Write and simplify polynomial expressions that represents the perimeter and area of the cornfield (7y) (6x)

Answer:

V = 226.08 ft³

Step-by-step explanation:

the volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius and h the height ) , then

V = 3.14 × 6² × 2

   = 3.14 × 36 × 2

  = 3.14 × 72

  = 226.08 ft³

After answering the given query, we can state that As a result, function  g(x) = 7x + 2 indicates the translation that occurs 1 unit to the left of f(x) = 7x - 5.

Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.

The function f(x) = 7x - 5 must be translated 1 unit horizontally to the left in order to determine g(x).

In order to solve for f, we must substitute x in the equation with (x + 1) when there is a horizontal translation of 1 unit to the left.(x). This is due to the fact that by replacing x with x + 1, we are actually moving the curve of f(x) to the left by one unit.

So, g(x) = f(x + 1) can be expressed as:

g(x) = 7(x + 1) - 5

g(x) = 7x + 2

As a result, g(x) = 7x + 2 indicates the translation that occurs 1 unit to the left of f(x) = 7x - 5.

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D)probability that the sample proportion is between 0.56 and 0.59 is 0.7912.

E)Probability that the sample proportion is less than 0.51 is 0.0002

D. To calculate the probability that the sample proportion is between 0.56 and 0.59, we can use the Standard Normal Probability Distribution Table. To do this, we first calculate the standard score, or z-score, for the lower bound and the upper bound of our desired range. The formula for calculating the z-score is:


z = (x - μ) / σ


where x is the value for which you want to find the z-score, μ is the population mean, and σ is the population standard deviation. In this case, x is the sample proportion, μ is 0.61, and σ is 0.01. Therefore, the z-score for the lower bound (0.56) is -2.90, and the z-score for the upper bound (0.59) is -0.33. We can then look up the corresponding probabilities in the Standard Normal Probability Distribution Table. The probability that the sample proportion is between 0.56 and 0.59 is 0.7912.

E. To calculate the probability that the sample proportion is less than 0.51, we can use the same process as above. The z-score for 0.51 is -3.90. We can look up the corresponding probability in the Standard Normal Probability Distribution Table, which is 0.0002. Therefore, the probability that the sample proportion is less than 0.51 is 0.0002.

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The rate of change of the number of vehicles in line with respect to the traffic intensity for x=0.2 is -1.2000. The formula used to calculate the rate of change is the derivative of the given function f(x).

To find the rate of change of the number of vehicles in line with respect to the traffic intensity at x = 0.2, we need to take the derivative of the function f(x) with respect to x and then evaluate it at x = 0.2.

f(x) = 5(2 - x)x^2

f'(x) = 5[(2 - x)(2x) + x^2(-1)]

f'(x) = 5(4x - 3x^2)

f'(0.2) = 5(4(0.2) - 3(0.2)^2) = 0.68

Therefore, the rate of change of the number of vehicles in line with respect to the traffic intensity for x = 0.2 is 0.68.

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It is vertically stretched by a factor of 200 and shifted 10 units up.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

You write functions with the function name followed by the dependent variable.

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Answer:

Step-by-step explanation:

i cant see the answer

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 6-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~6 - \cfrac{ 16 }{ 4 } \right) \\\\\\ \left( -2 ~~~~ ,~~~~ 6 -4 \right)\implies (-2~~,~~2)[/tex]

From the given information provided,  the quantity demanded at a price of $8 per ticket is 293 tickets.

The demand in this example refers to the relationship between the price of movie tickets and the quantity of tickets that people are willing and able to buy at that price.

From the given information, we know that the current price of a movie ticket is $8 and the quantity demanded at that price is 285 tickets. However, we would need additional data points at different prices to get a more accurate estimate of the demand function.

Assuming that the demand for movie tickets is downward sloping (i.e., as the price of tickets increases, the quantity demanded decreases), we can say that the demand is:

Inverse: The price and quantity demanded move in opposite directions. When the price of tickets goes up, the quantity demanded goes down, and vice versa.

Negative: The slope of the demand curve is negative, indicating that there is an inverse relationship between the price and quantity demanded.

To estimate the quantity demanded at different prices, we can use the formula for a linear demand function:

Q = a - bP

where Q is the quantity demanded, P is the price, a is the intercept (the quantity demanded when the price is zero), and b is the slope (the change in quantity demanded for a one-unit change in price).

Using the given data point of $8 and 285 tickets, we can estimate the intercept:

285 = a - 8b

Assuming a relatively elastic demand, we can use a slope of -2:

Q = a - 2P

Substituting the intercept value we solved for earlier, we get:

Q = 309 - 2P

This is the estimated demand function for movie tickets based on the given information.

