Subtracting polynomials

the total number of posts needed is, 56

Since, we know that the area of the horse corral is 10,000 square feet.

So, it is a square corral, we can find the length of each side by taking the square root of the area, which is 100 feet.

Now, For the total number of posts needed, we need to calculate the perimeter of the corral.

Since there are four sides of equal length, the perimeter of the corral is 4 times the length of one side.

Therefore, the total perimeter is 400 feet.

Now, we need to find the number of posts needed.

We know that each post is placed 10 feet apart along the sides of the corral.

Since there are 4 sides, we need 3 intervals of 10 ft between each post, which gives us a total of 4 posts for every 30 feet of fencing.

Therefore, the total number of posts needed is,

= (400 / 30) x 4 + 4

= 56 posts.

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The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at; -3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, for the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537.

After transformation, we will have the point as  (3, 5).  

A rotation is  described as a type of transformation which is a turn and that turns the figure in either a clockwise or counterclockwise direction.

The rotation does not alter the shape.

When we Rotate (4,-1) 90° anticlockwise centered at the origin yields the point (1, 4).

We next transform the point (1, 4) two units to the right and 1 unit up results in the point (3, 5).

We can also rotate 90° clockwise that would result in some different point on this coordinate system. We will also have some 2D figures like a triangle or a rectangle instead of a straight line

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the next two terms in the sequence would be 12 and 17.

Step-by-step explanation:

Answer: 149

Step-by-step explanation: 15 17 19 21

23 25 27 29 31 33 35 37 39 41

43 45 47 49 51 53 55 57 59 61

63 65 67 69 71 73 75 77 79 81

83 85 87 89 91 93 95 97 99 101

103 105 107 109 111 113 115 117 119 121

123 125 127 129 131 133 135 137 139 141

143 145 147 149 151 153 155 157 159 161

163 165 167 169 171 173 175 177 179 181

183 185 187 189 191 193 195 197 199 201

203 205 207 209 211 213 215 217 219 221

223 225 227 229 231 233 235 237 239 241

243 245 247 249 251 253 255 257 259 261

263 265 267 269 271 273 275 277 279 281

283 285 287 289 291 293 295 297 299 301

303 305 307 309 311 313 315 317 319 321

323 325 327 329 331 333

Answer:

188.33

Step-by-step explanation:

113 = .6n  Divide both sides by .6

188.33 = n  Rounded to the nearest hundredth.

Helping in the name of Jesus.

The calculated height of the prism​ is 5 inches

from the question, we have the following parameters that can be used in our computation:

Volume = 45 cubic inches

Base = square

The height of the prism​ is calculated as

Volume = Base length² * Height

substitute the known values in the above equation, so, we have the following representation

Base length² * Height = 45

So, we have

Base length² * Height = 3² * 5

This means that

Base length = 3

Height = 5

Hence, the height of the prism​ is 5 inches

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An exponential equation that best fit the data above is [tex]y = 535.02(1.15)^x[/tex]

a = 535.02

b = 1.15.

In this scenario, the x-values (x) would be plotted on the x-axis of the scatter plot while the y-values (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the x-values (x) and y-values (y), the exponential equation and the correlation coefficient are given by:

[tex]y = 535.02(1.15)^x[/tex]

Correlation coefficient, r = 0.9973006 ≈ 1.0

In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is is greater than 0.7;

0.7＜|r| ≤ 1.0   (strong correlation)

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The axis of symmetry of the given quadratic function f(x) = -(x - 2)(x + 4) is x = -1.

Given the function in the question:

f(x) = -(x - 2)(x + 4)

To find the axis of symmetry, first expand  quadratic function f(x) = -(x - 2)(x + 4).

f(x) = -(x - 2)(x + 4)

f(x) = (-x + 2)(x + 4)

f(x) = -x(x + 4) + 2( x + 4 )

f(x) = -x² - 4x + 2x + 8

Collect and add like terms

f(x) = -x² - 2x + 8

To find the axis of symmetry, we can use the formula:

x = -b/2a

Where a = -1 and b = -2.

