If a chain of 30 identical short springs linked end-to-end has a stiffness of 450 N/m, what is the stiffness of one short spring?

Answer:

See answer below

Step-by-step explanation:

the ratio of pv against nrt is called compressibility Z and measures the deviation from an ideal gas behaviour . When Z is plotted against pressure for CH₄ for 0°C and 200°C the curves will differ because there are

- negative deviations ( Z decreases) due to intermolecular forces

- positive deviations (Z increases ) due to molecular size of gas particles

then

- at 0°C the negative deviations prevail  respect to positive deviations at lower pressures ( so Z drops below the horizontal line first ) and then Z increases when pressure increases since the effect of positive deviation is higher ( then Z increases)

- Nevertheless, at 200°C the effect of intermolecular forces is lower and thus the positive deviations always prevail ( thus you observe only Z increasing(

Answer:

The answer to your question is 26

Step-by-step explanation:

Median is the middle number of a list order from lowest to highest.

Process

1.- Order the numbers from lowest to highest

              4   9   17   22   24   28   51   76   83   98

2.- Look for the middle number, if the total number of items is pair, take the 2 middle number and divide by two.

Middle numbers = 24 and 28

Median = (24 ´+ 28) / 2

Median = 52/2

Median = 26

Answer:

Step-by-step explanation:

First the numbers are arranged in ascending order from the least to the biggest number:

4 9 17 22 24 28 51 76 83 98

The numbers on the 5th and 6th position are in the middle

5th= 24

6th = 28

Since they are two numbers, we add them and divide by 2

= (24 + 28) / 2

= 52 / 2

= 26

Answer:

Step-by-step explanation:

∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹

This is a finite geometric series with n = 4, a₁ = -144, and r = ½.

S = a₁ (1 − rⁿ) / (1 − r)

S = -144 (1 − (½)⁴) / (1 − ½)

S = -270

If you wanted to find the infinite sum (n = ∞):

S = a₁ / (1 − r)

S = -144 / (1 − ½)

S = -288

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Answer:

The answer is C (40)

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].

The given coordinate points are (-3, 2) and (2, -8).

Substitute (x₁, y₁) =(-3, 2) and (x₂, y₂)= (2, -8) in the distance formula, we get

Distance = √[(2+3)²+(-8-2)²]

= √[5²+(-10)²]

= √125

= 11.18

≈ 11

The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.

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Answer: Yes, made a mistake by taking out 2 in second step.

Step-by-step explanation:

You have started with 15 sticks= 13+2

So you take 2 which is correct.

Now, your friend takes one 13=12+1, so that leaves 12.

Now 12=8+3+1 since this involves smallest number 1 so you should have taken 1 at this point instead you took two here. So it leaves you with 10. Now, your friend takes one from it i.e. 10=9+1  leaving 9 now. Now 9=8+1, you can still take 1 from it and still be in the game. The point is to take out the smallest number involved. in the sum equal to the number that is left behind.

In Fibonacci nim, you cannot take the same number of sticks as your opponent did on the previous turn. Your next move should be to take 2 sticks, as your opponent took 1 on their last turn. You haven't yet made any mistakes in the game.

In the game of Fibonacci nim, the only rule is that on each turn a player can take one or two sticks, but not the same amount as their opponent took on the previous turn. Let's track your game:

For the next move, you can take either 1 or 2 sticks, but since your friend took 1 on their last turn, you must take 2 to abide by the rules. So, your next move should be to take 2 sticks.

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Final answer:

To find the total number of possible license plates with two letters followed by five digits (with repetition allowed), multiply the number of options for each position: 26 letters and 10 digits result in 67,600,000 different license plates.

Explanation:

The question asks for the total number of license plates that can be produced when the first two symbols are letters from the alphabet and the following five symbols are digits from 0 to 9, with repetition allowed for both letters and digits. To find the number of possible license plates, we use the principle of counting, multiplying the number of choices for each position.

There are 26 possible letters for each of the first two positions (since there are 26 letters in the English alphabet) and 10 possible digits (0-9) for each of the last five positions.

Therefore, the total number of license plates that can be created is calculated as:26 * 26 * 10 * 10 * 10 * 10 * 10. This equals 67,600,000 possible license plates.

This calculation assumes that each symbol (letter or digit) can be repeated, meaning the same letter or digit can be used more than once in the license plate.

Final answer:

The work done against gravity in constructing the rectangular box is 3136000 J.

Explanation:

To calculate the work done against gravity in constructing the rectangular box, we need to first calculate the mass of the box. The density of the lightweight material is given as 800 kg/m³. Since the base of the box is a square with side lengths of 4 m and the height is 5 m, the volume of the box is V = (4 m)(4 m)(5 m) = 80 m³.

