The total price of a shirt and a cap is $12. If the price of the shirt was doubled and the price of the cap was three times its original price, the total price of a shirt and a cap would be $26. The following system of equations models this scenario:

x + y = 12
2x + 3y = 26

What is the price of each shirt and cap?

1 The price of a shirt is $7, and the price of a cap is $5.
2 The price of a shirt is $8, and the price of a cap is $4.
3 The price of a shirt is $9, and the price of a cap is $3.
4 The price of a shirt is $10, and the price of a cap is $2.

Gretchen's final score, out of 10, is 8.35 based on weighted averages of scores in four categories.

To calculate Gretchen's final score, we need to calculate the weighted average of her scores in each category.

The weight of each category is given, so we can calculate the weighted score for each category by multiplying the weight by the score.

For Taste, the weighted score is 0.30 * 8.6 = 2.58

For Presentation, the weighted score is 0.35 * 9.8 = 3.43

For Use of Ingredients, the weighted score is 0.25 * 7.7 = 1.93

For Practicality, the weighted score is 0.10 * 4.1 = 0.41

To find the final score, we add up the weighted scores for all categories:

2.58 + 3.43 + 1.93 + 0.41 = 8.35

Therefore, Gretchen's final score is 8.35 out of 10.

The question is incomplete, below is the complete question given -

Gretchen is a celebrity chef competing in a celebrity cooking competition. Contestants receive ratings ranging from 1 to 10, with 10 being the highest. There are four categories, each with its own weighting. The judges' scores were added together, and the results are presented in the table below. What is Gretchen's final score, out of 10? Do not round.

Table -
Category                   Weight      Score

Taste                             30%          8.6

Presentation                 35%          9.8

Use of Ingredients       25%           7.7

Practicality                    10%            4.1

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The function f(x) = 3x² - 3x has absolute extrema at (-1, -5/2)

To find the absolute extrema of the function f(x) = x³ - 3/2x² on the closed interval [-1, 2], we need to first find the critical points of the function in the interval and evaluate the function at those points as well as at the endpoints of the interval.

To find the critical points, we need to find where the derivative of the function is equal to zero or does not exist. The derivative of f(x) is:

f'(x) = 3x² - 3x

Setting f'(x) = 0, we get:

3x² - 3x = 0

3x(x - 1) = 0

x = 0 or x = 1

We also need to check if there are any values of x where the derivative does not exist. However, since the derivative is a polynomial function, it exists for all real values of x.

The absolute extrema is at (-1, -5/2)

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The angle of elevation is the angle between the horizontal line of sight and an upward direction to an object or point.

The angle of elevation is often used in trigonometry and geometry to solve problems involving distances and heights.

1) Cos x = 16/27

x = Cos-1(16/27)

= 54 degrees

2)Sin x = 4/19

x = Sin-1(4/19)

x = 12 degrees

3) Tan 34 = x/8

x = 8 Tan 34

= 5 feet

4) Tan 61 = 166/5.5 + x

1.8(5.5 + x) = 166

9.9 + 1.8x = 166

x = 87 feet

Height of the statue = 5.5 + 87 = 92.5 feet

5) Tan 46 = x/35

x = 35tan 46

x = 36 feet

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At a rate οf 160 cm per minute, the surface area is changing.

A twο-dimensiοnal figure's area is the amοunt οf space it takes up. In οther terms, it is the amοunt that cοunts the number οf unit squares that span a clοsed figure's surface.

One can calculate a shape's area by cοmparing it tο squares οf a specific size. The Internatiοnal System οf Units' standard unit οf area is the square metre (abbreviated as m2), which measures the surface area οf a square with sides that are οne metre lοng (SI).