Substituting these values, we get:

x = -(-2) / 2(-1)

Simplify

x = 2 / -2

x = -1

Therefore, the the axis of symmetry is x = -1.

Option D) x = -1 is the correct answer.

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Answer:

20π in.

Step-by-step explanation:

The central angle of minor arc SV is θ = 5π/6 radians, which is 150 degrees. The length of a minor arc is given by the formula s = rθ, where r is the radius of the circle. Substituting r = 24 in. and θ = 5π/6, we get:

s = 24 × 5π/6 = 20π in.

Therefore, the length of minor arc SV is 20π in.

The area of the trapezoid is 104 square yards

As given a table was made by Veronica which is in the shape of a trapezoid.

twice as long as the table's width

Let us find the area of the trapezoid by the given data and formula of trapezoid

The length of the bottom base is x= 16 yd.

Area A=(a+b)h/2

a=10 yd

b=16 yd

h =8 yd

Substitute the values of a, b and h in the area of trapezoid

Area =1/2(10+16)8

=208/2

=104 square yards

Hence, the area of the trapezoid is 104 square yards

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Answer:

29658

Step-by-step explanation:

N =  A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

N = 28337 (1 + 0.0153)^3

= 28337 (1.0153)^3

= 29658 to nearest number

Answer:

So 98 adult tickets were sold.

Step-by-step explanation:

Let's use a system of equations to solve the problem.

Let x be the number of child tickets sold and y be the number of adult tickets sold. Then we have:

x + y = 176 (equation 1)

5.10x + 8.20y = 1201.40 (equation 2)

We can solve for x by isolating y in equation 1 and substituting into equation 2:

y = 176 - x (from equation 1)

5.10x + 8.20(176 - x) = 1201.40 (substitute into equation 2)

5.10x + 1443.20 - 8.20x = 1201.40

-3.10x = -241.80

x = 78

Therefore, 78 child tickets were sold that day. We can find the number of adult tickets by substituting x into equation 1:

78 + y = 176

y = 98

So 98 adult tickets were sold.

The answer to all parts is shown below.

1. The diameter of a donut is 3 inches.

so the circumference is πd = 3π ≈ 9.42 inches.

2. 2.5 square feet is equal to 2.5 x 144 = 360 square inches.

3. The minimum length, width, and height of the box are equal to the diameter and height of the donut, which is 3 inches and 1.5 inches, respectively.

Adding 1/2 inch to each dimension gives a length of 4 inches, a width of 4 inches, and a height of 2 inches.

4. The area of the bottom of the new box is length x width

= 4 x 4 = 16 square inches.

The length and width of the new box meet Dave's requirements because they are each greater than or equal to the minimum length and width of 3.5 inches (3 inches + 1/2 inch).

5. The surface area of the new box can be calculated as follows:

Top and bottom: 2 x (length x width) = 2 x (4 x 4) = 32 square inches

Front and back: 2 x (height x length) = 2 x (2 x 4) = 16 square inches

Sides: 2 x (height x width) = 2 x (2 x 4) = 16 square inches

Total surface area = 32 + 16 + 16 = 64 square inches.

6. The surface area of one original box is equal to the sum of the areas of the top, bottom, and four sides.

Each side has dimensions of 3 inches by 1.5 inches,

so the area of each side is 3 x 1.5 = 4.5 square inches.

The area of the top and bottom is 3 x 3 = 9 square inches.

Therefore, the surface area of one original box is:

Top and bottom: 2 x 9 = 18 square inches

Sides: 4 x 4.5 = 18 square inches

Total surface area = 18 + 18 = 36 square inches.

The surface area of the new box is 64 square inches, so the total cardboard needed for one box is:

64 square inches / 144 square inches per square foot = 0.44 square feet

The cost of cardboard for one box is:

0.44 square feet x $0.20 per square foot = $0.088

To find the cost of 35 new boxes, we multiply the cost per box by the number of boxes:

35 boxes x $0.088 per box = $3.08

Therefore, the new box costs less than the original box, which costs $21.00 for 35 boxes.

