Simon bought a pack of butter for baking. The pack has 8 sticks of butter that are each 1/2 of a cup. Simon used 1 1/4 of butter to make brownies , 3/4 cup of butter to make a cake , and 1 1/4 cup of butter to make cookies . how much butter does Simon have left ?

After answering the prοvided questiοn, we can state that Befοre making equatiοn a decisiοn, it is alsο impοrtant tο cοnsider οther factοrs such as the lοcatiοn, facilities, and services prοvided by each health club.

In mathematics, an equatiοn is a prοclamatiοn stating the justice οr twο phrases. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine the value οr values οf the variable in the mοdel) that will allοw the equatiοn tο be true. Equatiοns can be simple οr cοmplex, regular οr nοnlinear, and include οne οr mοre factοrs. In the equatiοn fοr "x² + 2x - 3 = 0," example, the variable x is raised tο the secοnd pοwer. Lines are used in many mathematical areas, including algebra, mathematics, οr geοmetry.

We can create a table tο calculate the tοtal cοsts οver different time periοds tο cοmpare the cοsts οf jοining Let's Get Mοving versus Fitness fοr Life:

Membership Length Let's Get Mοving Fitness fοr Life

1 mοnth                                    $245             $50

6 mοnths                                 $455              $300

1 year                                       $630              $600

2 years                                    $1,290            $1,200

Accοrding tο this table, if Justin plans tο jοin fοr a shοrt periοd οf time, such as a mοnth οr six mοnths, Fitness fοr Life is a better οptiοn because it has a lοwer tοtal cοst. If Justin intends tο jοin fοr a lοnger periοd οf time, such as a year οr twο years, Let's Get Mοving may be a better οptiοn because the οne-time initiatiοn fee is spread οut οver time.

Befοre making a decisiοn, it is alsο impοrtant tο cοnsider οther factοrs such as the lοcatiοn, facilities, and services prοvided by each health club.

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The appropriate trend lines for the scatter plot include the following: B. scatter plot B.

In Mathematics and Statistics, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:

By critically observing the scatter plot using the aforementioned characteristics, we can reasonably infer and logically deduce that scatter plot B represent the line of best fit (trend line) because it is in a linear pattern, with equal number of data points on both sides of the line.

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The actual price of the television set is 9225.6 and the amount of VAT is 1061.35

Discount is a percentage deducted from the the actual selling price of a product. The discount given is 15% of the selling price 9605.

Therefore, discount = 15/100 × 9605

= 1440.75

Therefore the price of the television= 9605 - 1440.75

= 8164.25

After the discount the, VAT of 13 % is added

= 8164.25 × 13/100

= 1061.35

The new price of the television set = 8164.25 + 1061.35

= 9225.6

therefore the actual price of the television set is 9225.6 and the VAT is 1061.35

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To find the fraction of members between 150 and 160 cm tall, we need to look at the portion of the frequency polygon that corresponds to this height range.

First, we can calculate the total frequency of members between 150 and 160 cm by adding up the frequencies for the "150 < x ≤ 160" class and the "160 < x ≤ 170" class, which gives:

Total frequency = 5 + 0 = 5

Next, we can calculate the total frequency of all members by adding up all the frequencies, which gives:

Total frequency = 10 + 5 + 0 + 1 = 16

Therefore, the fraction of members between 150 and 160 cm tall is:

Fraction = Total frequency between 150 and 160 cm / Total frequency of all members

= 5 / 16

= 0.3125

So, approximately 31.25% of the members were between 150 and 160 cm tall.

The fraction of members between 150-160cm is found by dividing the frequency of the 150-160cm height segment by the total number of club members.

In order to find out the fraction of members who were between 150 and 160 cm tall, we first need to focus on the corresponding frequency value for the height segment - 150< x ≤160 in the table. This value gives us the count of people who stand within these heights. Simultaneously, we need the total number of club members, which can be derived by adding all the frequency values together.

Once we have these two values, the fraction of members is calculated by dividing the frequency of the 150-160 height segment by the total frequency (number of club members).

Please note that this fraction will be a 'raw' one, and you may need to simplify it to its smallest terms to make it more understandable.