To answer the question of what is the quantity demanded, we can use the given data point of $8 per ticket and plug it into the demand function:

Q = 309 - 2(8)

Q = 293

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The only multiple of 12 with a square root of 6 is 12 times 3, or 36 using generate multiples of 12 .

The multiples of 12 are numbers that are divisible by 12 without a remainder. We can generate multiples of 12 by multiplying 12 by any integer. For example, the first few multiples of 12 are 12, 24, 36, 48, 60, and so on.

To find which multiples of 12 have a square root of 6, we can use the following formula:

√(12n) = √(12) * √(n)

Since the square root of 12 is equal to 2 times the square root of 3, we can simplify the formula as follows:

√(12n) = 2 * √(3n)

If the square root of 12n is equal to 6, then we can set up an equation and solve for n:

2 * √(3n) = 6

√(3n) = 3

3n = 9

n = 3

In summary, we can use the formula √(12n) = 2 * √(3n) to find which multiples of 12 have a square root of 6. By solving for n, we find that the only multiple of 12 with a square root of 6 is 36.

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The volume of the frustum is 19840cm³

A frustum is a cut out section of a defined shape. The volume of the frustum is calculated as;

Volume of the Big shape - Volume of the small shape.

The shape here is a pyramid. And the volume of a pyramid is given as ;

1/3 bh

The height of the big pyramid is obtained by using similar shape theorem

10/10+x = 6/30

= 60+6x = 300

6x = 240

x = 240/6 = 40

Therefore the height of the pyramid = 40+10 = 50cm

Therefore volume of the big pyramid = 1/3 × 30×40× 50

= 10× 40 × 50

= 20000cm³

The volume of the small pyramid = 1/3 bh

The width of the small pyramid = 6/30 = x/40

30x = 240

x = 8

= 1/3 × 8× 6× 10

= 8× 2 × 10

= 160cm³

therefore the volume of the frustum = 20000-160

= 19840cm³

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The domain of the given function is (-∞, 1) ∪ [1, ∞) and  the range of the function is [1/4, ∞)

The domain of a function is the set of all possible values for which the function is defined. In the given function, there are two separate definitions: one for x < 1 and another for x ≥ 1. Hence, we can say that the domain of the given function is (-∞, 1) ∪ [1, ∞).b. Range: The range of a function is the set of all possible values that the function can take. Since the function is a quadratic function, it is always positive, and the minimum value occurs at x = -b/2a. The minimum value of the function occurs at x = -b/2a = 1/2.

Thus, the range of the function is [1/4, ∞). Computing the values of f(x): Now, we have to compute the following values of f(x): f(0), f(1/2), and f(2).f(0): The value of the function when x = 0 is given by the second part of the definition:f(0) = (0² + 3 - 0 + 1) = 4f(1/2): The value of the function when x = 1/2 is given by the first part of the definition: f(1/2) = (1/4 + 3 - 1/2 + 1) = 13/4f(2): The value of the function when x = 2 is given by the second part of the definition: f(2) = (2² + 3 - 2 + 1) = 8Therefore, f(0) = 4, f(1/2) = 13/4, and f(2) = 8.

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we need to know how many students each circle represents to calculate how many chose chicken Maybe try 4 3/4 but im not quite sure

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

24 students said veggie and there is 6 circles in the pictogram for veggie so we can divide 24 by 6 to find the value of one circle.

[tex]\frac{24}{6} = 4[/tex]

Now we have the value of a circle we can figure out how many students chose chicken.

There are 4 full circles which is [tex]4*4 = 16[/tex]

Finally, there is a 3/4 of a circle which is [tex]4*\frac{3}{4} = 3[/tex]

Then we add all the values together to find the number of students who chose chicken.

16+3=19

Hope this helps!

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The average rate οf change οf f(x) is equal tο the slοpe οf the line passing thrοugh the twο pοints, which is (y₂ - y₁) / 4.

The average rate οf change is a mathematical cοncept that describes the rate at which a quantity changes οver a certain periοd οf time οr οver a certain range οf values. In calculus, the average rate οf change is οften used tο estimate the instantaneοus rate οf change οf a functiοn at a specific pοint.

Tο find the average rate οf change οf a functiοn οver an interval [a, b], we calculate the slοpe οf the line cοnnecting the twο pοints (a, f(a)) and (b, f(b)). This is given by the fοrmula:

average rate οf change = (f(b) - f(a)) / (b - a)

Tο calculate the average rate οf change οf f(x) frοm x=-4 tο x=0, we need tο find the slοpe οf the line cοnnecting the twο pοints.

The fοrmula fοr the slοpe οf a line passing thrοugh twο pοints (x₁, y₁) and (x₂, y₂) is:

slοpe = (y₂ - y₁) / (x₂ - x₁)

In this case, the twο pοints are (-4, f(-4)) and (0, f(0)). We dοn't have the specific values οf f(-4) and f(0), sο we'll use variables tο represent them. Let's say f(-4) = y₁ and f(0) = y₂.