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a) The equation representing the total area of the pool and the pool deck is: A = (x + 25)(x + 9).

b) The area equation in standard form is A = x² + 34x + 225.

c) The vertex form is A = (x + 17)²- 289

d) The x-intercepts is (-4, 0).

a) The equation representing the total area of the pool and the pool deck is: A = (x + 25)(x + 9).

b) Re-writing the area equation in standard form using the FOIL method:

A = x² + 9x + 25x + 225

A = x² + 34x + 225

c) Re-writing the equation from part b in vertex form by completing the square:

A = (x + 17)²- 289

d) The vertex of the parabola is (-17, -289).

The x-intercepts can be found by setting A = 0:

(x + 17)² - 289 = 0

(x + 17)² = 289

x + 17 = ±17

x = -34, 0 (x-intercepts)

The y-intercept is found by setting x = 0:

A = (0 + 17)² - 289

A = 0 (y-intercept)

e) The graph of the parabola is a downward-opening parabola with vertex (-17, -289).

f) In this problem, only positive values of x make sense because the dimensions of the pool and deck cannot be negative.

g) The point on the graph that shows a total area that includes the pool but not the pool deck is the vertex (-17, -289).

h) When x = 6 yards, the total area of the pool and deck can be calculated by substituting x = 6 into the equation:

A = (6 + 17)² - 289

A = 23² - 289

A = 529 - 289

A = 240 square yards

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The inverse of function f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.So, the correct option is D.

To find the inverse of a function, we switch the x and y variables and solve for y. So, if f(x) = -2, we have:
x = -2
y = f(x) = -2
Switching x and y, we get:
x = f¯¹(y)
y = -2
Solving for f¯¹(y), we get:
f¯¹(y) = 2y + 3
Therefore, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
To find the inverse of a function, we need to swap the input (x) and output (f(x)), and then solve for the new input. Given f(x) = -2, let's find the inverse:
1. Swap the input and output: x = -2
2. Solve for the new input: Since the function f(x) is a constant function and doesn't involve x, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
Therefore, Option D is the correct inverse of f(x).

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The student's chances of answering all five questions correctly are 7/64.

This is an example of a binomial distribution, where each question has a probability of 1/2 of being answered correctly and there are 8 independent trials.

The probability mass function for a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials, p is the probability of success, and k is the number of successes.

In this case, n = 8, p = 1/2, and we want to find P(X = 5).

P(X = 5) = (8 choose 5) * (1/2)^5 * (1/2)^(8-5)

P(X = 5) = (8 choose 5) * (1/2)^8

Using the formula for combinations, (n choose k) = n! / (k! * (n-k)!) we get:

P(X = 5) = (8! / (5! * 3!)) * (1/2)^8

P(X = 5) = 56 * 1/256

P(X = 5) = 7/64

Therefore, the probability of the student getting 5 questions correct is 7/64.

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For the given function the value of limits are

[tex]\lim _{x\to 0^-}\left(f\left(x\right)\right)[/tex] is 5

[tex]\lim _{x\to 0^+}\left(f\left(x\right)\right)[/tex] is 0

[tex]\lim _{x\to 0}\left x^2+5[/tex]is 5

The given function is f(x)= x²+5, when x≤0

f(x)=2x when x>0

[tex]\lim _{x\to 0^-}\left(f\left(x\right)\right)[/tex]

Which is [tex]\lim _{x\to 0^-}\left x^2+5[/tex]

The given limit is a left hand limit as there is minus in the limits

When we apply x as 0 we get the value 5

Now [tex]\lim _{x\to 0^+}\left(f\left(x\right)\right)[/tex]

So [tex]\lim _{x\to 0^+}\left 2x[/tex]

The given limit is a right hand limit as there is positive in the limits

When we apply x as 0 we get 0

Now [tex]\lim _{x\to 0}\left(f\left(x\right)\right)[/tex]

Which is [tex]\lim _{x\to 0}\left x^2+5[/tex]

We get 5

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Answer:

  8.68 cm²

Step-by-step explanation:

You want the increase in surface area of a box with length and width 13 cm and 8.7 cm when the height is increased from 30 cm by 0.2 cm.

The increase in area is effectively the lateral area of the prism whose length and width are the same, but whose height is 0.2 cm. That is ...

  A = Ph = 2(L+W)h

  A = 2(13 cm +8.7 cm)(0.2 cm) = 8.68 cm²

The surface area increases by 8.68 cm².

We can find the total area of the box with the different dimensions, then subtract the original area from the increased area.

  A = 2(LW +H(L+W))

  A1 = 2(13·8.7 +30(13 +8.7)) = 1528.2 cm²

  A2 = 2(13·8.7 +30.2(13 +8.7)) = 1536.88 cm²

The increase in area is 1536.88 -1528.2 = 8.68 cm².

We prefer the first solution, as it requires a lot less arithmetic.

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[tex]6 + 3 = 9 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]

The probability of flipping heads twice followed by tails three times is 1/32 or approximately 0.031.

Each coin flip is an independent event, meaning the outcome of one flip does not affect the outcome of any other flip. Therefore, the probability of getting heads on any one flip is always 1/2, regardless of previous outcomes.

Using this information, we can calculate the probability of flipping heads twice followed by tails three times as:

P(heads) = 1/2

P(tails) = 1/2

P(heads on first flip) = 1/2

P(heads on second flip) = 1/2

P(tails on third flip) = 1/2

P(tails on fourth flip) = 1/2

P(tails on fifth flip) = 1/2

P(heads twice followed by tails three times)

= P(heads on first flip) x P(heads on second flip) x P(tails on third flip) x P(tails on fourth flip) x P(tails on fifth flip)

= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/32

Therefore, the probability of flipping heads twice followed by tails three times is 1/32 or approximately 0.031.

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Step-by-step explanation:

it says in the headline here : "college".

really ???

this is basic triangle calculation.

the yellow (shaded) area is the total area of the large triangle minus the area of the small (white) triangle.

both area right-angled triangles, so their areas are simple :

leg1 × leg2 / 2

the area of the full large yellow triangle is therefore

31.6 × 33.1 / 2 = 522.98 in²

the area of the small white triangle is

17.1 × 17.9 / 2 = 153.045 in²

that means the shaded area alone is

522.98 - 153.045 = 369.935 in² ≈ 369.94 in²

The measures of each of the arcs are: 16. m(MN) = 72°; 17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 193°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°.

Recall that in a circle, the measure of an intercepted arc is always the same or equal to the measure of the central angle it subtends.

Therefore, we have:

16. m(MN) = 72° (based on the vertical angles and inscribed angle theorems).

17. arc NQR is an half circle, therefore:

m(NQR) = 180°

18. m(NQ) = 180 - 72 = 108°

19. m(MRP) = 180 + (180 - 72 - 95)

m(MRP) = 193°

20. m(QR) = 72°

21. m(MR) = 180 - 72 = 108°

22. m(QMR) = 360 - 72

m(QMR) = 288°

23. m(PQ) = 180 - 72 - 95

m(PQ) = 13°

24. m(PRN) = 360 - 95

m(PRN) = 265°

25. m(MQN) = 360 - 72

m(MQN) = 288°

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1) According to Denis' article "The Definition of Neotraditionism," his encounter with a painting by Maurice Denis himself.

2) In his book "Concerning the Spiritual in Art," Kandinsky expressed his belief that art should go beyond mere representation of the physical world and instead aim to express the spiritual and emotional aspects of human experience.

3) In Part II, About Painting, VI: The Language of Form and Color of "Concerning the Spiritual in Art," Kandinsky wrote: "Color is a power which directly influences the soul.

Denis was influenced to write the first non-objective statement because of the limitations of representational art.

1) According to Denis' article "The Definition of Neotraditionism," his encounter with a painting by Maurice Denis himself, which featured a landscape that was "no longer a transcription of nature, but a creation" (Denis, 1914), influenced him to write the first non-objective statement.

This painting by Denis challenged the traditional notions of art as mere representation of nature, and instead presented a new idea of art as a creative act in its own right.

2) In his book "Concerning the Spiritual in Art," Kandinsky expressed his belief that art should go beyond mere representation of the physical world and instead aim to express the spiritual and emotional aspects of human experience. He wrote that "the artist must be blind to distinction between 'recognized' or 'unrecognized' conventions of form, deaf to the transitory teaching and demands of his particular age.

He must watch only the trend of the inner need, and hearken to its words alone" (Kandinsky, 1977, p. 8). This suggests that Kandinsky was motivated by a desire to break away from the conventional artistic norms of his time and create something that was more true to his own personal vision and inner creative impulses.

3) In Part II, About Painting, VI: The Language of Form and Color of "Concerning the Spiritual in Art," Kandinsky wrote: "Color is a power which directly influences the soul. Color is the keyboard, the eyes are the hammers, the soul is the piano with many strings. The artist is the hand that plays, touching one key or another purposively, to cause vibrations in the soul" (Kandinsky, 1977, p. 72).

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The point at coordinate 3 represents the weighted average.

Point E measures (-1) and has weight 2x weight of F

point F has a measure of 2 and no particular stated weight

point G measures 6 and has a weight of 3x weight of F

Since we can assign a weight to point F and the other weights will be based on that, let's just keep it simple and give point F a weight of 1.

That gives E a weight of 2, and G a weight of 3.

So, E value times E weight is   (-1)   x   2 = -2

F value times F weight is      2   x   1 =   2

G value times G weight is   6   x   3 = 18

Sum of (value x weight)  =  18

Sum of the weights = 2 + 1 + 3 = 6

we get the weighted average by taking the sum of (value x weight) products (18) and then dividing by the sum of the weights (6).

18/6 = 3, the weighted average

Hence, the point at coordinate 3 represents the weighted average.

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points E,F and G are plotted on a number line at -1, 2 and 6 respectively. Find the coordinate o f the point that represents the weighted average of E, F and G, if point E weighs twice as much as point F and point G weighs three times as much as point F.

It is not a polynomial function because polynomial functions have non-negative integer exponents, and the exponent in this function is -10, which is a negative integer.

The function f(x)=12x^-10 is a power function because it can be written in the form f(x)=kx^n where n is a negative integer. Specifically, this function can be written as f(x)=12/x^10.
Function f(x) = 12x^(-10), this function is a power function.
A power function has the form f(x) = kx^n, where k and n are constants. In this case, k = 12 and n = -10. Since the function fits the power function definition, it is a power function.
It is not a polynomial function because polynomial functions have non-negative integer exponents, and the exponent in this function is -10, which is a negative integer.

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Answer:

76%

Step-by-step explanation:

57/75

(57 X 100)/ 75

5700/75

1900/25

76/1

76

After the mathematical calculations, we can see that the value of z = 5 - 15i.

To simplify, let's square the complex number (2 - i):

[tex](2 - i)^2 = 2^2 - 2i + 2i - i^2 = 4 - 4i - 1 = 3 - 4i.[/tex]

Divide the complex number (7 - 4i) by (2 + i):

The approach we will take involves multiplying the top and bottom of the equation by the complex conjugate of the denominator.

[tex](7 - 4i) * (2 - i) / (2 + i) * (2 - i) = (14 - 7i - 8i + 4i^2) / (4 + 1) = (14 - 15i + 4(-1)) / 5[/tex]

= (10 - 15i) / 5

= 2 - 3i.

We have to minus 8i:

[tex](3 - 4i) + (2 - 3i) - 8i = 5 - 7i - 8i = 5 - 15i.[/tex]

Therefore, z = 5 - 15i.

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