Graph the equation and identify the asymptotes. y = x^2 - x + 1 / x + 1

The given function f(x) = 2 cos (x) is an even function because the result of the cosine of negative angles are the same with those of positive angles.

Function in mathematics?

The core of mathematical calculus is functions. The unique types of relations are the ones with functions. Mathematical functions are represented as a rule that, for each input x, produces a distinct result. In mathematics, a function is represented by a mapping or transformation.

The function is even if f(-x) = f(x)

The function is odd if f(-x) = -f(x)

We are given the function as; f(x) = 2 cos (x)

f(-x) = 2 cos (-x)

Now, we know that the cosine of a negative angle always gives the same value as the cosine of the positive angle and as such, we can say that;

2 cos (-x) = 2cos (x)

The same result as f(x) which tells us that it is an even function.

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The complete question is -

In two or more complete sentences, describe how to determine if the function f(x)=2cos(x) is even by looking at a graph.

The y-intercept of the line of fit is approximately 43.94 fluid ounces.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The answer is 35. If the theoretical probability of drawing two yellow socks is one fifth, then the experimental probability of drawing two yellow socks in one trial with replacement is also one fifth. Therefore, out of 175 trials, the number of times he will select two yellow socks can be predicted by multiplying the number of trials by the experimental probability: 175 * (1/5) = 35.

No, because for each input there is not exactly one output. The relation is not a function because for the input x = -5, there are two possible outputs: y = 1 and y = -1. Therefore, the relation violates the vertical line test, which requires that every vertical line intersects the graph at most once for the relation to be a function.

The y-intercept of the line of fit is approximately 43.94 fluid ounces. To find the y-intercept, we can look at the point where the line of fit intersects the y-axis (i.e., when x = 0). From the equation of the line of fit, we can see that the y-coordinate when x = 0 is approximately 43.94, which represents the initial amount of diet soda in the machine before it starts to be purchased.

Therefore,  The y-intercept of the line of fit is approximately 43.94 fluid ounces.

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The exponential function in this problem represents a decay, with a percentage rate of 6%.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function is classified as growth or decay as follows:

The function in this problem is defined as follows:

y = 15(0.94)^x.

As |b| = 0.94 < 1, the function is a decay function, and the rate is obtained as follows:

1 - r = 0.94

r = 1 - 0.94

r = 0.06

r = 6%.

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Answer:

Having outliers

Step-by-step explanation:

Let's observe one by one

#1

#2

Yes it can affect because outlier may differ from original one

#3

Using a large samples will make the error 0

Answer:

A:The Reqd. No. of Permutations=3360

Step-by-step explanation:

I couldn’t find the answer to B..sorry

PROBLEM

Function

Table

y =

The limit of [f(x + h) - f(x)]/h as it approaches 0 is (a) 12x²

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

f(x) = 1 - 4x³

The limit is given as

[f(x + h) - f(x)]/h

Calculate f(x + h)

So, we have

f(x + h) = 1 - 4(x + h)³

Expand

f(x + h) = 1 - 4(x³ + 3x²h + 3xh² + h³)

Substitute f(x + h) = 1 - 4(x³ + 3x²h + 3xh² + h³) in [f(x + h) - f(x)]/h

So, we have

[f(x + h) - f(x)]/h = [1 - 4(x³ + 3x²h + 3xh² + h³) - 1 + 4x³]/h

Open the brackets

[f(x + h) - f(x)]/h = [1 - 4x³ + 12x²h + 12xh² + 4h³ - 1 + 4x³]/h

Evaluate the like terms

[f(x + h) - f(x)]/h = [12x²h + 12xh² + 4h³]/h

Divide

[f(x + h) - f(x)]/h = 12x² + 12xh + 4h²

Limit h to 0

[f(x + h) - f(x)]/h = 12x² + 12x(0) + 4(0)²

Evaluate

[f(x + h) - f(x)]/h = 12x²

Hence, the limit is 12x²

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Expression would be,

\(E[r_n^2] = \sum \ x^2 * (n choose x) * (1/4)^x * (3/4)^(n-x)\)

What is Unrestricted symmetric ?

The unrestricted, one-dimensional, symmetric random walk represented as Pascal's triangle.

In a two-dimensional unrestricted symmetric random walk, the particle moves in one of four directions (up, down, left, or right) with equal probability at each step. The distance of the particle from the origin after the nth step, \(r_n,\) is given by the square root of the sum of the squared x and y coordinates of the particle at that time.

The expected value of\(r_n^2\), denoted as \(E[r_n^2]\), is given by:

\(E[r_n^2] = \sum\ P(r_n^2 = x^2) * x^2\)

where the sum is taken over all possible values of \(x^2\).

Since the particle moves with equal probability in each of the four directions, we can calculate the probability that the particle is at a particular x and y coordinate using the binomial distribution:

\(P(x, y) = (n \ choose\ x) * (1/4)^x * (3/4)^(n-x)\)

Substituting this expression into the formula for \(E[r_n^2]\) and summing over all possible values of x and y, we get:

\(E[r_n^2] = \sum \ x^2 * (n choose x) * (1/4)^x * (3/4)^(n-x)\)

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The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

Answer:

whats the queston ;-;

Step-by-step explanation:

Answer:

220 i think that the answer

Answer:

8

Step-by-step explanation:

First, let’s say the number is x

Then follow the steps

12x+6

36x+18

36x+9

12x+3=99

So x=8

The length of side X in simple radical form with a rational denominator is 10/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 2 × 5/√3

Hypotenuse, x = 10/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probabiltiy that when a marble is chosen from the bag at random then choosen marble is blue is 1/2.

