If p(x)=0.5(x-5)^2+14, what is the value of p(3)

Check the picture below.

so notice, the area of the pyramid is really just the area of the four triangles with an altitude of 3 and a base of "s", and a square that s² in area, and we happen to know that's 40 inches.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{s})(\underset{h}{3}) \right]}~~ + ~~\stackrel{ square }{(s)(s)}}~~ = ~~40\implies 6b+s^2=40\implies s^2+6b-40=0 \\\\\\ (s+10)(s-4)=0\implies s= \begin{cases} -10\\ ~~ ~~ 4 ~in~~ \textit{\LARGE \checkmark} \end{cases}[/tex]

now, let's notice, we can't use the negative value, because the sides are never negative.

The average value of f(x) over the interval [-14, 14] is 0.

The average value of the function f(x) = 14 - |x| over the interval [-14, 14] we need to use the formula:

[tex]f_{ave[/tex] = (1/(b-a)) × integral(a to b) f(x) dx

a and b are the limits of integration.

a = -14 and b = 14.

So we have:

[tex]f_{ave[/tex] = (1/(14 - (-14))) × integral(-14 to 14) (14 - |x|) dx

Simplifying the integral get:

[tex]f_{ave[/tex] = (1/28) × integral(-14 to 0) (14 + x) dx + (1/28) × integral(0 to 14) (14 - x) dx

Evaluating the integrals get:

[tex]f_{ave[/tex] = (1/28) × [(14x + (x²)/2)|(-14 to 0) + (-14x + (x²)/2)|(0 to 14)]

[tex]f_{ave[/tex] = (1/28) × [(0 + 98) + (-196 + 98)]

[tex]f_{ave[/tex] = (1/28) × 0

f_ave = 0

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For any positive number b not equal to 1 and any number or variable n, note that when evaluated, logb(bⁿ) = n.

A positive number is any integer that signifies something other than zero. Positive numbers include natural or counting numbers such as 1,2,3,4,5, fractions such as 3/5 or 232/345, and decimals such as 44.3.

Given logb(bⁿ)  and b is any positive number, not equal to 1 and n is any number

If Logₓ ([tex]y^{z}[/tex]) = z * logₓ (y)

Then

Log[tex]_{b}[/tex] (bⁿ) = n * Log[tex]_{b}[/tex] (b)

If logₓ(y) = log[tex]_{z}[/tex](y) / log[tex]_{z}[/tex](x)

Then

Log[tex]_{b}[/tex] (b) =  log[tex]_{z}[/tex] (b)/log[tex]_{z}[/tex] (b) = 1

Therefore,

Log[tex]_{b}[/tex] (bⁿ)  = n * Log[tex]_{b}[/tex] (bⁿ)

= n x 1

= n

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Full Question:

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

For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.

logb(b^n) =

with logb being the base

Answer:

Step-by-step explanation:

You want the quotient and remainder from division of (6x² +27x +17) by (x +4).

Synthetic division of a polynomial by a monic binomial is an easy way to perform the division without a lot of writing. The attachment pretty well describes the process.

The result is a quotient of 6x +3, and a remainder of 5.

__

Additional comment

A "monic" polynomial is one that has a leading coefficient of 1.

The number at upper left in the synthetic division tableau is the zero of the divisor. Using the negative of the divisor constant means we can add partial products, saving the confusion and error associated with subtraction.

Doing a change of units, we can see that 2.11 yd³ is equivalent to 1.7513 m³

We know that the relation between one yard and one meter is:

1yd = 0.91m

Then the relation between one cubic yard and one cubic meter is:

(1yd)³ = (0.91m)³

1 yd³ = 0.83 m³

Now we can perform a change of units between the volume in yards and the volume in meters, we will get:

2.11 yd³ = 2.11*(0.83 m³) = 1.7513 m³

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Answer:

The expression πr2h is a monomial because it is a single term that is the product of three variables: π, r2, and h. The term "mono" means "one," and "monomial" refers to a single term in algebraic expressions.

The degree of a monomial is the sum of the exponents of its variables. In this case, the degree of the monomial is 3, because the variables π, r, and h have exponents of 1, 2, and 1 respectively. Therefore, the degree of the monomial is 1 + 2 + 1 = 3.

Answer:

10.) 152 square feet

11.) 85 degrees

Step-by-step explanation: *Feel free to ask for an explanation*

The number of feet above the submarine is the shark is 23 feet.

Given that, a submarine is 42 feet below the surface of the water and shark is 19 feet below the surface of the water.

Here, location of shark = 42-19

= 23 feet

Therefore, the number of feet above the submarine is the shark is 23 feet.

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"Your question is incomplete, probably the complete question/missing part is:"

A submarine is 42 feet below the surface of the water a shark directly above the submarine is 19 feet below the surface of the water how many feet above the submarine is the shark.

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To calculate the area of her rectangular quilt, Mrs. Kuhn needs to multiply the length and width of the quilt in inches. Since each quilt square is 4 inches long, the calculation for the area of the quilt is:

Area of quilt = Length of quilt x Width of quilt x (4 inches) ^2

Therefore, the correct calculation for Mrs. Kuhn to determine the area of her quilt is the product of 4 inches times the sum of the length and width of the quilt.

The shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%. Option C

To determine the selling price of the pen in order to earn a 15% profit, we can use the concept of a profit margin.

Let's start by finding the cost price of the pen. Since the shopkeeper wants to make a 10% profit when selling the pen for Rs. 13.20, we can set up the equation:

Cost price + 10% profit = Selling price

Let's assume the cost price of the pen is C. Then, we can write theequation as:

C + 0.1C = 13.20

Simplifying the equation, we have:

1.1C = 13.20

Dividing both sides by 1.1, we find:

C = 12

So, the cost price of the pen is Rs. 12.

Now, to determine the selling price that will yield a 15% profit, we can use the formula:

Selling price = Cost price + Profit

Profit is calculated as a percentage of the cost price. In this case, the profit percentage is 15%. Substituting the values, we have:

Selling price = 12 + 15% of 12

Selling price = 12 + (0.15 * 12)

Selling price = 12 + 1.8

Selling price = 13.8

Therefore, the shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%.

The correct answer is option c. Rs. 13.80. Option C

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A statement that describes how the graph of his different from the graph of g include the following: D. The graph of h is the graph of g vertically shifted up 1 unit.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Conversely, the translation a geometric figure or graph upward simply means adding a digit to the numerical value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, we have:

(x, y)                               →                  (x, y + 1)

g(x) = x²

h(x) = g(x) + 1   → h(x) = x² + 1

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The value of the expression 20 − 9 ÷ m × 2 × n  for m = 3 and n = 2 is 8

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

20 − 9 ÷ m × 2 × n

The values of m and n are given as

m = 3 and n = 2

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

20 − 9 ÷ 3 × 2 × 2

Evaluate the quotient

So, we have

20 − 3 × 2 × 2

Evaluate the products

So, we have

20 − 12

Evaluate the difference

So, we have

8

Hence, the value of the expression is 8

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630 Liters of hardener will be added to 14 container of resins.

Given,

To add 45 of hardener to each container of resin.

Now,

Total number of containers = 14

Each container will have 45 hardener.

Let the amount of hardener to be added be x,

Then according to unitary method,

1 container = 45 hardener

14 container = x hardener

x = 630 liters.

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The area of the triangle is 85 square units

The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by:

A =  (1/2) [x₁(y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

Where:

B: (x₁, y₁) = (-8, 3)

O: (x₂, y₂) = (5, 4)

X: (x₃, y₃) = (-7, -10)

A =  (1/2) [x₁ (y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

A =  (1/2) [-8 (4 – (-10)) + 5(-10 – 3) + (-7)(3 – 4)]

A = (1/2) [-112 - 65 + 7]

A = 85 square units

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The actual distance from the starting point to the ending point is 39.96 miles.

For someone working with the map or scaled drawing, we can define the scale factor as the ratio between a distance on the drawing or map and the corresponding actual distance in the real world.

From the question,

1.5 inches on the map = 5 miles in actual distance

1 inch on the map =  x miles

Perform cross multiplication

1 inch on the map =  (5 x 1) / 1.5  = 3.33 miles/inch (scale factor)

The scale factor can then be expressed as ratio:

5/1.5 = 1:0.3

0r

5/1.5 = 10:3

So, the actual distance between the starting point and the ending point can be found by multiplying the length on the map by the scale factor:

Actual distance = Map distance x Scale factor

Actual distance = 12 inches x 3.33 miles/inch = 39.96 miles

Therefore, the actual distance from the starting point to the ending point is approximately 39.96 miles.

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The value of function (f о g) (5) would be,

⇒ (f о g) (x) = 26

We have to given that;

Functions f and g are,

⇒ f(x) = x + 1

⇒ g(x) = 5x

Now, We can formulate;

⇒ (f о g) (x)

⇒ f (g (x))

⇒ f (5x)

⇒ 5x + 1

At x = 5;

⇒ 5 × 5 + 1

⇒ 25 + 1

⇒ 26

Thus, The value of function (f о g) (5) would be,

⇒ (f о g) (x) = 26

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The difference of the expression in scientific notation is 1.2 * 10⁸

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

(5.6 * 10⁸) - (4.4 * 10⁸)

Factor out 10⁸ from the expression

So, we have

(5.6 * 10⁸) - (4.4 * 10⁸) = (5.6 - 4.4) * 10⁸

Evaluate the difference

(5.6 * 10⁸) - (4.4 * 10⁸) = 1.2 * 10⁸

Hence, the difference of the expression in scientific notation is 1.2 * 10⁸

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The relation shown in the graph is not a function because it violates the vertical line test.

We have,

The relation shown in the graph is not a function because it violates the vertical line test.

The vertical line test states that for a relationship to be a function, every vertical line drawn on the graph should intersect the graph at most once.

However, in this case, the U-shaped graph intersects the vertical line at multiple points, such as (-2, -2) and (2, 2).

Therefore, the relation does not meet the criteria of a function.

Thus,

The relation shown in the graph is not a function because it violates the vertical line test.

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The length of XY in the congruent triangle is 8 units.

'

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

Therefore, the triangle XYZ is congruent to the triangle MNL.

Hence,

ΔXYZ ≅ ΔMNL

Therefore,

XY = MN

XZ = ML

YZ = NL

Hence,

XY = MN = 8 units

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The range is 5 years.The median is 18 years.

To determine the range and median from the given dot plot of ages, we need to analyze the distribution of the data points.

The range represents the difference between the maximum and minimum values in a dataset. Looking at the dot plot, the minimum age appears to be 16, while the maximum age is 21. Therefore, the range can be calculated as:

Range = Maximum age - Minimum age = 21 - 16 = 5 years.

Thus, the range of the ages of employees at the summer camp is 5 years.

The median represents the middle value in a dataset when it is arranged in ascending or descending order. To determine the median, we need to organize the ages in order from least to greatest:

16, 17, 18, 19, 20, 21

Since there are six data points, the median would be the value in the middle. In this case, the median would be the third value, which is 18.

Therefore, the median of the ages of employees at the summer camp is 18 years.

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The probability that exactly 3 of those games were won by the colonies is 25%.

We are given that;

Number of colonies= 4

Number of games= 3

Now,

To find the probability of exactly 3 wins out of 4 games, we can use the binomial probability formula1:

P(X = 3) = nCx * p^x * q^(n-x)

where n is the number of trials (4 games), x is the number of successes (3 wins), p is the probability of success (0.5), q is the probability of failure (1 - p = 0.5), and nCx is the combination of n things taken x at a time.

P(X = 3) = 4C3 * 0.5^3 * 0.5^(4-3) P(X = 3) = (4! / (3! * (4-3)!)) * 0.125 * 0.5 P(X = 3) = (24 / (6 * 1)) * 0.0625 P(X = 3) = 4 * 0.0625 P(X = 3) = 0.25

Therefore, by the probability the answer will be 25%.

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The mean of the test is 45.

Let's use the formula for z-score:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the raw score, μ is the mean, and σ is the standard deviation.

For the first score of 30, we know that it falls three standard deviations below the mean:

-3 = (30 - μ) / σ

Simplifying this equation, we get:

-3σ = 30 - μ

μ = 30 + 3σ

For the second score of 60, we know that it falls three standard deviations above the mean:

3 = (60 - μ) / σ

Simplifying this equation, we get:

3σ = 60 - μ

μ = 60 - 3σ

Now we can set these two equations equal to each other, since they both equal μ:

30 + 3σ = 60 - 3σ

6σ = 30

σ = 5

Now we can plug this value of σ back into one of the equations for μ:

μ = 30 + 3σ

μ = 30 + 3(5)

μ = 45

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The area of the given kite is,

⇒ A = 26 units²

Now, In this case we have that the area of the kite is given by the area of two triangles,

And, the triangles share the same base with length,

2 + 2 = 4.

And, One of the triangles has height of 6 and the other has height of 7.

So, the total area of kite is,

A = 1/2 × 4 × 6 + 1/2 × 4 × 7

A = 12 + 14

A = 26 units²

Therefore, The area of the given kite is,

⇒ A = 26 units²

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Answer:6??

Step-by-step explanation:

A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

Given that;

Function is,

⇒ f (x) = x³ - 3x² - 7x + 6

Now, We can check (x + 2) is a factor of function or not as;

If x + 2 is a factor of function, then x = - 2 is satisfy the function.

So, Put x = - 2;

⇒ f (x) = x³ - 3x² - 7x + 6

⇒ f (- 2) = (- 2)³ - 3 (- 2)² - 7 (- 2) + 6

⇒ f (- 2) = - 8 - 12 + 14 + 6

⇒ f (- 2) = 0

Thus, (x + 2) is a factor of the function,

Hence, We can find all the zeroes as;

(x + 2) ) x³ - 3x² - 7x + 6 (x² - 5x + 3

          x³ + 2x²

         ------------

              - 5x² - 7x

              - 5x² - 10x

              ----------------

                       3x + 6

                       3x + 6

                      ------------

                              0

Thus, We get;

⇒ x³ - 3x² - 7x + 6

⇒ (x + 2) (x² - 5x + 3)

Since, x² - 5x + 3 = 0

x = - (- 5) ± √(- 5)² - 4×1×3 / (2×1)

x = (5 ± √25 - 12) / 2

x = (5 ± √13)/2

Thus,

A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

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Answer:  C  y-1=7 (x+4)

Step-by-step explanation:

Point slope formula

y - y₁ =  m ( x - x₁ )        Where m= slope and (x₁ , y₁) is your point

Given:

point: (-4, 1); slope: 7

plug in to formula

y -  1 = 7 (x+4)

Answer:

1 is a

2 is c

3 is b

Step-by-step explanation:

The setting of a novel is important because it provides the reader with context on the time, place, and environment that the story takes place in.

It aids in setting the tone, showcasing personalities and tensions, and offering hints about the story's message.

One can establish an ambiance or emotional tone in a novel by means of its setting. One illustration can be seen in the book "The Great Gatsby" authored by F. Scott Fitzgerald uses the backdrop of the Jazz Age to generate a feeling of splendor and exhilaration.

The rapid tempo of the book mirrors the busy lives led by the characters, while the opulent festivities and luxurious habits of the affluent are employed to cultivate an air of indulgence and debauchery.

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The full question is:

On the importance of setting in the novel, comment on how it can be used to create a sense of realism, atmosphere, and meaning?