Which statement describes the meteors motion?
(10 brainly points)

Interval of convergence of the power series [tex]\frac{(x+3)^{n} }{n}[/tex] ; n = 1 is -5 < x < -1.

A power series is a special type of infinite series representing a mathematical function in the form of an infinite series that either converges or diverges.

The series is aₙ =  [tex]\frac{(x+3)^{n} }{n}[/tex]

To generate aₙ₊₁ term replace 'n' with 'n + 1'

aₙ₊₁ =  [tex]\frac{(x+3)^{n+1} }{n+1}[/tex]

Now plugging aₙ and aₙ₊₁ in the formula L = [tex]\lim_{n \to \infty} |\frac{an+1}{an}|[/tex]

L = [tex]\lim_{n \to \infty} |\frac{\frac{(x+3)^{n+1} }{n+1} }{\frac{(x+3)^{n} }{n} }|[/tex]

L = [tex]\lim_{n \to \infty} |{\frac{(x+3)^{n+1} }{n+1} }/{\frac{(x+3)^{n} }{n} }|[/tex]

L = [tex]\lim_{n \to \infty} |{\frac{(x+3)^{n+1} }{n+1} }*{\frac{n }{(x+3)^{n} }|[/tex]

L = [tex]\lim_{n \to \infty} |{\frac{(x+3) }{n+1} }*{n}|[/tex]

L = [tex](x+3)\lim_{n \to \infty} |{\frac{n}{n+1} }|[/tex]

L = [tex](x+3)\lim_{n \to \infty} |{\frac{n*(\frac{1}{n}) }{(n+1)*(\frac{1}{n}) } }|[/tex]

Since n = 1

L = [tex](x+3)\lim_{n \to \infty} |\frac{1}{1+1} |[/tex]

L = [tex](x+3)\lim_{n \to \infty} |\frac{1}{2} |[/tex]

L = [tex]\frac{1}{2} * |x+3|[/tex]

The ratio tells us that if L < 1 then the series will converge

[tex]\frac{1}{2}*(x+3) < 1[/tex]

[tex](x+3) < 2[/tex]

The interval of convergence will be

-2 < (x + 3) < 2

-5 < x < -1

The interval of convergence for the power series  [tex]\frac{(x+3)^{n} }{n}[/tex] is -5 < x < -1

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Answer:

1. 26, cuz 17+9=26

2. 50, cuz 60-10=50

3. 19, cuz 33-14=19

Hope these will help you as you can't just ask for answers.

The rate of change of y with respect to x for given function is -0.2

We know that, the slope of a function is nothing but the rate of change of y with respect to x of a function.

In this question, we have been given a linear function passing through points (-3, 3.6) and (5, 2)

We need to find the slope of the line passing through points (-3, 3.6) and  (5, 2)

Let m be the slope.

By using the formula of the slope,

m = (2 - 3.6) / (5 - (-3))

m = -1.6 / 8

m = -0.2

Therefore, the rate of change of y with respect to x for given function is -0.2

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110% percent of female students visited the math lab.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages.

During the final exam, the number of students that visited the math lab is 172 in total.

Of the total number of students, 4 out of 11 were male.

Therefore, the total number of females that visited the math lab is:

no. of females = 11 - 4 = 7.

Therefore, the percentage of female students who visited the math lab is :

[tex]F=\frac{7}{11} \times 172\\\\F=109.4\\F=110[/tex]

Therefore, the percentage of female students who visited the math lab is 110%.

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The amount that the students should charge for the wristbands will be at least $1.40.

From the information, the students want to buy 500 wristbands for just $0.90 each and they want to make at least $250.

Therefore, the amount that they should charge for each will be:

Total cost = 500 × $0.90 = $450

Therefore, the amount charged be:

500x - 450 >= 250

Collect like terms

500x >= 250 + 450

500x >= 700

x >= 700/500

x>= $1.4

They should charge at least $1.40.