The mass of the box can be calculated using the formula mass = density × volume. Therefore, the mass of the box is [tex](800 kg/m^3)(80 m^3) = 64000 kg.[/tex]

The work done against gravity is given by the formula work = mass × gravity × height. Assuming the acceleration due to gravity is approximately 9.8 m/s², the work done against gravity is [tex](64000 kg)(9.8 m/s^2)(5 m) = 3136000 J.[/tex]

Answer:

  8/3 = 2 2/3

Step-by-step explanation:

(2/7)y + (3 1/7)y = (3 3/7)y = (24/7)y

For y=7/9, this is ...

  (24/7)(7/9) = 24/9 = 8/3

The value of the expression for y=7/9 is 8/3.

The points in the diagram are neither collinear (lying on the same line) nor coplanar (lying on the same plane) as some points are not in alignment or on the same level.

The correct answer is option C.

Collinearity and coplanarity are geometric concepts used to describe the relative positions of points in space. To clarify, collinear points lie on the same straight line, while coplanar points lie on the same flat plane.

In your specific scenario, it is evident that the points under consideration do not satisfy the criteria for either collinearity or coplanarity. Here's an expanded explanation:

Collinearity:

Collinear points are points that can be connected by a single straight line. In simpler terms, if you can draw a straight line that passes through all the points without lifting your pen, those points are collinear. However, based on the provided diagram and description, it is clear that not all the points can be connected in this way. Some points are positioned in such a manner that a single straight line cannot pass through all of them.

Coplanarity:

Coplanar points are points that lie within the same flat plane. If you can imagine a flat surface that contains all the points, those points are coplanar. In the given scenario, it is apparent that the points are not all situated within the same plane. Some points are at different heights or elevations compared to others, indicating that they do not lie within a common flat plane.

In conclusion, the points in the diagram do not meet the conditions for either collinearity or coplanarity. They cannot be connected by a single straight line, nor do they all reside on the same flat plane.

Therefore, from the given options the correct one is C.

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Answer:  34.57 inches.

Step-by-step explanation:

Given : Diameter of tree's trunk =  11 inches

Then, the length of ribbon needed just to reach around the tree = Circumference of trunk.

We know that the circumference of the circle is given by :-

[tex]C=\pi d[/tex] , where d= diameter

Then, Circumference of trunk. = [tex]\pi (11)[/tex]

Put [tex]\pi=\dfrac{22}{7}[/tex] , we get

Circumference of trunk. = [tex]\dfrac{22}{7}\times(11)\approx34.57\text{ inches}[/tex]

Hence , the length of ribbon needed just to reach around the tree = 34.57 inches.

Answer:

15.6 liters

Step-by-step explanation:

Let the porridge eaten by Papa bear be 'x' liters.

Given:

Mama Bear ate 80% as much porridge as Papa Bear did.

Baby Bear ate as much as Mama Bear did.

Papa Bear ate 1.2 liters more porridge than Mama Bear did

So, porridge eaten by Mama Bear = 80% of 'x' = [tex]0.80x[/tex]

Now, Baby Bear eats same amount as Mama Bear. So,

Porridge eaten by Baby Bear = [tex]0.80x[/tex]

Papa Bear ate 1.2 liters more than Mama Bear.

Framing in equation form, we get:

[tex]x = 1.2 + 0.80x[/tex]

[tex]x-0.80x=1.2[/tex]

[tex]0.20x=1.2[/tex]

[tex]x=\frac{1.2}{0.20}=6\ liters[/tex]

So, Papa Bear ate 6 liters of porridge.

Mama Bear ate = 0.80 × 6 = 4.8 liters

Baby Bear ate = 4.8 liters.

So, total porridge = Papa Bear + Mama Bear + Baby Bear

Total porridge eaten = 6 + 4.8 + 4.8 = 15.6 liters

Answer:

Step-by-step explanation:answer is 20%

Answer:

Step-by-step explanation:

The formula for determining average is expressed as

Average = the total cost of the televisions/ the sum of the televisions

Total number of model A television that was sold is 21

Total cost of 21 televisions = 299 × 21 = $8671

Total number of model B television that was sold is 13

Total cost of 13 televisions = 549 × 13 = $7137

Total number of model C television that was sold is 6

Total cost of 6 televisions = 619 × 6 = $3714

Total number televisions sold is 21 + 13 + 6 = 40

Total cost of the televisions is 8671 + 7137 + 3714 = 19522

Therefore, the average price per TV Sold is

19522/40 = $488.05 per television

Answer:the answer is life

Step-by-step explanation:

well life is life that you need

Answer:

$550 i think

Step-by-step explanation:

Answer:

38.9 square inches.