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a) B', complement of B =  {a, b, d, f, h}

b) AN B', A intersection B' =  {b, h}

c) (A/B), or A - B = {a, b, h}

d) BU (CNA)​, B union (C intersection A) = {a, b, c, d, e, g, h}

a) The complement of B, denoted B', consists of all elements in U that are not in B. Thus, we have:

B' = {a, b, d, f, h}

b) A intersection B' consists of all elements that are in A but not in B. From the given sets, we have:

B' = {a, b, d, f, h}

A = {a, b, c, e, h}

Thus, A intersection B' = {b, h}

c) A/B, also denoted A - B, consists of all elements in A that are not in B. From the given sets, we have:

A = {a, b, c, e, h}

B = {c, e, g}

Thus, A/B = {a, b, h}

d) CNA is the union of C and A. From the given sets, we have:

A = {a, b, c, e, h}

C = {a, c, d, g, e}

Thus, A union C = {a, b, c, d, e, g, h}.

Finally, BU(A union C) is the union of B with A union C. From the given sets, we have:

B = {c, e, g}

A union C = {a, b, c, d, e, g, h}

Thus, BU(A union C) = {a, b, c, d, e, g, h}

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Answer: 625.528.618,26

Step-by-step explanation: The answer will be in the pictures

Using calculus, we can find the functions of the inverse functions as follows:

a. f(x) = x/5.

b. f(x) = ∛ 2x

c. f(x) = x - 10

d. f(x) = 2x/3 - 17

One of the most crucial areas of mathematics that addresses ongoing change is known as calculus. Calculus is primarily built on the two ideas of derivatives and integrals. A function's integral measures the area under its curve, whereas a function's derivative measures its rate of change.

Whereas the integral adds together a function's discrete values over a range of values, the derivative explains the function at a particular point.

Here in the question,

The inverse of the functions is:

f(x) = x/5.

f(x) = ∛ 2x

f(x) = x - 10

f(x) = 2x/3 - 17

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[tex]\tan(68^o )=\cfrac{\stackrel{opposite}{AC}}{\underset{adjacent}{7}}\implies 7\tan(68^o)=AC\implies 17.3\approx AC[/tex]

Make sure your calculator is in Degree mode, as opposed to Gradians or Radians mode.

Quick Clarification:

if your put in your calculator tan(68) in Radians mode, your calculator assumes you meant 68 radians, if in Gradians mode, your calculator assumes you meant 68 Gradians, now, if you have it on Degree mode, your calculator thinks you meant tan(68°).

All trigonometric calculations depend on the mode used, since a circle can be divided in many ways and thus different modes mean, different angles, 68 Radians are extremely different than 68°.

Answer:

what you would do is 23.89x18%=4.3 so you do 23.89-4.3=19.59 then you do 19.59x7%=1.37 then you do 19.59+1.37=20.96 so 20.96 is your answer.

Step-by-step explanation:

Answer: To calculate the final price that Lin's father pays for the meal, we need to apply the discount first and then add the sales tax.

Discount = 18% of $23.89

= 0.18 x $23.89

= $4.30

The discounted price of the meal is therefore:

$23.89 - $4.30 = $19.59

Next, we need to add the sales tax of 7%:

Sales Tax = 7% of $19.59

= 0.07 x $19.59

= $1.37

Therefore, the final price that Lin's father pays for the meal is:

$19.59 + $1.37 = $20.96

So, Lin's father pays $20.96 for the meal after applying the discount and sales tax.

Step-by-step explanation:

Answer:

Step-by-step explanation:

cos

cos^-1(26/52)=?

?=30

The deer made 8 tracks, the fox made 4 tracks, and the dog made 12 tracks.

Let's start by defining variables for the number of tracks made by each animal.