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Answer:

2(s+20)

Step-by-step explanation:

hope this helps

Answer: son is 10 years old and father is 40 years old

Step-by-step explanation:

Let the present age of son is x years

Then the present age of father is 4x years

4x+20=2(x+20)

4x+20=2x+40

4x+20-20=2x+40-20

4x=2x+20

4x-2x=2x+20-2x

2x=20

Divide both parts of the equation by 2:

x=10 years

4x=4(10)

4x=40 years

After the evaluation of the given expression n² + 4, the correct option is (3) 85, 68, and 40.

So, n² + 4:

Therefore, after the evaluation of the given expression, the correct option is (3) 85, 68, and 40.

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Mid point of the points  A(-5, 3) and B(5, -1) is point C(0,1)

Mid point is a point that lies at the center of any measured distanced.

The points are written in the coordinate forms having first term as 'x' coordinate value called as abscissa and second term as 'y' coordinate value called as ordinate.

A = (x₁ , y₁) = (-5 , 3)

B = (x₂ , y₂) = (5 , -1)

Mid point formula  [tex]( \frac{x1 +x2}{2} , \frac{y1+y2}{2} )[/tex],  is used to find the midpoint of a line.

Mid point of the points  A(-5, 3) and B(5, -1) ,

x₁ = -5

x₂ = 5

y₁ = 3

y₂ = -1

So, mid point C =  [tex]( \frac{(-5)+5}{2} , \frac{3+(-1)}{2} )[/tex]

C =  [tex]( \frac{0}{2} , \frac{2}{2} )[/tex]

C = (0 , 1) = (x , y)

The mid point of the points A(-5, 3) and B(5, -1) is point C(0 , -1)

The plotting of line segment is shown in the picture.

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The function written in vertex form is

[tex]g(x) =4x^2+88x =4(x+ 11)^2 - 484[/tex]

This is further explained below.

Generally, the equation for the function is  mathematically given as

g(x) = 4x2 + 88x

Therefore,

g(x) = a(x +11)2 + k

[tex](x +11)x^{2} as\ x^2 + 22x +121[/tex]

[tex]g(x) = a(x^2 +22x +121) + k\\\\g(x) = ax^2+ 22ax +121a + k[/tex]

Equate eq(a) with eq(b) We obtain,

[tex]4x^2 + 88x = ax^2 + 22ax +121a + k[/tex]

Examine the x coefficients on both sides of the equation.

a=4 and 22a= 88 ; 121a + k = 0

121(4) = -k

k = -484

[tex]g(x) =4x^2+88x =4(x+ 11)^2 - 484[/tex]

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CQ

Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = ___ (x +11)² +____.

Answer:

27(-⁴)

³

= 3³(-⁴/³)

= 3(-⁴)

= 1

81

Cost of 20 yards of ribbon is $13.32.

Given,

The cost of 6 ½ yards of ribbon = $9.75

We have to find the cost of 20 yards of ribbon.

First of all we have to find the cost of 1 yard of ribbon:

Cost of 1 yard of ribbon = ( 6 ½ yards of ribbon) / (cost of 6 ½ yards of ribbon)

Cost of 1 yard of ribbon = 6 ½ / 9.75 = 6.5 / 9.75 = 0.66666

That is cost of 1 yard of ribbon is $0.666 approximately.

Now, we have to find the cost of 20 yards of ribbon:

Cost of 20 yards of ribbon = (cost of 1 yard of ribbon) x 20

Cost of 20 yards of ribbon = 0.666 x 20 = 13.32

That is cost of 20 yards of ribbon is $13.32.

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Alex has received a rate of return of 0.25, or 25%, on his investment.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the rate of return that Alex has received, we can use the formula:

rate of return = (final value - initial value) / initial value

where the final value is the value of the investment after the period of time in question, and the initial value is the value of the investment at the beginning of that period.

In this case, the final value is $1,250 and the initial value is $1,000, so we have:

rate of return = (1250 - 1000) / 1000 = 0.25

Therefore, Alex has received a rate of return of 0.25, or 25%, on his investment.