Step-by-step explanation:

We are asked to find the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees.

We will use area of sector formula to solve our given problem as:

[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where, r represents radius and theta represents central angle.

Let us find area of sector with central angle 140 degree and radius 3 inch.

[tex]\text{Area of sector}=\frac{138}{360}\times \pi (3)^2[/tex]

[tex]\text{Area of sector}=\frac{138}{360}\times 9\pi[/tex]

[tex]\text{Area of sector}=10.83849[/tex]

Now, we will find area of sector with central angle 114 degree and radius 5 inch and multiply by 2 as:

[tex]\text{Area of sector}=2(\frac{114}{360}\times \pi (5)^2)[/tex]

[tex]\text{Area of sector}=2(\frac{114}{360}\times 25\pi)[/tex]

[tex]\text{Area of sector}=\frac{114}{360}\times 50\pi[/tex]

[tex]\text{Area of sector}=49.74188[/tex]

Let us find difference of area as shown below:

[tex]\text{Difference of areas}=49.74188-10.83849[/tex]

[tex]\text{Difference of areas}=38.90339[/tex]

[tex]\text{Difference of areas}\approx 38.9[/tex]

Therefore, the difference in area covered is approximately 38.9 square inches.

Final answer:

Calculate the areas covered by differently sized and angled windshield wipers to find the difference.

Explanation:

Single 3-inch wiper:

Pair of 5-inch wipers:

The difference in area cleaned by the pair of 5-inch wipers compared to the single 3-inch wiper is:

A-diff = A-combined - A-single ≈ 31.50 sq in - 7.07 sq in ≈ 24.43 sq in

Therefore, the pair of 5-inch wipers cleans approximately 24.43 square inches more area than the single 3-inch wiper.

Answer:

  17

Step-by-step explanation:

For n cups, the height of the stack is ...

  4 + (1/4)(n -1)

For a height of 8 inches, we can find n from ...

  8 = 4 +(1/4)(n -1)

  4 = (1/4)(n -1) . . . . . . subtract 4

  16 = n -1 . . . . . . . . . .multiply by 4

  17 = n . . . . . . . . . . . .add 1

There are 17 cups in the stack.

Yo sup??

This question can be solved by just imagining the object formed or practically trying it out.

Therefore the correct answer to this question is option 2 ie

a cylinder with a radius of 1 unit.

Hope this helps.

The figure created is a cone with a height of 2 units and a radius of 1 unit.

Notice that we have a triangle, so if we rotate it around the y-axis, we will get a cone.

Because the rotation is around the y-axis, the height of the cone will be equal to the side AB of the triangle, so the height of the cone is 2 units.

And the radius of the cone is equal to BC, then we can see that the radius measures 1 unit.

Then the figure created is a cone with a height of 2 units and a radius of 1 unit.

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Answer:

[tex]m\angle R=69.4^o[/tex]

Step-by-step explanation:

we know that

In the right triangle PQR

[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)

substitute the given values

[tex]tan(R)=\frac{8}{3}[/tex]

using a calculator

[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]

Answer:

[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]

[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]

The 99% confidence interval would be given by (0.172;0.228)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

If we replace the values given we got:

[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]

[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]

The 99% confidence interval would be given by (0.172;0.228)

The confidence interval for the proportion is CI = 0.20 ± 0.0275.

The formula for calculating the confidence interval for proportion is expressed as:

[tex]CI=p \pm z \cdot \sqrt{\frac{p(1-p)}{n} }[/tex]

where:

Substitute into the formula;

[tex]CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(1-0.2)}{1400} }\\CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(0.8)}{1400} }\\CI = 0.20 \pm 0.0275\\[/tex]

Hence the confidence interval for the proportion is CI = 0.20 ± 0.0275.

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Know the properties of each shape:

A square has all sides of equal length plus all corners are right angles

A rectangle has all right angles, but has two pairs of parallel sides

A parallelogram is a quadrilateral that has two pairs of parallel sides

A rhombus is where all sides are equal length, but no right angles at all

So the best choice given the diagram is C: parallelogram

Hope this helped you to understand better.

Answer:

The answer to your question is letter A

Step-by-step explanation:

Expression

                        - 3x - (x - 1) + 3/2(3x + 3)

1.- Expand

                        - 3x - x + 1 + 3/2(3x) + 3/2(3)

2.- Simplify

                        - 3x - x + 1 + 9/2 x + 9/2

3.- Associate like terms

                      (-3x - x + 9/2x) + (1 + 9/2)

4.- Simplify like terms

                      (-4x + 9/2x) + (2 + 9)/2

                      (-8x + 9x)/2 + 11/2

                                1/2x + 11/2

Where do I share a photo of my work

Answer:

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.