Let:

d be the number of tracks made by the deer,

f be the number of tracks made by the fox, and

x be the number of tracks made by the dog

From the problem, we know that:

d + f + x = 24 ......(1)

We also know that:

d = x - 4   .......(2)

d = f + 4   ..........(3)

from this we can rightfully assume that the dog made half the tracks hence

x = 12 tracks

d = 12 - 4 = 8

solving for f

d = f + 4

f = d - 4 = 8 - 4 = 4

we can therefore say that the dog made 12 tracks, the deer made 8 tracks while the fox made 4 tracks

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o find the local extrema of the polynomial, we first take the derivative of the polynomial and set it equal to zero:

f(x) = 10x^5 + 22x^4 + 20x^3 - 0x^2 + 6

f'(x) = 50x^4 + 88x^3 + 60x^2

Setting f'(x) = 0, we can factor out a 2x^2 from the expression to get:

f'(x) = 2x^2(25x^2 + 44x + 30) = 0

Using the quadratic formula to solve for x, we get:

x = (-44 ± sqrt(44^2 - 4(25)(30))) / (2(25))

x = (-44 ± sqrt(784)) / 50

x = (-44 ± 28) / 50

x = -0.32 or -0.56

Using binomial probability and cumulative distribution function, the probability of having 24 heads is 0.000022

This problem can be solved using the binomial distribution. Let X be the number of heads that occur in 27 tosses of the fair coin. Then X follows a binomial distribution with parameters n = 27 and p = 0.5.

We want to find the probability that at most 24 heads occur, which is equivalent to finding the probability that X is less than or equal to 24. We can use the cumulative distribution function (CDF) of the binomial distribution to calculate this probability:

[tex]P(X \leq 24) = \sum_{k=0}^{24} {27 \choose k} (0.5)^{27}[/tex]

We can use a calculator or software to evaluate this sum, or we can use the complement rule to find the probability of the complement event (i.e., 25 or more heads) and subtract from 1:

[tex]P(X \leq 24) = 1 - P(X \geq 25) = 1 - \sum_{k=25}^{27} {27 \choose k} (0.5)^{27}[/tex]

Using a calculator or software, we find that the probability is approximately 0.000022, which corresponds to answer choice (a).

Therefore, the answer is (a) 0.000022.

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Answer:

The answer is A: 2500 pi

Step-by-step explanation:

To find the volume of a cylinder use the formula:

π[tex]r^{2}h[/tex]

So we know that the diameter is 10, so radius must be 10/2 or 5.

Now we square 5 to get 25.

Multiply 25 times height which is 100.

So 25 x 100 is equal to 2500

Now multiply the pi or just let it stay like that

The answer is 2500π.

Hope this helps!

I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

For any rectangle ABCD the statement;

1. ∠A ≅ ∠D is always true

2. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is sometimes true

A rectangle is a quadrilateral that has two pairs of parallel and congruent opposite sides and four right angles (90 degree angles). A rectangle is a special case of a parallelogram.

1. ∠A ≅ ∠D

The above statement is always true for rectangles. In Euclidean geometry, by the definition of a rectangle, the four interior angles are right angles, which means m∠A = m∠B = m∠C = m∠D = 90°, therefore; ∠A ≅ ∠B ≅ ∠C ≅ ∠D.

The statement; ∠A ≅ ∠D, according to the above expression and the transitive property of congruence, is always true.

Please find attached the drawing of the rectangle, created with MS Word that can be used to illustrate the congruence of the angles with the angle marks indicating perpendicular sides, forming 90° angles, which indicates that the angles are congruent.

   A_____[tex]{}[/tex]_____B

    |            [tex]{}[/tex]          |

    |           [tex]{}[/tex]           |

    |          [tex]{}[/tex]            |

    |          [tex]{}[/tex]            |

    |           [tex]{}[/tex]           |

    |____[tex]{}[/tex]______|

    D                     [tex]{}[/tex] C

2. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]

The above statement is sometimes true for rectangles. The definition of a rectangle indicates that the two pairs of opposite sides are congruent. In particular, [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are congruent, aa well as sides [tex]\overline{BC}[/tex] and [tex]\overline{AD}[/tex] are also congruent. The sides [tex]\overline{BC}[/tex] and [tex]\overline{CD}[/tex] are congruent if or when the rectangle is a square, therefore, the statement [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is sometimes true.

