How are lim p(x) and lim p(x) calculated if p is a polynomial function?

If the angle of depression to the buoy is 250, then the buoy is approximately 47.2 meters from the base of the lighthouse.

What is angle of depression ?

The angle of depression is the angle between a horizontal line of sight and the line of sight from an observer to a point or object that is lower than the observer. It is commonly used in trigonometry and geometry problems that involve the height or depth of an object relative to an observer or the ground.

We can start by drawing a diagram to visualize the situation.

In the diagram, A represents the location of the lighthouse, B represents the location of the buoy, and x represents the distance from the base of the lighthouse to the buoy that we want to find.

Since the angle of depression from the lighthouse to the buoy is 25 degrees, we know that angle ABx is also 25 degrees. We also know that the height of the lighthouse above sea level is 22 meters.

We can use the tangent function to find the value of x:

tan(25°) = opposite / adjacent

tan(25°) = 22 / x

Solving for x, we get:

x = 22 / tan(25°)

x ≈ 47.2 meters

Therefore, the buoy is approximately 47.2 meters from the base of the lighthouse.

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The function rule for the line that passes through the origin and (-6,-12) is y = 2x.

In mathematics, a function is a rule that assigns to each element in a set a unique output value.

To find a function rule for the line that passes through the origin (0,0) and the point (-6,-12), we first need to determine the slope of the line. The slope of a line represents the rate of change between the x and y coordinates. We can find the slope using the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) represents the coordinates of the first point, and (x₂, y₂) represents the coordinates of the second point.

Using the given points, we can substitute in the values:

slope = (-12 - 0)/(-6 - 0)

slope = -12/-6

slope = 2

Now that we have the slope, we can use the point-slope form of a linear equation to find the function rule:

y - y₁ = m(x - x₁)

where m is the slope, and (x₁, y₁) represents the coordinates of a point on the line.

Substituting in the values we have so far, we get:

y - 0 = 2(x - 0)

y = 2x

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The polynomial (x-a)(x-b)(x-c)....(x-z) has a coefficient of -351 for the x²⁵ term. Since there are 26 variables, the sum of all coefficients is 2²⁵, or 33554432.

The polynomial (x-a)(x-b)(x-c)....(x-z) can be written as

x²⁶ - (a+b+c+...+z)x²⁶ + (sum of products of pairs)x²⁴ - ... - abc...xyz

The coefficient of x²⁵ is the negative sum of the constants, which is -(a+b+c+...+z). Since there are 26 variables in total, the sum of the constants is just the sum of the first 26 letters of the alphabet, which is

(a+b+c+...+z) = 1 + 2 + 3 + ... + 26 = 351

So the coefficient of x²⁵ is -351.

To find the sum of all the coefficients, we can simply evaluate the polynomial when x = 1. At x = 1, each term in the polynomial is just the product of some combination of (1-a), (1-b), (1-c), ..., and (1-z). Since each variable is a letter from the alphabet, each term is either 0 or 1, depending on whether the corresponding letter is equal to 1 or not.

The sum of all the coefficients is therefore just the number of terms in the polynomial that are equal to 1.

Since there are 26 variables, there are 2²⁶ possible combinations of (1-a), (1-b), (1-c), ..., and (1-z), and exactly half of them are equal to 1 (since each variable is either 0 or 1 with equal probability). Therefore, the sum of all the coefficients is

2²⁵ = 33554432

So the sum of the coefficients of the polynomial (x-a)(x-b)(x-c)....(x-z) is 33554432.

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The expression equivalent to  -2x +3+ 7y + 4x -5 is 2x+7y-2.

What exactly are expressions?

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.

Now,

Given expression is   -2x +3+ 7y + 4x -5

writing same terms together

=4x-2x+7y+3-5

=2x+7y-2

hence,

             The expression equivalent to  -2x +3+ 7y + 4x -5 is 2x+7y-2.

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Answer:

JGK = 29 degrees

Step-by-step explanation:

i hope this helped :)

We can write (15 + 45) as a product of 2 factors using GCF and the distributive property 15(1 + 3).

We are given the following expression-

15 + 45

Now, we can factorize 15 into prime factors as follows -

= 3 × 5 (15 × 1)

Similarly, we can factorize 45 into prime factors as follows -

= 3 × 3 × 5 (15 × 3)

Thus, the greatest common factor of 15 and 45 is 15, so we can

= 15 × 1 = 15 and 15 × 3 is 45

Hence, we can write (15 + 45) as 15(1 + 3).

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Answer:

Step-by-step explanation:

i have no idea sorry

Answer:

Ac = 0.833334.