Surface Area οf Sphere (S)= 4πr²-------(1)]

Given: dr/dt =  2 cm/minute, r= 10 cm

Differentiating bοth sides with respect tο 't', we get

dS/dt = 4π * 2*r*  dr/dt

dS/dt = 4π * 2*10*  2 =  160π   cm/minute

The surface area is changing at the rate οf   160π   cm/minute

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Answer:

a is true

x=72

Step-by-step explanation:

4/6 doesnt make sense. where did they get the denominator 6 from, it wasnt in the problem

b is false

Answer:The probability that a shopper buys shoes and a book is 0.015

Step-by-step explanation:

An equation for a circle with centre (-15, 3√7) and an area of 2π in standard form is (x + 15)² + (y - 3√7)² = 2.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

For the radius, we have:

Area of a circle = πr²

2π = πr²

r = √2

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-15))² + (y - 3√7)² = (√2)²

(x + 15)² + (y - 3√7)² = 2.

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This is a binomial distribution problem with the following parameters:

We want to find the probability that at least 20 characters are numbers. We can use the complement rule and find the probability that fewer than 20 characters are numbers, and subtract that from 1:

P(at least 20 numbers) = 1 - P(fewer than 20 numbers)

Using the binomial probability formula, we have:

P(fewer than 20 numbers) = Σ[k=0 to 19] C(n,k) * p^k * q^(n-k)

where C(n,k) is the binomial coefficient "n choose k". This can be calculated using a calculator or software that has a binomial probability function. For example, in Python, we can use the scipy.stats.binom.cdf() function:

from scipy.stats import binom

n = 32

p = 5/8

q = 3/8

prob_fewer_than_20 = binom.cdf(19, n, p)

This gives prob_fewer_than_20 = 0.04903110366420758.

Therefore,

P(at least 20 numbers) = 1 - 0.04903110366420758 = 0.9509688963357924

Rounding to three decimal places, the answer is 0.951.

The area of the sector OPR is approximately 5.20 cm².

What is an area?

First, we need to find the length of PR. Since O is the center of the circle, we know that OP and OR are both 6 cm long (the radius of the circle). By the triangle inequality, we have:

PR < OP + OR = 6 + 6 = 12

Since QR = 14, we have:

PR > QR - OP - OR = 14 - 6 - 6 = 2

Therefore, 2 cm < PR < 12 cm.

Next, we can use the formula for the area of a sector of a circle:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.

To find the central angle θ, we can use the law of cosines:

(PR)² = (OP)² + (OR)² - 2(OP)(OR)cos(θ)

Substituting in the known values, we get:

(PR)² = 6² + 6² - 2(6)(6)cos(θ)

(PR)² = 72 - 72cos(θ)

cos(θ) = (72 - (PR)²)/72

Using the known values, we have:

cos(θ) = (72 - (PR)²)/72 = (72 - x²)/72

where x is the length of PR.

Since OPQ is a triangle, we know its area:

25 = (1/2) base × height

25 = (1/2) QR × OP

25 = (1/2) (14) × 6

25 = 42

Therefore, the height of triangle OPQ is:

height = (2)(25)/QR = (2)(25)/14 = 25/7

The height of the triangle is also the distance from O to the line PQ, which is also the distance from O to the chord PR. Therefore, the area of sector OPR can be calculated as follows:

A = (θ/360)πr² = (θ/360)π(6)²

A = (θ/360)(36π) = (θ/10)π

where θ is the central angle of the sector in degrees. To find θ, we can use the formula:

sin(θ/2) = (PR/2)/r = x/6

Substituting in the known values, we get:

sin(θ/2) = x/6

θ/2 = [tex]sin^{-1}[/tex](x/6)

θ = 2[tex]sin^{-1}[/tex](x/6)

Finally, substituting this value of θ into the formula for the area of the sector, we get:

A = (θ/10)π = [2[tex]sin^{-1}[/tex](x/6)]/10 * π

To find the value of x that gives the area of the sector, we can use trial and error or a numerical solver. Using a calculator, we find that x ≈ 5.5 cm gives an area of the sector of:

A ≈ 5.20 cm²

Therefore, the area of the sector OPR is approximately 5.20 cm².