Please find attached the drawings created with MS Word which illustrates when [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] and when [tex]\overline{BC}[/tex] [tex]\ncong[/tex] [tex]\overline{CD}[/tex]

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Answer:

9 x 17 is greater than 9 x 15

Step-by-step explanation:

You can tell without finding the product because 17 is greater than 15, and the higher the number you multiply by, the larger the solution will be. I hope this helped :)

We need to add 6 mL of the 14% solution to the 8 mL of the 7% solution to obtain a 10% medication solution.

An equation is a mathematical statement that indicates that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to describe relationships between different variables, to solve problems, and to make predictions.

Let's call the number of milliliters of the 14% solution we need to add "x".

First, let's figure out how much medication is in the 8 mL of the 7% solution. Since the solution is 7%, we know that 7% of the solution is medication. We can convert that to milliliters by multiplying by the total volume of the solution:

0.07 x 8 mL = 0.56 mL of medication in the 7% solution

Next, let's figure out how much medication we want in the final solution. We want a 10% solution, so we want 10% of the total volume to be medication. We can write that as:

0.10 (x + 8 mL) = 0.1x + 0.8 mL

Now we can set up an equation based on the amount of medication in the 14% solution we add and the amount of medication in the final solution:

0.14x + 0.56 mL = 0.1x + 0.8 mL

Simplifying the equation, we get:

0.04x = 0.24 mL

Dividing both sides by 0.04, we get:

x = 6 mL

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Answer:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33

Step-by-step explanation:

All of these work. I hope this helps! Pls give brainliest!

Answer:

Your answer would be  

x/3<12

Answer:

[tex]16 {cm}^{3} [/tex]

Step-by-step explanation:

First, we can find the volume of tank A:

[tex]v(a) = 20 \times 24 \times 20 = 9600[/tex]

Now, let's write an equation for tank B's volume:

[tex]9600 = 600 \times h(b)[/tex]

[tex]h(b) = \frac{9600}{600} = 16[/tex]

(i) The domain of f(x) is all real numbers, since there are no restrictions on the input variable x.

(ii) We have:

f(x) = x^4 - 2x^3

f'(x) = 4x^3 - 6x^2

f''(x) = 12x^2 - 12x

(iii) To find the critical points, we need to solve the equation f'(x) = 0:

4x^3 - 6x^2 = 0

2x^2(2x - 3) = 0

x = 0 or x = 3/2

So the critical points are (0,0) and (3/2, -27/16).

(iv) To determine where f(x) is increasing or decreasing, we need to examine the sign of f'(x) on different intervals. We can make a sign chart for f'(x):

| x | -∞ | 0 | 3/2 | +∞ |

|---------|--------|-------|-------|--------|

| f'(x) | - | 0 | + | + |

From the sign chart, we see that f(x) is decreasing on the interval (-∞, 0) and increasing on the interval (0, 3/2) and (3/2, +∞).

(v) To find the relative extrema, we need to examine the sign of f'(x) around the critical points. We can make a table:

| x | 0- | 0+ | 3/2- | 3/2+ |

|---------|-------|-------|-------|-------|

| f'(x) | - | + | - | + |

| f(x) | 0 | 0 | -27/16| -27/16|

From this table, we see that f(x) has a relative minimum of -27/16 at x = 3/2, and no relative maximum or minimum at x = 0.

(vi) To find the intervals where f(x) is concave up or concave down, we need to examine the sign of f''(x) on different intervals.

We can make a sign chart for f''(x):

| x | -∞ | 0 | 1 | +∞ |

|---------|--------|-------|------|--------|

| f''(x) | + | - | + | + |

From the sign chart, we see that f(x) is concave down on the interval (-∞, 0) and concave up on the intervals (0, 3/2) and (3/2, +∞).

(vii) To find the points of inflection, we need to solve the equation f''(x) = 0:

12x^2 - 12x = 0

12x(x - 1) = 0

x = 0 or x = 1

So the points of inflection are (0,0) and (1, -1).

(viii) To sketch the graph of f(x), we can use the information we have gathered so far.