Then the slοpe οf the line is:

slοpe = (y₂ - y₁) / (0 - (-4)) = (y₂ - y₁) / 4

Sο the average rate οf change οf f(x) frοm x=-4 tο x=0 is equal tο the slοpe οf the line passing thrοugh the twο pοints, which is (y₂ - y₁) / 4.

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Mr. Razon paid 87 percent of his Php 100 for his lunch.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage. The relative reduction in comparison to the starting value is then determined using this difference, and it is expressed as a percentage.

The response denotes a percentage increase if the percent change number is positive. If the value is negative, it can be expressed as a positive number and designated as a reduction in percentage.

To find the percentage that Mr. Razon paid for his lunch, we can use the formula:

percentage = (part / whole) x 100%

Substituting the values we get:

percentage = (87 / 100) x 100%

percentage = 87%

Therefore, Mr. Razon paid 87% of his Php 100 for his lunch.

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Answer:

-7x - 12

Step-by-step explanation:

To simplify the expression, we need to get rid of the parentheses and combine like terms. We can use distributive property to multiply each term inside the parentheses by the sign outside.

Therefore, the expression (-2x-10) - (-5x + 2) - 10x simplified is -7x - 12.

the average rate of change in the number of cattle from 2006 to 2014 is approximately -1.1125 million head of cattle per year.

To find the average rate of change in the number of cattle from 2006 to 2014, we need to divide the total change in the number of cattle over that period by the number of years.

The total change in the number of cattle is:

87.7 million - 96.6 million = -8.9 million

The number of years is:

2014 - 2006 = 8

So, the average rate of change is:

-8.9 million / 8 years = -1.1125 million per year

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The measure of the lengths of the following line segments using online ruler are given as follows:

KL = 5.11cm or  = 51.1mm

FG = 8.67cm or = 86.7mm

Length is a physical quantity that refers to the measurement of the extent of an object or distance between two points. It is usually measured in units such as meters, centimeters, or feet.

A line segment is a part of a line that is bounded by two distinct endpoints. It is the shortest distance between two points on a straight line.

To convert cm to mm, we multiply by 10 because there are 10 millimeters in 1 centimeter.

Therefore, to convert 5.11 cm to mm, we can multiply 5.11 by 10:

5.11 cm * 10 = 51.1 mm

So, 5.11 cm is equal to 51.1 mm.

Also to convert 8.67 cm to mm, we can multiply 8.67 by 10:

8.67 cm * 10 = 86.7 mm

So, 8.67 cm is equal to 86.7 mm.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

If the area of a pad is 17. 5 square yards, the length of the pad is 5 yards, the width of the pad is 3.5 yards.

The formula for the area of a rectangle is:

Area = length x width

We know that the area of the pad is 17.5 square yards, and the length is 5 yards. We can use this information to solve for the width.

Let's substitute the values we know into the formula:

17.5 = 5 x width

To solve for the width, we need to isolate it on one side of the equation. We can do this by dividing both sides by 5:

17.5/5 = width

Simplifying the left side gives:

3.5 = width

In conclusion, Mr. Tomas should make a rectangular concrete pad that is 5 yards long and 3.5 yards wide to have an area of 17.5 square yards.

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By looking at the degree, we conclude that we have 4 roots.

Here we want to see how many roots the function:

x⁴ - 2x³ - 6x² + 22x - 15 = 0

The numer of roots (repeated, complex, or real) is given by the degree of the g

In this case we can see that the maximum exponent is 4, so the degree is 4, which means that we have 4 roots

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Answer: y - intercept is c = 4.

Step-by-step explanation:

The line equation is 3x + y = 4.

The slope-intercept form of the line equation is y = mx + c.

Where m is the slope of line c is the y-intercept.

The equation is 3x + y = 4.

subtract 3x  from each side.

y - intercept is c = 4.

Answer:

14490 meters

Step-by-step explanation:

0.69 x 3weeks which is (21) days , so 0.69•21 =14.490km 14.490km=14490 meters

There were 332500 tourists who traveled to Nepal in 2011.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Number of tourists in 2010 = 95% of number of tourists in 2009

= 0.95 x 250000

= 237500

Number of tourists in 2011 = 140% of number of tourists in 2010

= 1.4 x 237500

= 332500

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Step-by-step explanation:

4 1/2(2)=9. Multiply by 2 to get total

9- 3 1/2=z. Subtract 3 1/2 from total to get Z

5 1/2= Z

The proportional equation us y = 2.5x and the constant is 2.5

6 bottles would have a volume of 15 liters.

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

Let y represent the volume in liters and x represent the number of bottles.

A proportional relationship is in the form:

y = kx; where k is the constant of proportionality.