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Answer:

awnser is 288 seriously  15 x 12 = 180

and 9 x12 =108 add together is 288

If cοs θ equals negative 5 square rοοt 29 οver 29 and θ is in quadrant 2  sin(θ) = οppοsite/hypοtenuse = 2√21/29.

The links between triangles' sides and angles are studied in the mathematic discipline knοwn as trigοnοmetry.

We knοw that cοsine is negative in quadrant 2, sο we can draw a triangle in quadrant 2 where the adjacent side is negative and the hypοtenuse is pοsitive. Let's call the οppοsite side οf the triangle "a", the adjacent side "b", and the hypοtenuse "c".

Using the Pythagοrean theοrem, we can find the length οf the third side οf the triangle:

c² = a² + b²

29² = a² + (-5√29)²

29² = a² + 725

a² = 29² - 725

a² = 84

a = √84 = 2√21

Nοw that we knοw the lengths οf the οppοsite and adjacent sides οf the triangle, we can use the definitiοn οf sine:

sin(θ) = οppοsite/hypοtenuse = 2√21/29

Therefοre,  sin(θ) equals 2√21/29.

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Complete Question:

Given that cos(θ)=−5√29/29, and θ is in Quadrant II, what is sin(θ)? Give your answer as an exact fraction with a radical, if necessary.

According to the table, the complete sentence would be: 96 students chose art as their favorite subject.

To complete the sentences correctly we must read the information and analyze the table. Once we have done these procedures we can establish how many students chose each of the subjects as their favorite. According to the above, the sentence would be as follows:

96 students chose art as their favorite subject.

According to Riley's survey, 12 out of 53 students chose art as their favorite. We then divide the total number of students (424) by the sample size (53) and multiply the number of students who chose art in the sample by the result of the division.

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* The probability that Ahmad has to stop at both P and Q is: 7/40

* The probability that Ahmad has to stop at least once is: 27/50

* The probability that Ahmad would have stopped at P if he stops at Q is 7/13.

What is probability ?

The study of randomness or experiments falls within the canopy of the mathematical discipline of probability. When represented as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certain event, it is the gauge of the probability or chance that an event will occur. When making predictions based on a statistical study of the data at hand, probability is employed to characterise uncertain events. To aid in decision-making and risk assessment, it is utilised in a variety of disciplines, including science, architecture, finance, finance, and social sciences. Concepts like likelihood function, random variables, and anticipated values are all part of the study of probability.

given

We multiply the chances of stopping at P and Q assuming that he has already stopped at P to determine the likelihood that he must stop at both locations:

Stop at P Equals P(Stop at P and Q) P(Stop at Q | Stop at P)=7/20*7/10

= 49/200

P(Stop at least once) = 1 - P(Not stop at P) * P(Not stop at Q | Not stop at P) = 1 - (13/20) * P(Not stop at Q | Not stop at P) (2/5)\s= 37/50

The chance that he likewise stopped at P must be determined if he had stopped at Q.

Stopping at P and Q equals P(Stop at P and Q) / P(Stop at Q) = (7/20 * 7/10) / (7/20) = 7/10.

Hence, the likelihood that he would have stopped at P is 7/10 if he must stop at Q.

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The answer of the given question based on inequality is (1) D , (2) B . (3) A , (4) C

A number line is a visual representation of the real numbers in a linear format. It is a straight line that is divided into equal segments or intervals, each of which represents a specific value on the number scale.

Number lines are usually oriented horizontally, with negative numbers to the left of zero and positive numbers to the right of zero. The distance between each point on the line is usually consistent, which means that the scale is evenly spaced.

For the first inequality, 7x/9 > -14/3, we can start by multiplying both sides by 9 to eliminate the fraction:

7x > -42

x > -6

So the solution to this inequality is x > -6, which means that all values of x greater than -6 satisfy the inequality.

