, a square is a special type of parallelogram that combines the properties of both rectangles and rhombuses. It has four equal sides and four right angles, making it a unique shape. The diagonals of a square are equal in length, bisect each other, and are also perpendicular bisectors.

In conclusion, rectangles, rhombuses, and squares are all parallelograms with distinct properties. Rectangles have right angles and equal opposite sides, rhombuses have equal sides and diagonals that are perpendicular bisectors, and squares possess all the properties of both rectangles and rhombuses.

To know more about parallelograms, refer to the link below:

https://brainly.com/question/22598125#

#SPJ11

48 pound mass will stretch the spring approximately 12.31 inches.

If the spring's force is directly proportional to how far it is stretched, we can express this relationship mathematically as follows:

F = kx

Where

We can use the first value of the spring scale to determine k:

39 = k(10)

k = 3.9

Now, using this value of k, we can calculate how far the spring is stretched when a 48-pound mass is applied:

F = kx

48 = 3.9x

x = 48/3.9

x = 12.31

Therefore, a 48 pound mass will stretch the spring approximately 12.31 inches.

Learn more about Hooke's Law here : brainly.com/question/14477435

#SPJ4

Answer:

  x = 3  or  x = 12

Step-by-step explanation:

You want the possible values of x that make it true that ...

  (x +1)²/(x -2) = 16 +(x -3)/(x -2)

The given division expression can be written in terms of quotient and remainder as  ...

  p/q = a +r/q   ⇒   p = aq +r

Here, this means ...

  (x +1)² = 16(x -2) +(x -3)

  x² +2x +1 = 16x -32 +x -3

  x² -15x = -36

  x² -15x +56.25 = 20.25 . . . . . complete the square

  (x -7.5)² = 4.5²

  x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5

  x = 3 or 12

__

Additional comment

The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).