From the table, using the value (2, 5):

y = kx

substituting:

5 = 2k

k = 2.5

The proportional equation us y = 2.5x and the constant is 2.5

For 6 bottles:

y = 2.5(6) = 15 liters

6 bottles would have a volume of 15 liters.

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Step-by-step explanation:

workers = k× number of days (k= constant of proportionality)

w = k× days

20= 15× k

k = 20/15

w = k× days

substitute the values

w = 20/15 × 12

w = 16

Number of workers required = 16

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Answer:

5

Step-by-step explanation:

15d -- 20l

12d -- (x)l

x= 15×20

12

x= 25

25-20= 5

Ans = 5.

We can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

Given the triangles EFG and BCD, you can identify that:

By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.

In this case, you can identify that you know two pairs of corresponding sides. Then, you can find that they are in proportion. Set up that:

[tex]\frac{EF}{BC}=\frac{FG}{CD}[/tex]

Substituting values and simplifying, you get:

[tex]\frac{18}{90}=\frac{16}{80}\\\\\frac{1}{5}=\frac{1}{5}[/tex]

Notice that they are in proportion.

You can also identify that the corresponding angles F and I are congruent because they have equal measures.

Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

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The lateral area of this paper weight is 61.42 sq inches.

Every solid object's lateral area may be calculated using the lateral area formula. Every figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as a cuboid, cube, cylinder, cone, or sphere, is made easier with the use of lateral area formulae. The object's base and the face parallel to the base are not included in the lateral area.

The surface area of the composite figure is the addition of the area of all the shapes.

The area of triangle with height 3.5 in is:

A1 = 1/2(6.5)(3.5)

A1 = 11.375 sq. in.

There are two such triangles thus, 2A1 = 2(11.375) = 22.75.

The area of the two triangle with height 6.5 in is:

A2 = 2(1/2)(4.3)(6.5) = 27.95 sq. in.

The area of the rectangle is:

A3 = (l)(w)

A3 = (6.5)(4.2) = 27.3 sq. in.

The total lateral area is:

LA = 11.375 + 22.75 + 27.3 = 61.42 sq inches.

Hence, the lateral area of this paper weight is 61.42 sq inches.

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The average rate of change of g(x) from x = 3 to x = 7 is -5.

To find the average rate of change of the function g(x) = -x² + 4x + 2 over the interval [3, 7], we need to calculate the change in the function values over this interval and divide by the length of the interval.

The change in the function values between x = 3 and x = 7 is:

g(7) - g(3) = (-7² + 47 + 2) - (-3² + 43 + 2) = (-49 + 28 + 2) - (9 + 12 + 2) = -20

Therefore, the average rate of change of g(x) over the interval [3, 7] is:

average rate of change = change in function values / length of interval

= -20 / (7 - 3)

= -5

This means that on average, the function g(x) decreases by 5 units for every 1 unit increase in x over the interval [3, 7].

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Answer:

Option C: The skaters path intersect twice, but only one of those points is inside the rink.

Step-by-step explanation:

Coordinates of center of ice rink: (0,0) Radius of ice rink circle = 35 m

We know that the equation of a circle with center coordinates (a,b) and radius of (r) is given as; (x - a)² + (y - b)² = r²

Thus, the total area on which the skaters are skating will be given by the equation;

x² + y² = 35²

Now, we are told the path along which Susan is skating is modeled by the equation: y = 6x - x² - 5

While Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9)

From equation of a parabola, the path along which like is skating can be modeled by;

(x - 8)² = 4a(y + 9)

To find a, we will substitute the coordinate started at to get;

(10 - 8)² = 4a(-21 + 9)

4 = 4a × -12

Divide both sides by 4 to get;

a = -1/12

Thus;

(x - 8)² = 4(-1/12)(y + 9)

(x - 8)² = (-1/3)(y + 9)

This gives: 3(x - 8)² = -(y + 9)

I've drawn the graph on demos and attached it.

From the graph we can see that the skaters points intersect twice but one is inside the rink circle while the other is outside the rink circle. The point at which they intersect outside the rink was slightly cropped out because of size. But it is clearly seen that they are both approaching point of intersection.

Thus, correct answer is Option C.

The height of the base if it is 2 in. wide  is 3 inches. Option B

Let's call the height of the triangular base h (in inches).

The volume of the triangular prism can be calculated using the formula:

Volume = (1/2) x Base x Height x Length

In this case, the length is given as 4 inches, the width (or base) is given as 2 inches, and the volume is given as 12 cubic inches. Substituting these values into the formula, we get:

12 = (1/2) x 2 x h x 4

Simplifying this equation, we get:

12 = 4h

Dividing both sides by 4, we get:

h = 3

Therefore, the height of the triangular base is 3 inches.

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Answer: 3

Step-by-step explanation: