Find the ratio, n, between the length of side DE and length of the corresponding side AB.

Answer:

The expression a2+a4+a6+a8+......a20 can be written in sigma notation as:

∑ a(2n) where n = 1 to 10

To expand this summation, we can substitute in the values of n and evaluate the series:

a(21) + a(22) + a(23) + ... + a(210) = a2 + a4 + a6 + ... + a20

The expression (-1) + 2 +(-3) + 4 + (-5) ....+(-25) can be written in sigma notation as:

∑ (-1)^n*n where n = 1 to 25

To expand this summation, we can substitute in the values of n and evaluate the series:

(-1)^11 + (-1)^22 + (-1)^33 + ... + (-1)^2525 = -1 + 2 - 3 + 4 - 5 +... - 25

Note that the series (-1)^n*n is an alternating series, where the signs of the terms alternate between positive and negative. This series has no closed form solution, but we can evaluate them by adding and subtracting each term.

Answer:

[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}[/tex]

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]

Step-by-step explanation:

Sigma notation means the sum of the series.

Given series:

Therefore:

So each term is a₂ₙ

Therefore, the expression in sigma notation is:

[tex]\displaystyle \sum_{n=1}^{10}a_{(2n)}[/tex]

Given series:

The absolute value of each term of the series is n.

The signs of each term alternate between negative and positive.

Therefore, the expression in sigma notation is:

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]

The expansion of each summation has been given in Part I.

However, the full expansions are:

[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=(-1)+2+(-3)+4+(-5)+6+(-7)+8+(-9)+10+(-11)+12+\\\phantom{wwwwwwww}(-13)+14+(-15)+16+(-17)+18+(-19)+20+(-21)+22+\\\\\phantom{wwwwwwww}(-23)+24+(-25)[/tex]

The evaluation of each series is:

[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=-13[/tex]

Answer:

[tex]\boxed{12.7\;inches}[/tex]

Step-by-step explanation:

For a circle of radius r, the circumference is given by the expression

C = 2πr

So for this circle of radius 9", the circumference is 2 x π x9 = 18π

The entire circle covers a total angle of 360°

If there is a sector of the circle that is subtended by an angle Ф, then the length of that arc will be Ф/ 360  x C

Here Ф = 81°

So length of arc is

[tex]\dfrac{81}{360} \times 18 \pi\\\\\\\textrm {Using a calculator this works out to }\\\\[/tex]

[tex]\dfrac{81}{360} \times 18 \pi = 12.72345\\\\[/tex]

Rounded to the nearest tenth of an inch this would be
[tex]\boxed{12.7\;inches}[/tex]      ANSWER

Check the picture below.

The end-behavior of the polynomial is:

A) f(x) → -∞, as x → -∞

f(x) →∞, as x → ∞

What in mathematics is a polynomial?

The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation. In mathematics, variables are occasionally referred to as indeterminates. An example of a polynomial with a single variable x is x2 4x + 7.

The leading term of the polynomial is -2x⁴, which is negative for negative x and positive for positive x. As x approaches negative infinity, -2x⁴ approaches negative infinity, so the entire polynomial approaches negative infinity. Similarly, as x approaches positive infinity, -2x⁴ approaches positive infinity, so the entire polynomial approaches positive infinity.

Therefore, the end-behavior of the polynomial is:

f(x) → -∞, as x → -∞

f(x) →∞, as x → ∞

E) None of these

The polynomial is continuous for all real values of x. The only way for a polynomial to not be continuous is if there is a hole or a vertical asymptote in its graph. Since the graph of a polynomial is a smooth curve, there are no holes or vertical asymptotes, so the polynomial is continuous for all real values of x.

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Answer:

Data analytics. Data analytics is a set of tools which helps in organizing, presenting information, and extracting meaning from raw data.

Pls mark me as brainliest :)

The correct statement regarding the two functions in this problem is given as follows:

f(2) = g(2).

The graphic solution of a system of equations is given by the point of intersection of all the equations that compose the system.

The points through which each function passes in this problem are given as follows:

The point that is common to both function is given as follows:

(2,0).

Meaning that the two functions intersect at x = 2, which is the solution to the system of equations, also meaning that they have the same numeric value at x = 2.

The fact that the two functions have the same numeric value at x = 2 means that the correct statement is given as follows:

f(2) = g(2).

Which is the first statement.

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Answer: [tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex][tex]= 0[/tex]

Step-by-step explanation:

[tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex]

[tex]\lim_{n \to \infty} \frac{sinh(\infty)}{e^(\infty)}[/tex]

As x approaches infinity, the exponential term e^x becomes much larger than the hyperbolic sine function sinh(x), so the entire expression sinh(x)/e^x becomes very close to zero.

Therefore, the limit of the expression as x approaches infinity is 0:

The area enclosed by the curve x = t² - 2t, y = √(t), and the y-axis is 0.754 square units.

First, find the value of t at x = 0

x = t² - 2t

⇒ t² - 2t = 0

⇒ t(t - 2) = 0

Therefore, t = 0, t = 2.

Derivative of area, dA/dy

dA/dy = (0 - x)

dA = (0 - x) × dy

Since the curve has a negative x in this region.

y = √t (given)

dy/dt = (1/2)/√t

dA = [0 - (t² - 2t)] [(1/2)/√t]dt

dA = [2t - t²]/[(1/2)/√t]dt

dA = [[tex]t^{1/2}[/tex] - (1/2)[tex]t^{3/2}[/tex]]dt

Integrating to obtain A,

A = (2/3)[tex]t^{3/2}[/tex] - (1/5)[tex]t^{5/2}[/tex]

Now apply the limits t = 0 to t = 2

Area = [(2/3)[tex]2^{3/2}[/tex] - (1/5)[tex]2^{3/2}[/tex]] - [0]

Area = √[2(4/3 - 4/5)]

Area = √[2(8/15)]

Area = √(16/15)

Area = 0.754

Thus, the area enclosed by the given curves is 0.754 square units.

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Answer:

Raimi earns more per hour than Taylor.

Step-by-step explanation:

There are 6 ways to choose two rotten apples out of a sample of three.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include the manipulation of equations and formulas using the rules of arithmetic, the solution of equations, and the study of the properties and behaviors of functions.

There are two rotten apples out of 15 total apples, so the probability of choosing a rotten apple is 2/15. The probability of choosing two rotten apples out of a sample of three is (2/15) * (1/14) * (3 choose 2) = (2/455) * 3 = 6/455. So there are 6 ways to choose two rotten apples out of a sample of three.

Hence , There are 6 ways to choose two rotten apples out of a sample of three.

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Answer:

L = -7

Step-by-step explanation:

5L - 6 - 7L = 8

combine like terms

5L - 7L - 6 = 8

-2L - 6 = 8

add 6 to both sides

-2L = 14

divide by -2

L = -7

The whole response to the specified differential equation. (x + 1) dy/dx + (x + 2) y = 2xe is equal to y1(x), y2(x), f(x), and W(y1, y2), where dx = (ex)(1/2 e2x) = 1/ 2 e3x.

fixing a problem by an action or process; providing a solution explanation. an assortment of variable values that satisfy an equation, specifically Any value of a variable in an equation that fulfills the equality, that is, makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal, is the solution. Finding the solution(s) to an equation is what it means to solve it. The percentage of a solute in the solvent is one way to express a solution's concentration. the ratio of the mass of the solute to the mass of the solution

given

The characteristic equation is: r2 − 3r + 2 = 0

Factor: (r − 1)(r − 2) = 0

r = 1 or 2

So the general solution of the differential equation is y = Aex+Be2x

So in this case the fundamental solutions and their derivatives are:

Find the particular solution using the formula:

yp(x) = −y1(x)∫ y2(x)f(x) /W(y1, y2) dx + y2(x)∫ y1(x)f(x) /W(y1, y2) dx

4. First we solve the integrals:

∫ y2(x)f(x) / W(y1, y2) dx

= ∫ e2xe3xe3x dx

= ∫e2xdx

=  1 / 2 e2x

So:

−y1(x)∫ y2(x)f(x) / W(y1, y2) dx = −(ex)( 1/2 e2x) = − 1 / 2 e3x

the whole response to the specified differential equation. (x + 1) dy/dx + (x + 2) y = 2xe is equal to y1(x), y2(x), f(x), and W(y1, y2), where dx = (ex)(1/2 e2x) = 1/ 2 e3x.

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An absolute value graph is a V-shaped graph that opens either upwards or downwards, depending on the equation. To determine if an absolute value graph opens up or down, you need to examine the value of the constant k in the equation. If k is positive, the graph opens upwards and if k is negative, the graph opens downwards.

The general form of an absolute value equation is y = |x| + k, where k is a constant. The graph of this equation will open upwards if k > 0, and downwards if k < 0.

For example, if the equation is y = |x| + 2, the graph will open upwards and will have vertex at the point (0, 2)

On the other hand, if the equation is y = |x| - 2, the graph will open downwards and will have vertex at the point (0,-2)

The vertex of the graph is the point where the graph changes direction. The x-coordinate of the vertex is always 0 and the y-coordinate is the value of k.

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Mr. Johnson leaves on a trip planning to travel with speed of 24 mph. His son leaves 2.5 hours after him. To catch his father in 5 hours, James must travel at 36 mph.

The relation between distance and speed is given by:

distance = speed x time.

In this case:

Ms' Johnson's speed = 24 mph

Mr Johnson's time = 2.5 + 5 = 7.5 hours

His travelled distance = 7.5 x 24 = 180 miles.

His son's time = 5 hours ( since he starts 2.5 hours after Mr Johnson left.)

He must catch distance of 180 miles in 5 hours. Therefore, his speed must be:

speed = distance / time

speed = 180 / 5 = 36 mph.