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The correct answer regarding the factoring of the expression 25x² - 15x + 2 is:

B. The expression is the sum of two terms. He needs to factor out the common factor. The correct factored form is (5x - 1)(5x - 2).

An expression is factored placing the common terms in evidence, and then simplifying the entire expression according to these terms.

For this problem, the expression is:

25x² - 15x + 2.

After the first step, he found the following factorization:

5x(5x - 1) - 2(5x - 1).

However, this procedure is incomplete, as (5x - 1) is common to both terms of the subtraction. Thus the completely simplified expression is:

(5x - 1)(5x - 2).

As:

The correct option is:

B. The expression is the sum of two terms. He needs to factor out the common factor. The correct factored form is (5x - 1)(5x - 2).

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Answer:

150x8=1,200 so that much more

Step-by-step explanation:

Darryl will need to save an additional $187.50 per month for the next 8 months in order to accomplish his original goal of saving $150 per month for 18 months.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a quantity.

Expressions can be simple or complex, and they can be used to perform mathematical operations, make comparisons, or evaluate functions.

An expression can contain any combination of numbers, variables, and operators, such as addition, subtraction, multiplication, division, and exponentiation.

For example, 3 + 5, 2x - 7, and (4a + 2b) / (3c - d) are all examples of expressions.

We have,

Darryl intended to save $150 a month for 18 months, which would have given him a total savings of:

$150/month x 18 months

= $2,700

However, after 10 months, he has only managed to save $1,200.

This means he fell short of his goal by:

$2,700 - $1,200

= $1,500

To accomplish his original goal, he will need to save an additional $1,500. Since he has 8 months left to save, he will need to save:

$1,500 / 8 months

= $187.50 per month

Therefore,

Darryl will need to save an additional $187.50 per month for the next 8 months in order to accomplish his original goal of saving $150 per month for 18 months.

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Bill Murray has 16 3/4 days in total of vacation per year.  Bill entitled to  8 1/6 days more vacation time.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Bill Murray has 16 3/4 days in total.

(16×4 + 3)/4 = 67/4 days.

Then;

1 3/4 = (1×4 + 3)/4 = 7/4 days

4 2/3 = (4×3 + 2)/3 = 14/3 days

2 1/6 = (2×6 + 1) = 13/6 days

To add and then subtract them directly, we need to bring all fractions to the same denominator.

we have to multiply each fraction by a fitting n/n factor to bring the denominators to 12

67/4 = 67/4 × 3/3 = 201/12

7/4 = 7/4 × 3/3 = 21/12

14/3 = 14/3 × 4/4 = 56/12

13/6 = 13/6 × 2/2 = 26/12

Thus the remaining vacation time will be

201/12 - 21/12 - 56/12 - 26/12 = 98/12 = 49/6

49/6 = 8 and remainder 1 = (8×6 + 1)/6 = 8 1/6 days

Hence, Bill Murray has 16 3/4 days in total of vacation per year.  Bill entitled to  8 1/6 days more vacation time.

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Answer:

there is a 5 by 5 square

Step-by-step explanation:

Answer:

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equalStep-by-step explanation:

Answer:

14.

Step-by-step explanation:

1) if mr. Oliveros spent 10$ for his ticket, then the rest sum of his money is 45-10=35$;

2) according to the condition mr. Oliveros spends 35$ for unknown number tickets for students, where 2.5$ for each student. Using this conditiion it is possible to calculate the number of student tickets:

35/2.5=14.

The area of park in terms of scale drawing is 79200 square yards with scale drawing of a rectangular park is 8 inches wide and 11 inches long.

Area of rectangle=Length * width.

Given:

scale length of rectangular park = 11 inch =

scale width of rectangular park = 8 inch

scale length / actual length of park = scale width/ actual width of park

11/330= 8/ actual width of park

1/30 =  8/ actual width of park

actual width of park = 240

So,

Area = length* width

=330*240

= 79200 square yards

Hence, the area of the actual parking is 79200 square yards.