Given that the bag has 6 red marble and 6 blue marbles. Now, a marble is chosen from the bag at random. Therefore, the probabiltiy that choosen marble is blue is:

Probability(Blue Marble)

= Number of blue marbles / Total number of marbles in the bag

= 6/ 12

= 1/ 2

Hence, the probability is 1/2.

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The complete question must be:

A bag with 6 red marbles has 6 blue marbles. A marble is chosen from the bag at random. What is the probability that it is blue? Write your answer as a fraction in simplest form.

There are three area options for the number of bricks:

The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:

n = A / A'

A' = w · h

Where:

There are three possible answers:

Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm

A' = 22.5 · 10

A' = 225

n = 93750 / 225

n = 416.667

n = 416

Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm

A' = 22.5 · 7.5

A' = 168.75

n = 93750 / 168.75

n = 555.556

n = 555

Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm

A' = 10 · 7.5

A = 75

n = 93750 / 75

n = 1250

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Answer:

C. 101 3/4; $1017.50

Step-by-step explanation:

Correct on E2020!

The correct answer is System 1: Infinitely many solutionsSystem 2: One solutionSystem 3: No solution

Let's analyze each system of linear equations and determine the number of solutions they have.

y = x + 6 and 3x - 3y = -18

In this system, the first equation is a linear equation in slope-intercept form, and the second equation is a linear equation in standard form. The two equations represent the same line. Since they are the same line, they intersect at infinitely many points. Therefore, this system has infinitely many solutions.

y = -4x + 11 and -6x + y = 11

Both equations in this system are in slope-intercept form. The slopes of the two lines are different (-4 and -6), indicating that the lines are not parallel. Since the lines are not parallel and have different slopes, they intersect at a single point. Therefore, this system has one solution.

y = -2x + 5 and 2x + y = -7

Both equations in this system are in slope-intercept form. The slopes of the two lines are equal (-2 and 2), but their y-intercepts are different. When the slopes are equal and the y-intercepts are different, the lines are parallel and do not intersect. Therefore, this system has no solution.

Matching the systems with the correct number of solutions:

System 1: Infinitely many solutions

System 2: One solution

System 3: No solution

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Answer:

175%

Step-by-step explanation:

70 = p * 40

p = 1.75 or 175%

Answer:

Step-by-step explanation:

175%

Answer:

1.y=-2x+7

2. no

3.yes

Step-by-step explanation:

The population of the island after 10 years will be approximately 2385.

The formula for exponential growth is \(y = y_0e^{(kt)}.\)

The formula for exponential decay is \(y = y_0e^{(-kt)}\).

Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.

Given,  an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.

∴ The population be 10 years from now will be,

\(y_{10} = y_0e^{(0.03)\times10}\).

We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.

\(y_{10} = 1767e^{0.3}\).

\(y_{10} = 1767\times1.35\).

\(y_{10} = 2385\).

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Answer:

128

Step-by-step explanation:

32 + 32+32+32=128

SIMPLE

*this answer i made was incorrect please avoid it*

Answer:

15

Step-by-step explanation:

Pythagoras theorem

a^2+b^2=c^2

12*12=144

9*9=81

144+81=225

sq root of 225 = 15

Answer:

Profit function: P(x) = -0.5x^2 + 40x - 300  

profit of $50: x = 10 and x = 70

NOT possible to make a profit of $2,500, because maximum profit is $500

The maximum profit is of $500, So it is impossible to achieve the profit of $2500.

Profit = Revenue - Cost

Given information:

The function which shows revenue is \(90x-0.5x^2\)

The cost function \(C(x) = 50x+300\)

\(R(x) = 90x-0.5x^2\)

Profit = Revenue - Cost

\(P(x) = 90x-0.5x^2 - 50x - 300\\\\P(x) =-0.5x^2 - 40x - 300\)

On equating with profit of $50,

We get,

\(P(x) =-0.5x^2 - 40x - 300\\\\50 =-0.5x^2 - 40x - 300\\\\x^{2} - 80x +700 = 0\)

The profit of $50: x = 10 and x = 70

Hence, for the maximum value of profit the coordinate of vertex is given;

x = 80 / 2 = 40

Putting the above value in profit equation

\(x^{2} - 80x +700 = 0\\\\40^{2} - 80(40) +700 \\\\P(40) = 500\)

Hence, the maximum profit is of $500, So it is impossible to achieve the profit of $2500.

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Answer:

4

Step-by-step explanation:

8+y+g+0= 4

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

The 164° and 81° located with the angle x at a point indicates that the size of the angle x is 115°

The angles that are arranged around a point add up to 360°. The angles at a point are the angles which together, produce a rotation of 360°.

The sum of angle at a point can be used to find the measure of the angle x as follows;

The addition of angles at a point = 360°

Therefore; 164° + 81° + x = 360°

Therefore; x = 360° - (164° + 81°) = 115°

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6,900 times is the answer,also can i get brainliest

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

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

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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Answer:

second option

Step-by-step explanation:

Answer:

In mathematics, a function is a binary relation between two sets that associates each element of the first set to exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers.

Ex 1: x2 (squaring) is a function.

Ex 2: x3+1 is also a function.

Step-by-step explanation: really hope this helps.