At x = 0, f(x) has a relative minimum of 0 and is concave down. At x = 3/2, f(x) has a relative minimum of -27/16 and is concave up. The point (1, -1) is a point of inflection.

Based on this information, we can sketch a graph of f(x) that looks like this:

```

|

|

|

|

|

|

|

--------o------------o-------

0 3/2 x-axis

```

The graph is a "U" shape that opens upward, with a relative minimum at (3/2, -27/16) and a point of inflection at (1, -1).

The standard error of the mean is 0.3125 mpg.

The sample mean will fall within the interval (19.9859, 20.0141)

A decimal is a number system that uses the base ten, which means it uses ten digits (0,1,2,3,4,5,6,7,8,9) to represent all numbers. Each digit in a decimal number represents a power of ten. For example, in the number 123.45, the digit "1" represents 1 x 10², the digit "2" represents 2 x 10¹, the digit "3" represents 3 x 10⁰, the digit "4" represents 4 x 10⁻¹, and the digit "5" represents 5 x 10⁻².

(a) The standard error of the mean (SE) can be calculated using the formula:

SE = s / √(n)

where s is the sample standard deviation, n is the sample size, and √ represents the square root. In this case, n = 16 and s = a = 1.25 mpg. Substituting these values, we get:

SE = 1.25 / √(16)

  = 0.3125

Rounding to 4 decimal places, the standard error of the mean is 0.3125 mpg.

(b) To find the interval within which we would expect the sample mean to fall with 90% probability, we need to use a confidence interval. Since the sample size is large enough (n >= 30) and the population standard deviation is known, we can use the z-distribution to construct a confidence interval. The z-value for a 90% confidence level is 1.645 (found using a standard normal distribution table or calculator).

The 90% confidence interval for the sample mean can be calculated using the formula:

CI = Xbar ± z*(SE)

where Xbar is the sample mean, z is the z-value for the desired confidence level, and SE is the standard error of the mean.

Substituting the given values, we get:

CI = 20.5 ± 1.645*(0.3125)

  = 20.5 ± 0.5141

Rounding to 4 decimal places, the 90% confidence interval for the sample mean is:

CI = (19.9859, 20.0141)

Therefore, we would expect the sample mean to fall within the interval (19.9859, 20.0141)

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The cοndensed οr cοmbined fοrm is thus: 2x³y + 8x²y2 + 17xy³ = (2x²)xy + (8x)xy + (17xy²) = (2x2)xy + (8x)xy + (17xy²).

An expressiοn in mathematics is a set οf digits, symbοls, and οperatοrs that depicts a quantity οr a relatiοnship between twο quantities. Expressiοns can be straightfοrward, using a single number οr variable, οr cοmplicated, including a variety οf phrases and prοcedures. Expressiοns include things like "3 + 5" and "2x - 4", fοr instance.

The first phrase is straightfοrward and represents the additiοn οf twο numbers, whereas the secοnd expressiοn is mοre intricate and includes a variable, multiplicatiοn, and subtractiοn.

As the expressiοns yοu prοvided lack an equal sign and hence are nοt equatiοns, it is unclear what yοu mean when yοu say that yοu are "sοlving" the prοblem.

Hοwever if yοu wish tο cοmbine οr simplify these expressiοns, yοu can utilize the factοring apprοach.

We can factοr it οut because xy is a cοmmοn factοr thrοughοut the expressiοns:

8x²y² = (8x)xy, while 17xy³ = (17)xy²

We can nοw see that each expressiοn's remaining factοrs are (2x²), (8x), and (17), respectively.

Since these factοrs dο nοt share any cοmmοn factοrs, further simplificatiοn is nοt pοssible. In terms οf the cοmmοn factοr xy.

The cοndensed οr cοmbined fοrm is thus: 2x³y + 8x²y² + 17xy³ = (2x²)xy + (8x)xy + (17xy2) = (2x²)xy + (8x)xy + (17xy2).