For the second inequality, -75x/4 > 225/2, we can start by multiplying both sides by -4 to eliminate the fraction and flip the inequality:

75x < -450

x < -6

However, we need to remember to flip the inequality back since we multiplied both sides by a negative number:

x > 6

So the solution to this inequality is x > 6, which means that all values of x greater than 6 satisfy the inequality.

For the third inequality, x/4 <= -3/2, we can start by multiplying both sides by 4 to eliminate the fraction:

x <= -6

So the solution to this inequality is x <= -6, which means that all values of x less than or equal to -6 satisfy the inequality.

For the fourth inequality, 2x/3 > -16/3, we can start by multiplying both sides by 3 to eliminate the fraction:

2x > -16

x > -8

So the solution to this inequality is x > -8, which means that all values of x greater than -8 satisfy the inequality.

Now, let's match each inequality to the number line that represents its solution:

The first inequality, 7x/9 > -14/3, corresponds to the number line with an open circle at -6 and an arrow pointing to the right, indicating that all values of x greater than -6 satisfy the inequality.

The second inequality, -75x/4 > 225/2, corresponds to the number line with an open circle at 6 and an arrow pointing to the left, indicating that all values of x less than 6 satisfy the inequality.

The third inequality, x/4 <= -3/2, corresponds to the number line with a closed circle at -6 and an arrow pointing to the left, indicating that all values of x less than or equal to -6 satisfy the inequality.

The fourth inequality, 2x/3 > -16/3, corresponds to the number line with an open circle at -8 and an arrow pointing to the right, indicating that all values of x greater than -8 satisfy the inequality.

So the correct pairs are:

7x/9 > -14/3: ( )-------------●--->

-75x/4 > 225/2: <---●-------------( )

x/4 <= -3/2: [ ●]--------------<--

2x/3 > -16/3: ( )-------------●--->

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The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).

The frequency distribution statistics method identifies the frequency with which a given value or variety of values exists in a data set. The process is dividing the data into intervals, or "bins," and counting a number of values that fall within every bin.

A graph, such as a statistic or a frequency polygon, can be used to show the frequency distribution. The table displays the categories or intervals as well as the frequency or count for each interval.

The y-axis on the graph represents frequencies, while the x-axis represents intervals. The bars or polygons on the graph reflect the count or % of data within every interval.

given

The totals for each row and column make up the marginal frequencies in the table.

The frequencies for each category in the first variable are represented by the row totals, while the frequencies in the second variable are represented by the column totals.

In order to choose a marginal frequency from the available options:

A. The frequency of 23, which is not a marginal frequency, is in the first row and first column.

B. 46 is not a marginal frequency; it is the frequency in the first row and second column.

The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).

D. A marginal frequency is represented by the frequency in the second row and third column (the column total for the third column).

Options C and D therefore have negligible frequencies.

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No mayfly in the group can live for a full day (24 hours), as the maximum life span is 6 hours.

We can start by calculating the lower and upper limits of the range of possible values for the life spans of the mayflies.

The lower limit can be found by subtracting the MAD from the mean, and the upper limit can be found by adding the MAD to the mean:

Lower limit = mean - MAD = 4 - 2 = 2 Upper limit = mean + MAD = 4 + 2 = 6

Since we know there are 10 mayflies in the group, we can fill in the table below with values between 2 and 6 (inclusive) that add up to 40 (the total number of hours for all 10 mayflies combined):

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The equation is 84= h₀ -16t² and

Solving the equation we get the time taken by the object will be √6 seconds.

What is equation?

An equation is a mathematical statement which is built by two expressions connected by an equal sign ('='). There must be  at least one unknown variable which is to be determined. For example, 3x – 8 = 16 is an equation. Solving this equation, we get  x = 8.

When an object is dropped vertically from a platform, its height after

seconds can be estimated with the formula shown.

ℎ=ℎ₀−16t²

where ℎ is the height of the object in feet.

and ℎ₀ is the initial height of the object in feet.

t is the time in seconds after the drop.