Step-by-step explanation:

Let an exponential growth function is [tex]f(x) = a(b)^{x}[/tex].

Now, [tex]f(1) = a(b)^{1}[/tex], [tex]f(2) = a(b)^{2}[/tex] , [tex]f(3) = a(b)^{3}[/tex] and [tex]f(4) = a(b)^{4}[/tex].

So, the values of the function corresponding to the x-values 1, 2, 3, and 4, are in G.P. and the common ratio of b.

Now, 'a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16' will be the exponential function as the values are in G.P. with common ratio 2. (Answer)

Answer:

its  D

Step-by-step explanation:

just did the assignment

Answer:

C(x) = 175√(x² + 360000) + 528000 - 100x

Step-by-step explanation:

See the attachment below (Line PR = 1mile)

C(x) = Cost of Distance across the river + Cost of Distance along the land

Calculating Distance Across the river:

In triangle OPQ,The distance across the river is represented by line y

Line y is the hypothenus of the triangle

Pythagoras theorem states that:

if one angle of a triangle is 90 degrees, then the square of the length of the hypotenuse - the side opposite the right angle - is equal to the sum of the squares of the lengths of the other two sides.

So,

y² = x² + 600²

y² = x² + 360000

y = √(x² + 360000)

If it costs $175 per foot across the river then It'll cost

175 * √(x² + 360000) to lay cables across the river.

Calculating Distance along the land

Distance along the land is represented by line QR

Line QR = Line PR - PQ.

Where PR = 1 Miles (1 mile = 5280 feet)

So, PR = 5280

Line PQ = x

So, QR = 5280 - x

If it costs $100 per foot along the land,then it'll cost

100 * (5280 - x) to lay cables along the land

= 528000 - 100x

C(x) = 175√(x² + 360000) + 528000 - 100x

Answer: x = 3

Step-by-step explanation:

x^2 = 9

x = [tex]\sqrt{9}[/tex]

x = 3

Another way to think about it:

We think what number can be multiplied by itself to get 9.

since 3*3=9, our answer is 3

Answer:

24

Step-by-step explanation:

Answer:

= 20.83%

Step-by-step explanation:

5/24 * 100

= 20.83%

To find what percent of people did not like the movie when 5 out of every 24 people did not, we calculate 5/24 as a percentage which is approximately 20.83%, rounded to about 21% of the people.

To calculate the percentage of people who did not like the movie, we need to set up a proportion where the number of people who did not like the movie is to the total number of people. Given that 5 out of every 24 people did not like the movie, we can express this as a fraction: 5/24. To find the equivalent percentage, we set up a fraction with 100 as the denominator and cross-multiply:

5/24 = x/100

Now we cross-multiply and solve for x:

24x = 5imes 100

x = (5 imes 100) / 24

x = 500 / 24

x = 20.833...

This equates to approximately 20.83%, which can be rounded to about 21%. Therefore, about 21% of the people did not like the movie.

Answer:

16 women per 1 000

Step-by-step explanation:

The data was likely to be obtained from a survey. The question states how the information was gathered - most probably from questionnaires.

c. A simple model will be 16 women per 1 000 women. Proportion has been taken into account here.

Let 63 correspond with those that are going to get cancer out of 3980. The women have 63/3980 chance of getting cancer.

For 1 000 women that will be 1000/3980 × (63) = 16

Therefore the probability of a person getting cancer is 16 per 1 000 Ans

e. Large samples are essential to ensure that the results are representative of the actual population. In addition, large samples reduce inherent errors from deviations. Furthermore, useless data can be discarded and the remaining data still represent the actual population size. Lastly, large amounts of data are easy to scale up and use to develop models.

The two populations compared in the study were women whose mothers took the drug DES during pregnancy and those whose mothers did not. The data in the study were obtained through an observational study. A descriptive statistic can be used to estimate the number of women with tissue abnormalities out of 1000 in the population of women whose mothers took the drug DES during pregnancy.

a. The two populations in the study were: 1) women whose mothers took the drug DES during pregnancy and 2) women whose mothers did not take the drug.

b. The data in this study were obtained through an observational study, specifically a cohort study. This means that the researchers observed and compared the outcomes between the two groups of women without directly manipulating any variables.

c. A descriptive statistic that could be used to estimate the number of women out of 1000 in the population of women whose mothers took the drug DES during pregnancy and developed tissue abnormalities is:

Number of women with tissue abnormalities in the sample: 63

Descriptive statistic: (63 / 3980) * 1000 = 15.83

Therefore, an estimate is that 15.83 out of 1000 women in this population have tissue abnormalities that might lead to cancer.

d. Since the study only reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities, without providing an exact percentage, it is not possible to estimate the number of women without more specific information.

e. Medical studies often use a relatively large sample size, like 3980, to increase the reliability and representativeness of the findings. A larger sample size helps to reduce the chance of biased or random results and increases the generalizability of the findings to the larger population.