Step-by-step explanation:

SINCE THE QUESTION IS PYTHAGORAS THEOREM.

THE FORMULA IS

[tex] tan = \frac{ |bc| }{ac} [/tex]

From the question tan = 18°

bc = 15

ac= ?

making ac = x

therefore

[tex] tan = \frac{ |bc| }{ |ac| } \\ tan 18 = \frac{15}{x} \\ tan18(x) = x \times \frac{15}{x} \\ tan18x = 15 \\ = \frac{tan18x}{18} = \frac{15}{18} \\ x = 0.8333334[/tex]

therefore x = 0.8333334.

The inequality 26/9 > x represents a line with an open circle at 26/9 going toward positive infinity represented by an arrow.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality [tex]2\frac{8}{9} > x[/tex].

26/9 > x.

Now, As the inequality is strictly greater than 26/9 it would be represented by a line open circled at 26/9 and going towards +∞.

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Answer:

C. Addition Property of Equality

Step-by-step explanation:

From step 4 to step 5, 20 is added to both sides.

Answer: Addition Property of Equality

The required adult tickets and 104 child tickets, which gives a total revenue of $1820.

An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 = 10. "X" in this case is a variable.

Let x be the number of adult tickets sold and y be the number of child tickets sold.

We know that the total number of tickets sold is 220:

x + y = 220

We also know that the total revenue from ticket sales is $1820:

13x + 3y = 1820

We can use the first equation to solve for y in terms of x:

y = 220 - x

Substituting this into the second equation, we get:

13x + 3(220 - x) = 1820

Simplifying this equation:

10x + 660 = 1820

10x = 1160

x = 116

Therefore, the theater sold 116 adult tickets last night.

To check, we can substitute x = 116 into the equation for y:

y = 220 - x = 220 - 116 = 104

So, the theater sold 116 adult tickets and 104 child tickets, which gives a total revenue of $1820.

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The probability that the ninth woman to appear is in position 17 is about 5.59%

We can approach this problem by using the binomial probability distribution. Let X be the number of women among the first 16 people in the line. Then X follows a binomial distribution with parameters n = 16 and p, the probability that any given person among the first 16 is a woman. We want to find the probability that X = 8, since this means that the ninth woman to appear is in position 17.

The probability of any given person being a woman is not specified in the problem, but we can assume that it is 0.5 for simplicity. Therefore, p = 0.5, and we can use the binomial probability formula:

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

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. In this case, it gives the number of ways to choose k women from the first 16 people in the line.

Using this formula with n = 16 and k = 8, we get:

P(X = 8) = (16 choose 8) * 0.5^8 * 0.5^8

= 12870 * 0.00390625

= 50.27

This means that the probability of exactly 8 women appearing among the first 16 people in the line is about 50.27%.

Given that there are 8 women among the first 16 people, the probability that the ninth woman appears in position 17 is 1/9, since there are 9 possible positions for the ninth woman to appear, and they are all equally likely.

Therefore, the overall probability that the ninth woman to appear is in position 17 is:

P(X = 8) * (1/9) = 50.27% * (1/9) = 5.59%

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a) Number of kgs independent variable, the amount charged by the company is the dependent variable.

b) The equation is y= 400+ 0.04x.

c) The equation is used to calculate a table of values with four sets of values to show the moving costs for 0 – 25,000 kg.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

It is given that a moving company charges $400 plus 0.04 per kg to move a family from Toronto to Windsor.

a) The number of kgs is the independent variable and the amount charged by the company is the dependent variable because it depends on the number of kgs the family is willing to move.

b) The equation that represents the given data is y= 400+ 0.04x

where y is the total amount charged by the company, and x is the number of kgs.

c) For 4 different values of x between 0 - 25,000 we will find values of y.

x                      y= 400+ 0.04x

6250               650

12500             900

18750              1150

25000             1400

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Option D (x, y)→ (-2x, 2y) is the transformation that maps triangle UVW to triangle EFG.

In mathematics, a transformation refers to a process of changing the position, size, or orientation of a geometric shape. It is a fundamental concept in geometry, algebra, and other branches of mathematics that studies the properties of objects and their relationship with space.

Transformations can be classified into two main types: rigid and non-rigid transformations. Rigid transformations preserve the size and shape of the object while changing its position and orientation. Common examples of rigid transformations are translations, rotations, and reflections. Non-rigid transformations, on the other hand, change the size and shape of the object as well as its position and orientation.

Transformations are used in various areas of mathematics and science, such as computer graphics, physics, and engineering. They are also important in real-world applications, such as in designing and modeling objects, analyzing data, and solving practical problems.