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =280 \end{cases}\implies s=\cfrac{(280)\pi (7)}{180}\implies s=\cfrac{98\pi }{9}\implies s\approx 34.21[/tex]

The original number is represented by x So, the result is the multiplier of 2.

Quotients are the number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

It is given that Multiply the number 4. Add 6 to the product. Divide this sum by 2. Subtract 3 from the quotient.

Let x = original number

(4x + 6)/2 - 2

= (4x /2 + 6/2) - 2

= 2x + 3 -2

= 2x+1

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The complete question is;

Write a conjecture that relates the result of the process to the original number selected. Represent the original number as x. What is the result?

The final endpoint values are: (12,-6)

The midway point of a line or segment is referred to as the midpoint. It creates an evenly spaced division in the line. In essence, it divides the lines into two.

According to the question, the coordinates of a line LN is given as:  N (-8,2) and Midpoint M M(2,-4).

To calculate the midpoint, use the standard midpoint formula which is represented as below:

Midpoint =[tex]\frac{x1 + x2 }{2}[/tex] and [tex]\frac{y1 + y2 }{2}[/tex]

From the given data, the values are:

X1 = -8; Y1 = 2; X = 2; Y = -4

Therefore, the calculated midpoint is:

2 = -8 + [tex]\frac{x2}{2}[/tex] = 12

4 = 2 + [tex]\frac{y2}{2}[/tex] = -6

Hence, the final endpoint values are (12,-6)

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Answer:

x=37

Step-by-step explanation:

If you stare at the picture long enough you can tell that you have six straight angles, which add up to [tex]180\°\times 6 = 1080\°[/tex]. You now need to take away the internal angles, that add up to [tex]180\° \times 6-360\° = 720\°[/tex]*

What you have left is two expression of the same quantity - the sum of the external angles. In one case is [tex]360\°[/tex] (the difference between the two values) and in the other is the sum of the various expressions containing x.[tex]2x +(x+10)+(x+18)+3x+(x-1)+x = 360\\9x = 360 - 27 \rightarrow 9x = 333\rightarrow x=37[/tex]

*Pick any point inside the polygon, and join it to the corners. You will create as many triangles as you have sides - in our case 6. Sum of angles will be 180 times the number of sides, minus a whole round angle - the one in the center.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 5 and that it passes through (-1 , 2)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-1)}) \implies y -2= 5 (x +1) \\\\\\ y-2=5x+5\implies {\LARGE \begin{array}{llll} y=5x+7 \end{array}}[/tex]

Answer:

26 < d < 30

Step-by-step explanation:

D is greater than 26 but less than 30.

Someone older than 26​, but less than 30 years of age will be written as 26 < x < 30.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

A certain population demographic may be defined as someone older than 26​, but less than 30 years of age.

Let 'x' be the age of someone.

If the age of someone is greater than 26, then the inequality is written as,

26 < x            ...1

If the age of someone is smaller than 30, then the inequality is written as,

x < 30           ...2

Combine both inequalities, then we have

26 < x < 30

Someone older than 26​, but less than 30 years of age will be written as 26 < x < 30.

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Corresponding terms are those that appear in identical places in two similar situations.

Generate two numerical patterns given their rules. Understand that a term is a number in a pattern and corresponding terms are numbers in two patterns that show up in the same place in each pattern (e.g., the second term of each pattern are corresponding terms

.1) use the rule add 8 to find the cost of 6 t-shirts

 cost of 5 t-shirts to get the cost of 6 t-shirts.

the cost of 5 t-shirts plus $8 is $40+$8= $48

2) the second number is 4 times the first number.

one pattern starts at 0 and follows the rule add 2.

another pattern starts at 0 and follows the rule add5.

corresponding terms as ordered pairs

0,0

2,8

4,16

6,24

8.32

10,40

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Answer:

3 miles

Step-by-step explanation:

[tex]\large \bf \implies{53.1 \degree}[/tex]

[tex] \bf \longrightarrow \: sin \: α = \frac{8}{10} = 0.8 \\ \\\bf \longrightarrow \: α = arc \: sin (0.8)= 53.1°[/tex]