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle

AC represents the hypotenuse of the right angle triangle.

With ∠A as the reference angle,

AB represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine the ratio of Tan A , we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan A = 28/45

Step-by-step explanation:

[tex]m \angle \: WXZ = m \angle \: WYZ \\ ..(angles \: formed \: in \: same \: arc) \\ \therefore \: x \degree = (2x - 54)\degree \\ \therefore \: x = 2x - 54 \\ \therefore \: x - 2x = - 54 \\ \therefore \: - x = - 54 \\ \huge \purple{ \boxed{\therefore \: x = 54}}[/tex]

Answer:

The correct answer is D or 54.

Step-by-step explanation:

Answer:

The answer to your question is it sold 7 cakes.

Step-by-step explanation:

Data

cakes = c = $5

pies = p = $7

total pieces = 15

total sell = $91

Process

1.- Write equations to solve this problem

                  c + p = 15      ------------ l

                5c + 7p = 91    ----------- ll

2.- Solve the system of equations by elimination

Multiply equation I by -5      

               -5c - 5p = -75

                 5c + 7p = 91

                 0   + 2p = 16

Solve for p

                            p = 16/2

                            p = 8

3.- Substitute p in equation l to find c

                 c + 8 = 15

solve for c

                 c = 15 - 8

                 c = 7

4.- Conclusion

It sold 7 cakes and 8 pies.

Answer: 7 cakes were sold.

Step-by-step explanation:

Let x represent the number of cakes that were sold.

Let y represent the number of cakes that were sold.

The cakes are $5 and the pies are $7. The store makes a total of $91. This means that

5x + 7y = 91- - - - - - -- -1

The store sold a total number of 15 goods. This means that

x + y = 15

Substituting x = 15 - y into equation 1, it becomes

5(15 - y) + 7y = 91

75 - 5y + 7y = 91

- 5y + 7y = 91 - 75

2y = 16

x = 16/2 = 8

x = 15 - y = 15 - 8

x = 7

Answer:

The dimensions of the room are length is 16 feet and the width is 11 feet.

Step-by-step explanation:

Given:

The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide.

Now, to get the dimensions.

Let the width be [tex]x.[/tex]

So, the length = [tex]x+5.[/tex]

Area = 176 square foot.

So, we put formula of area to get the dimensions:

Area = length × width.

[tex]176=(x+5)\times x[/tex]

[tex]176=x^2+5x[/tex]

Subtracting boths sides by 176 we get:

[tex]0=x^2+5x-176\\x^2+5x-176=0[/tex]

On solving the equation:

[tex]x^2+16x-11x-176=0\\x(x+16)-11(x+16)=0\\(x+16)(x-11)=0[/tex]

As,

[tex]x+16[/tex] = 0

[tex]x=-16[/tex]

So, we would not take the negative result.

Thus,

[tex]x-11=0\\x=11[/tex]

So, the width = 11 feet.

Now, to get the length by substituting the value of [tex]x[/tex]:

[tex]x+5\\=11+5\\=16[/tex]

The length = 16 feet.

Therefore, the dimensions of the room are length is 16 feet and the width is 11 feet.

The width is 11 feet, and the length is 5 feet longer, making it 16 feet.

To determine the dimensions of the family room, we start by defining the width of the room as w. According to the problem, the length (l) is 5 feet longer than the width, so we can write this as:

l = w + 5

We also know the area of the room is 176 square feet. The area of a rectangle is calculated by multiplying the width and length:

Area = width × length

Therefore, we get the equation:

w × (w + 5) = 176

Expanding this equation gives us:

w² + 5w = 176

We rearrange this into a standard quadratic equation:

w² + 5w - 176 = 0

Now we solve for w using the quadratic formula, w = (-b ± √(b² - 4ac)) / 2a, where:

This gives us:

w = (-5 ± √(25 + 704)) / 2

w = (-5 ± √729) / 2

w = (-5 ± 27) / 2

Which simplifies to:

w = 11 or w = -16

Since width cannot be negative, we have:

w = 11

Then the length l is:

l = 11 + 5 = 16

Therefore, the dimensions of the family room are 11 feet by 16 feet.