The transformation involves a reflection across the y-axis (multiplication by -1 on the x-coordinate) and a dilation by a factor of 2 in the y-direction (multiplication by 2 on the y-coordinate).

Applying this transformation to the coordinates of triangle UVW:

(0, -2) -> (0, -4)

(2, 0) -> (-4, 0)

(-2, 2) -> (4, 4)

These transformed coordinates match the coordinates of triangle EFG, so option D is the correct answer.

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The value of x is given as follows:

x = 131º.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Considering the above text, the measure of the top angle of the bottom triangle is given as follows:

a = 180 - 98

a = 82.

The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence:

2b + 82 = 180

2b = 98

b = 49.

(the sum of the measures of the internal angles of a triangle is of 180º).

Considering the vertical angles, the base angles of the top triangle are given as follows:

b = 49.

Hence the value of x is given as follows:

x = 180 - 49

x = 131º.

(as the top triangle is also isosceles, and the angle measure x is the exterior angle of an interior angle with measure of 49º).

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Answer:

no solution

Step-by-step explanation:

- x + 6y = 9 → (1)

- 4x + 24y = 48 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x and y

4x - 24y = - 36 → (3)

add (2) and (3) term by term

0 + 0 = 12

0 = 12 ← false statement

this false statement indicates the system has no solution

Answer: To solve the system of equations using substitution, we'll start by rearranging one of the equations so that one of the variables can be expressed in terms of the other. In this case, we'll rearrange the second equation to find y in terms of x.

y = 2x + 4

Next, we'll substitute this expression for y into the first equation:

+3x + 5(2x + 4) = 7

Expanding the right-hand side:

+3x + 10x + 20 = 7

Combining like terms:

13x + 20 = 7

Subtracting 20 from both sides:

13x = -13

Dividing both sides by 13:

x = -1

Finally, we'll use the expression we found for y in terms of x to find the corresponding value of y:

y = 2x + 4

y = 2(-1) + 4

y = -2 + 4

y = 2

So the solution to the system is (x, y) = (-1, 2).

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{250 {h}^{4} {k}^{5} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(2 \times 5 \times 5 \times 5) \times (h \times h \times h \times h )\times (k \times k \times k \times k \times k} )[/tex]

[ take out one of the pair ~ ]

[tex]\qquad \sf  \dashrightarrow \: 5 \times h \times h \times k \times k \sqrt{2 \times 5 \times k} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 5 {h}^{2} {k}^{2} \sqrt{10k} [/tex]

That's our simplified answer ~

Answer:

<--> V 250h4k5

√(2 × 5 × 5 × 5) × (h×h×h×

[ take out one of the pair ~]

5 xhxhxkx k√2 × 5 × k

--> 5h2k2✓10k

Answer:

Cos A: [tex]\frac{15}{17}[/tex]

Tan A: [tex]\frac{8}{15}[/tex]

Sin C: [tex]\frac{8}{17}[/tex]

How I did it:

Cos A: [tex]\frac{Base}{Hypotenuse}[/tex] This is the basic " fraction "

Or in similar terms: = [tex]\frac{ab}{bc}[/tex]

Cos A = [tex]\frac{15}{17}[/tex]

Tan A = [tex]\frac{Perpendicular}{Base}[/tex]

Similar terms once again = [tex]\frac{ac}{ab}[/tex]

Tan A = [tex]\frac{8}{15}[/tex]

Sin A = [tex]\frac{Perpendicular}{Hypotnuse}[/tex]

Similar terms = [tex]\frac{ac}{bc}[/tex]

Since A = [tex]\frac{8}{17}[/tex]

Thus your answers are:

Cos A = [tex]\frac{15}{17}[/tex]

Tan A = [tex]\frac{8}{15}[/tex]

Sin A = [tex]\frac{8}{17}[/tex]

Answer: the perimeter of the polygon is 29cm

Step-by-step explanation:

Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice

What is a formula of area of triangle?

To calculate the area of a triangle, use the formula area = 1/2 * base * height.

To find the area of triangle ABC, we can use the formula:

Area = (1/2) * base * height

where the base and height are the dimensions of the triangle that form a right angle.

In this case, we don't have the dimensions of the triangle that form a right angle, but we know that the triangle has two angles that are 60 degrees each. This tells us that the triangle is an equilateral triangle, and all three sides are equal.

Let's call the length of each side "s". Then, we can use the formula for the area of an equilateral triangle:

[tex]Area = (\sqrt(3)/4) * s^2[/tex]

Plugging in the given value of 12 for s, we get:

[tex]Area = (\sqrt{(3)/4) * 12^2}\\\\ Area \ = (\sqrt{(3)/4) * 144} \\\\Area = 36\sqrt{(3)}[/tex]

Therefore, the area of triangle ABC is [tex]36\sqrt(3)[/tex] square units.

Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice.

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Answer: (2) $17,200

Step-by-step explanation:

We know the commission = 4,300. So we need to find a number (Let's x) times 25% (equal to 0.25) equal to 4,300

Put all that into an equation: x times 0.25 = 0.25x

0.25x=4,300

Now, all we need to do is solve for x.

Divide both sides by 0.25 to get 17200

Answer:

The sum of the digits in the mystery year is 9

Step-by-step explanation:

Let me try to help you

given the number of packages of hot dogs is d

given the number of packages of buns is b

so the total of hot dogs = total of buns

=> 8d = 6b or 4d = 3b

The number can be only integers like 1, 2, 3, 4, 5

So the smallest integer for d is 3 and b is 4

If you buy 3 packages of hot dogs, the number of hot dogs is 3 x 8 = 24

If you buy 4 packages of bun, the number of buns is 4 x 6 = 24

Divide #hot dogs by #packages of buns

So 24/4 = 6

Divide the result by 1/3

6 / (1/3) = 18

Sum of the digits

1 + 8 = 9

Hope this helps

Answer: You have read 560 pages.

Step-by-step explanation:

70 divided by 100 x 800 = 560.

Answer:

Step-by-step explanation:

800(.70)= 560 pages that have been read

In the context of John's baking, the vertex with the maximum profit represents the point where John can maximize his profit. The vertex of a parabola represents the point at which the function reaches its maximum or minimum value.

The profit function is often modeled as a quadratic equation, where the vertex represents the maximum point of the parabola. In this case, the profit function may be a function of the number of cakes or pastries sold, the price at which they are sold, and the cost of producing them. When the profit is maximized at the vertex, it means that John is producing and selling the optimal number of cakes and pastries at the optimal price to maximize his profit. The vertex represents the sweet spot for John's baking business, where he can earn the most profit with the least amount of costs. Therefore, understanding the meaning of the vertex with the maximum profit is important for John to make informed decisions about his business, including the optimal number of cakes and pastries to produce, the price to sell them, and how to allocate his resources to maximize his profits.

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Answer:

Step-by-step explanation:

no idea. i  have a idea!

do it your self

Answer:

y=5

divide 40 by 8

times 5 by 8 to check your solution

Answer:

see explanation

Step-by-step explanation:

40 = 8y ( isolate y by dividing both sides by 8 )

5 = y

As a check

substitute y into the right side of the equation and if both sides are equal then it is the solution.

right side = 8y = 8 × 5 = 40 = left side

since both sides are equal then y = 5 is the solution to the equation

The axis of symmetry of the function is x=-1.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is h(x)=(x+1)²-4.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (-1,-4)

Focus: (-1,-15/4)

Axis of Symmetry: x=-1

Directrix: y= -17/4

Plot the points (-3, 0), (-2, -3), (-1, -4), (0, -3) and (1, 0)

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (1,0),(-3,0)

y-intercept(s): (0,-3)

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

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The statement that correctly compares the two functions is

They have the same x-intercept and the same end behavior as x approaches ∞.

A function's final behaviour is represented by the value of f(x) as x approaches infinity. Both functions in this scenario have the same final behaviour because they both have unbounded growth, or they both go to positive infinity.

To find y-intercept of a function we have to put x= 0

So, The y-intercept of f(x) is y = -3.

and, The y-intercept of g(x) is y = -4.

To  find x -intercept of a function put y = 0

So, The x-intercept of f(x) is x = 1.

and, The x-intercept of g(x) is x = 1.

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Answer:

[tex]\mbox{\large a_n = 2 + 5n}[/tex]

Step-by-step explanation:

The sequence is 7  12  17  22

This is an arithmetic sequence where any two successive terms is a constant known as the common difference

The difference between any two successive terms is 5

The common difference is 5

The nth term can be found by the expression

[tex]a_n = a_1 + d(n-1)[/tex]

where

[tex]a_n \textrm{ is the $n^{th}$ term}[/tex]

[tex]\mathrm{a_1\;is\;the\;first\;term}[/tex]

[tex]\mathrm{d\;is\;the\;common\;difference}\\[/tex]

In this sequence

[tex]a_1 = 7\\d = 5\\[/tex]

[tex]a_n = 7 + 5(n-1)\\\\a_n = 7 + 5n - 5\\\\a_n = 2 + 5n[/tex]

We can verify that this is correct is to determine the 5th term of the sequence which should be 22 + 5 = 27

Applying the expression for 5th term

[tex]a_5 = 2 + 5(5)\\= 2 + 25\\= 27[/tex]