Hence, hisr son's speed is 36 mph.

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Answer: 22

Step-by-step explanation:

f(2)=3*2^2+5*2

     =3*4+10

     =12+10

     =22

Case 2

The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)

Case 3

We need to add + 64 to both sides. (Correct choice: B)

Case 4

We need to add + 16 to both sides. (Correct choice: C)

In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:

Case 2

x² - 14 · x + 48 = 0

x² - 14 · x + 49 = 1

(x - 7)² = 1

x - 7 = ± 1

x = 7 ± 1

The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.

Case 3

x² - 16 · x = - 21

x² - 16 · x + 64 = 64 - 21

(x + 8)² = 43

The first step consists in adding both sides by + 64.

Case 4

x² - 8 · x = 0

x² - 8 · x + 16 = 16

(x - 4)² = 16

The first step consists in adding both sides by + 16.

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According to the concept of probability, the smallest number of yellow marbles that Marcy could have is 24

The term probability is known as the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Here we have given that all of Marcy's marbles are blue, red, green, or yellow. one third of her marbles are blue, one fourth of them are red, and six of them are green.

Here we know that the 6 green marbles and yellow marbles form is calculated as,

=> 1 - 1/3 - 1/4 = 5/12 of the total marbles.

Here let us consider that the total number of marbles is x.

And here we know the number of yellow marbles is is written as,

=> 5/12x - 6 and a positive integer.

Now, we have to divide 12 by x, then we get,

Then we get the value of x as 24.

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T3(x) = x - x^2/2 + x^3/6.

The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:

T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3

= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!

= x - x^2/2 + x^3/6

So T3(x) = x - x^2/2 + x^3/6.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.

The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.

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The difference in rates between the 2 peoples is 2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

John y=5x

For sally we have to find the equation

m=28-14/4-2

m=14/2=7

14=7(2)+b

b=0

So for Sally y=7x

Hence, the difference in rates between the 2 peoples is 2.

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Answer:

$355

Step-by-step explanation:

if each pear is 60c and apples are 5c less...

60×5=300

300+55=355

because 60-5=55

The equation of the line is y = (2/3)x + 2, having a y intercept of 2 and slope of 2

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

The equation of a line with slope m passing through (x₁, y₁) is:

y - y₁ = m(x - x₁)

The line that passes through (0, 2) and has a slope of 2/3, hence:

y - 2 = (2/3)(x - 0)

y = (2/3)x + 2

The equation of the line is y = (2/3)x + 2

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?

my guess would be to pick the THIRD ONE

3

x=9.5 y= -2.0

Answer:

5. False.

Look at the graph.

Every one day, the cost jumps $30 instead of $60.

Therefore, it is false.

6. True.

Like I said, Every one day, the cost jumps $30.

So when x increases by 1, y increases by 30.

So, y = 30x is correct.

7. False.

Use the equation in the 6th question.

y = 30x.

Put x = 7.

You get y = 210, not 200.

So. it is false.

8. True

Again, same thing.

Use the equation in the 6th question.

y = 30x.

Put x = 9.

You get y = 270.

So the statement is correct.

Pls mark as brainliest for no apparent reason. Cheers

Answer:

it's the second

Step-by-step explanation:

i did this before and it was the second one

Answer: 10.5 miles

Step-by-step explanation:

The factorise form of the trinomial  6x² + 11x - 10 is (3x - 2)(2x + 5).

Trinomials is a polynomial that has three terms. Let's factorise the trinomial by grouping as follows:

6x² + 11x - 10

The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.

Hence, let's find the factor of 6x² + 11x - 10

6x² + 11x - 10

let's find two numbers we can multiply to get -60 and add to get 11.

6x² + 15x - 4x - 10

3x(2x + 5) - 2(2x + 5)

Hence,

(3x - 2)(2x + 5)

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The number of Empire State building‑height stacks of dimes required is 589,008.

The height of the  Empire States Building including the antenna is 1,454 feet.

here, we have,

The height of a stack of 100 dimes is 5.3 inches.

The value of a stack of 100 dimes is 10 dollars.

The 2017 U.S. gross domestic product (GDP) = 19,390,604,000 dollars.

Number of stacks of dimes needed = $19,390,604,000 / $10 = 1,939,060,400 stacks of 100 dimes

Height of 1,939,060,400 stacks of 100 dimes in feet = 1,939,060,400 x 5.3/12

Height of 1,939,060,400 stacks of 100 dimes in feet = 856,418,343.3 feet

Number of Empire State building‑height stacks of dimes = 856,418,343.3 / 1,454

Number of Empire State building‑height stacks of dimes = 589,008

In conclusion, the number of Empire State building‑height stacks of dimes required is obtained from the height of the Empire State building and the height of a stacks of 100 dimes.

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Answer:

Step-by-step explanation:

90 inches

10%=9 inches

5%=4.5 inches

5x5=25

4.5 inches x5=22.5 inches

90-22.5=67.5

the new couch is 67.5 inches long