If the object reach the height 84 feet then the equation will be,

                     84= h₀ -16t²

If the initial height is 180 feet then the equation will be

                        84 = 180- 16t²

Solving the equation we get,

                       ⇒ 16t² = 180- 84

                        ⇒ 16t² = 96

                       ⇒ t² = 6

                      ⇒ t= ±√6

As time can't be negative so t= √6

Hence solving the equation we get the time taken by the object will be √6 seconds.

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The population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

A number can be expressed as a fraction of 100 using a percentage. It is represented by the number %.

A decimal or fraction can be multiplied by 100 to become a percentage. For instance, multiplying 0.75 (a decimal) by 100 yields 75% when converted to a percentage. The same can be done to convert 3/4 (a fraction) to a percentage by dividing 3 by 4 to get 0.75, then multiplying that number by 100 to get 75%.

To calculate the population of Medina, Ohio in 7.3 years, we can use the formula:

Population after n years = Population before ×(1 + r/100)²

where r is the annual growth rate and n is the number of years.

Substituting the given values, we get:

Population after 7.3 years = 26,190 × (1 + 3.7/100)^7.3

Population after 7.3 years = 26,190 * 1.037^7.3

Population after 7.3 years = 26,190 * 1.301

Population after 7.3 years = 34,052.9

Rounding to the nearest hundredth, we get:

Population after 7.3 years = 34,052.90 ≈ 34,052.89

Therefore, the population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

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Answer:

The term that completes the sentence is "variance".

Step-by-step explanation:

In statistics, variance is a measure of how spread out a set of numerical data is. It is calculated by finding the average of the sum of the squared differences of each element in the set from the mean of the set. The formula for variance is:

Variance = (Σ(x - μ)²) / n

where Σ is the sum, x is each element in the set, μ is the mean of the set, and n is the number of elements in the set.

Answer:

D

Step-by-step explanation:

The parabola of m(x) is thinner than the parabola of f(x) since 4 times 2 squared is 16 while 2 squared is 4

The answer is (B) 125 1/3×, which is equivalent to (3/125) times approximately 18.048.

Equivalent fractions are fractions that have the same value but are written in different forms. They represent the same portion of a whole or a set, but their numerators and denominators may have different values.To find equivalent fractions, you can multiply or divide both the numerator and denominator of a fraction by the same number. This does not change the value of the fraction, but it changes its form.

The expression is (3/125) times something, but the value of that something is missing.

To solve the problem, we can simplify the expression (3/125) as a fraction in its lowest terms:

(3/125) = (3/5³)

Now, let's look at each of the answer choices:

125

If we multiply (3/5³) by 125, we get:

(3/5^3) * 125 = 3/5

Therefore, 125 is not equivalent to (3/125) times something.

1/3 × 125

If we multiply (3/5³) by (1/3 × 125), we get:

(3/5^3) * (1/3 × 125) = 1/5

Therefore, 1/3 × 125 is not equivalent to (3/125) times something.

125 1/3 ×

If we interpret "125 1/3 ×" as 125 and one-third multiplied by something, then we can write it as a mixed number fraction:

125 1/3 = 376/3

If we multiply (3/5³) by 376/3, we get:

(3/5³) ×(376/3) = 2256/125 = 18.048

Therefore, 125 1/3 × is equivalent to (3/125) times approximately 18.048.

125× 3x

If we interpret "125 3x" as 125 multiplied by 3 times something, then we can write it as:

125 ×3x = 375x

Therefore, 125 3x is not equivalent to (3/125) times something.

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Answer: w = -13

Step-by-step explanation:

    To solve, we will isolate the variable with inverse operations.

Given:

   4 + w = -9

Subtract 4 from both sides of the equation:

   w = -13

ln[(5x)² × (2x)⁻³ × (8x)⁷] . The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.

The base number is the number that is raised to a certain power, the exponent is the power that the base number is raised to, and the logarithmic function is the equation which is used to calculate the result of the base number and the exponent.