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Complete Question

Write this expression  2x³y, 8x²y², 17xy³  in combined form

Let us assume that the variables:

d = distance

t = time (in seconds)

~

The question assumes that the horse will move 15 meters every second. Therefore:

d = 15t

IF:

t (time) = 1 seconds, then:

d = 15(1)

d = 15

IF:

t (time) = 2 seconds, then:

d = 15(2)

d = 30

IF:

t (time) = 5 seconds, then:

d = 15(5)

d = 75

~

As you can see, the graphed numbers are much more larger than the numbers that you have already written, and so it is best to change the numbers. Generally the y-axis is used for time (in this case, seconds), whlie the x-axis is used for distance (in this case, meters).

~

For function f(t) = 1.25^t, it is an exponential growth.

The percent rate of change per unit t is found by taking the derivative of the function:

f'(t) = ln(1.25) * 1.25^t ≈ 9.2%

Since f'(t) is positive, the function represents exponential growth.

For function g(t)=5^-t:

The percent rate of change per unit t is found by taking the derivative of the function:

g'(t) = -ln(5) * 5^-t ≈ -13.9%

Since g'(t) is negative, the function represents exponential decay.

For function h(t) = 1.20(t/11):

The percent rate of change per unit t is found by taking the derivative of the function:

h'(t) = 1.20/11 ≈ 10.9%

Since h'(t) is positive, the function represents exponential growth.

For function k(t) = 0.63t:

The percent rate of change per unit t is found by taking the derivative of the function:

k'(t) = 0.63 ≈ 63.0%

Since k'(t) is positive, the function represents exponential growth.

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The fraction of the production run that was defective is 2/25.

What is the fraction?

A fraction is a numerical quantity that represents a part of a whole or a ratio between two quantities. It is expressed as one integer divided by another integer, with a horizontal line separating the two numbers. The number above the line is called the numerator and the number below the line is called the denominator.

The fraction of a production run that was defective is 0.08. This can be written as a fraction with a numerator of 0.08 and a denominator of 1:

0.08/1

To express this fraction with a denominator other than 1, we can multiply both the numerator and denominator by the same number, without changing the value of the fraction. For example, we can multiply by 100 to get:

(0.08/1) * (100/100) = 8/100

Simplifying this fraction gives:

8/100 = 2/25

Therefore, the fraction of the production run that was defective is 2/25.

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Answer:a=9  b=27.5  c=41.25

Step-by-step explanation:

the internet

Step-by-step explanation:

N = 50 000   and  N = 1000 * 2^t

so

50 000 = 1000 2^t      divide both sides of the equation by 1000

50 = 2^t      LOG both sides

log 50 = t log 2

log 50 / log 2 = t = 5.64 hours

Answer: 4 cans of tuna

Step-by-step explanation:

5 1/2 x 4 = 22

Answer:

To find which tuna is a better deal, divide the cost by the number of ounces of tuna you are getting to get the cost per ounce.

$0.90/5  = $0.18 per ounce

$2.40/12 = $0.20 per ounce

Since the 5-ounce can of tuna has a cheaper unit rate price, meaning you are getting a better value, makes this the best option. I hope this was helpful and have a great day! :)

Step-by-step explanation:

Let's assume that the width of the rectangular poster is "x".

According to the problem, the length is 8 more inches than half the width, which can be expressed as:

length = (1/2)x + 8

The area of the poster is given as 40 square inches, so we can write the equation:

Area = length × width

Substituting the values of length and width in terms of "x", we get:

40 = ((1/2)x + 8) × x

Simplifying the equation:

40 = (x^2)/2 + 8x

Multiplying both sides by 2 to eliminate the fraction:

80 = x^2 + 16x

Rearranging the equation in standard quadratic form:

x^2 + 16x - 80 = 0

Using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 16, and c = -80

x = (-16 ± sqrt(16^2 - 4(1)(-80))) / 2(1)

x = (-16 ± sqrt(736)) / 2

x = (-16 ± 8sqrt(9)) / 2

We can discard the negative solution since width cannot be negative:

x = (-16 + 24) / 2

x = 4

So, the width of the poster is 4 inches.

Using the equation for length:

length = (1/2)x + 8

length = (1/2)(4) + 8

length = 2 + 8

length = 10

Therefore, the dimensions of the poster are 10 inches by 4 inches.