The given expression can be written as a logarithm as follows:

ln[(5x)² × (2x)⁻³ × (8x)⁷]

This can be simplified to

2ln(5x) - 3ln(2x) + 7log2(8x)

The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.

The logarithm expression can be used to simplify complex equations and calculations, and it can also be used to solve for a particular variable.

This expression can be used to solve for x if the other values are known. The value of x can be calculated by taking the antilogarithm of each term and then solving the equation.

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Answer:

27 18*3=2*r18/2*3=r9*3=rr=27

Step-by-step explanation:

Option B is the correct option for the total area of the shape which is approximate 8049 ft².

An isosceles triangle is a polygon with three sides, where two of the sides have equal length.

Suppose the equal sides of Isosceles triangle is 'a',

so we can say that by Isosceles triangle rule: 70 = a√2

or side of Isosceles triangle (a) = 35√2 ft         (by Pythagoras theorem)

Area of isosceles triangle (A₁) = [tex]\frac{1}{2}[/tex] × (Side of Isosceles triangle)²

                                                 = [tex]\frac{1}{2}[/tex] × (35√2)² = 1225 ft²

Area of two square (A₂) =  2 × a × a

                                       = 2 × 35√2 × 35√2  = 4900 ft²

Area of quadrant circle (A₃) = (πr²)/4

                                              = 3.14 × (35√2)² × (1/4) = 1923.25 ft²

Total area of the shape = A₁ + A₂ + A₃

                                       = 1225 + 4900 + 1923.25 = 8048.25 ft²

Therefore, the total area of the shape is approximate 8049 ft²

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Therefore, the equation of the circle that passes through the point (2, -5) and has its center at (4,0) is.[tex](x - 4)^2 + y^2= 29[/tex].

A circle is a closed, two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of all points in a plane that are at a given distance (called the radius) from the center point. The circumference of a circle is the distance around its outer boundary, and the diameter is the distance across the center of the circle. Circles have several important properties and are used extensively in mathematics, science, and engineering.

To find the equation of a circle, we need to know the coordinates of its center and its radius. We are given the center of the circle, which is (4,0). To find the radius, we can use the distance formula between the center and the point on the circle (2, -5):

[tex]radius = \sqrt{[(4 - 2)^2 + (0 - (-5))^2]}[/tex]

[tex]= \sqrt{[2^2 + 5^2]}[/tex]

[tex]= \sqrt{29}[/tex]

So the equation of the circle can be written in the standard form as:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is its radius.

Substituting the values we found, we get:

[tex](x - 4)^2 + (y - 0)^2 = (\sqrt{29})^2[/tex]

Simplifying, we get:

[tex](x - 4)^2 + y^2 = 29[/tex]

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Answer:

w = 6 ft.; l = 9 ft.

Step-by-step explanation:

We know that the formula for area of a rectangle is A = lw, where l is the length and w is the width.

Because we're told that the length of the flower bed is 3 ft less than twice its width, we have l = 2w - 3

To find the length and width, can plug in 54 into the equation and substitute our formula for length into the equation.

This gives us 54 = (2w - 3)*w

If we rewrite the equation, we'll see that its quadratic:

[tex]54=(2w-3)w\\54=2w^2-3w\\0=2w^2-3w-54[/tex]

Now, we can first solve for width using the quadratic formula, which yields a positive and negative solution.

(For the sake of the quadratic equation, 0= ax^2 + bx + c is the standard form of quadratic equation and in our equation 2 is a, -3 is b, and -54 is c)

Positive:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)+\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3+\sqrt{441} }{4}\\ \\w=\frac{3+21}{4}\\ \\w=\frac{24}{4}\\\\w=6[/tex]

Negative:

[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)-\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3-\sqrt{441} }{4}\\ \\w=\frac{3-21}{4}\\ \\w=\frac{-18}{4}\\\\w=-4.5[/tex]

We know that we can't have a negative measure, so the width is 6 ft.

Twice the width is 12 (6 * 2) and 3 less than this is 9 (12 - 3), so the length is 9 ft.