if a + b + c = 1, ab + bc + ca = -1 and abc = -1. find the value of a³+b³+c³​

[tex]HOLA!![/tex]

Answer:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=e^{\frac{1}{3} } }}[/tex]

Explanation:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=}}[/tex]

For this we have to take into account:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{x^{n} }{n!} =e^{x} }}[/tex]

Using the properties of factorials and exponents we have:

          [tex]n!=(n-1)n![/tex]  Also.    [tex]\frac{n^{x} }{ n^{y} }=n^{x-y}[/tex]  

We replace:

[tex]{\boxed{ \sum_{n=1}^{\infty}\ \frac{1}{3^{n-1}.(n-1)! } }}[/tex]

Shape it:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} }}[/tex]

Finally:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} =e^{\frac{1}{3} } }}[/tex]

Answer:

Accuracy is the degree of closeness between a measurement and the measurement's true value. Precision is the degree to which repeated measurements under the same conditions are unchanged.

Definition With Example

Accuracy refers to the closeness of a measured value to a standard or known value. ... Precision refers to the closeness of two or more measurements to each other. Using the example above, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise.

Step-by-step explanation:

my answer is in the image above

The solution is m=70miles.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

If k kilometers is the same distance as m miles.

k is given approximately by the formula.

k=8m/5

the number of miles in 112km,

then, we get

k=8m/5

i.e. m= 5k/8

now, k=112

so, m= 5/8 * 112

i.e. m=70

Hence, The solution is m=70miles.

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Answer:

10

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Scaled length of the pool = 50 / 5 = 10cm

Answer:

Descriptive Statistics

Step-by-step explanation:

Descriptive statistics is the analysis of data which involves describing or summarizing the data we have at a given time at our disposal. It gives us a clear idea of the characteristics of the sample under study. It however cannot be used testing hypotheses. Using of simple percentages is an example of descriptive statistics. Thus, the use of percentage in the case stated above is a descriptive statistics.

Answer:

Step-by-step explanation:

The answer you have chosen is not correct. Let's walk through the simplification process, shall we?

Begin by adding over the 1/4, after you find the common denominator, that is. 5/2 with a denominator of 4 is 10/4:

[tex]\frac{2}{3}(cx+\frac{1}{2})=\frac{11}{4}[/tex] and then multiply both sides by the reciprocal of 2/3:

[tex]cx+\frac{1}{2}=\frac{33}{8}[/tex] then subtract the 1/2 in the form of 4/8 (common denominator and all...) to get

[tex]cx=\frac{29}{8}[/tex] and finally divide both sides by c to get

[tex]x=\frac{29}{8c}[/tex]  That's choice C.

Answer:

It takes _8_ s for an object to fall 1000 feet. In 10 s, an object will fall _1600_ feet.

Step-by-step explanation:

A. Determination of the time it takes for the object to 1000 ft.

Distance (d) = 1000 ft

Time (t) =?

t = √(d/16)

t = √(1000/16)

t = 8 s

B. Determination of how much feet an object will fall in 10 s.

Time (t) = 10 s

Distance (d) =?

t = √(d/16)

10 = √(d/16)

Take the square of both side

10² = d/16

100 = d/16

Cross multiply

d = 100 × 16

d = 1600 ft

SUMMARY

It takes _8_ s for an object to fall 1000 feet. In 10 s, an object will fall _1600_ feet.

Answer:

0.5

LxW=A

0.5x0.5=0.25

Answer:

the side length of square is 0.5 unit.

Step-by-step explanation:

area of square = l^2

0.25 = l^2

[tex]\sqrt{0.25[/tex] = l

0.5 = l

Answer:

4) 93°

5) 1°

6) 51°

7) 6°

Step-by-step explanation:

4)

180 - 36 - 51 =  93

93 °

5)

(4x + 27 ) = 180 - 64 - 85

4x + 27 = 31

x = 1

6)

theory of exterior angles in a triangle:

21 + 30 = x

x = 51

7)

3x + 42 = 46 + 44

3x + 42 = 90

3x = 48

x = 16

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

5

Step-by-step explanation:

To start, you use the formula a/b=c, in which a is bigger than b. In this case, that's 95/20=c. The greatest common factor is 5.

Answer: uhh 10%??

Step-by-step explanation:

I'm not rlly good at percentage-

Answer:

LCM = 1440

Step-by-step explanation:

           2 | 72 , 96 , 120

           2 | 36, 48, 60

           2 | 18 , 24 , 30

           2 | 9 , 12 , 15

           2 | 9 , 6 , 15

           3 | 9 , 3 , 15

           3 | 3 , 1 , 5

           5 | 1 , 1 , 5

             | 1 , 1 , 1

LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 = 1440

==========================================================

Explanation:

One square face has an area of

(length)*(width) = (3x+10)(3x+10) = 9x^2+30x+30x+100 = 9x^2+60x+100

after using the FOIL rule

Multiply that by 6 to get the total area of all 6 faces

6*(9x^2+60x+100) = 54x^2+360x+600

The surface area units are in square feet.

Answer:

(X+6)(x-8)

Step-by-step explanation:

Answer:

(x-8)(x+6)

Step-by-step explanation:

Factor the trinomial using the AC method.

x * x = x^2

-8 + 6 = -2

-8 * 6 = -48

Answer:

B. The solution is valid because all steps to solve the inequality for F are correct.

Step-by-step explanation:

F - 32 ≤ 0

Add 32 to both sides of the equation to have;

F -32 + 32 ≤ 0 + 32

F ≤ 0 + 32

F ≤ 32

It can be observed that to solve for F, the steps are correct. Thus the solution is valid. Therefore, the correct choice in the given question is the solution is valid because all steps to solve the inequality for F are correct.

Answer:

D

Step-by-step explanation:

because it's the highest out of the other letter

The number does not make the comparison true is 23.195 >23.189. Therefore, option C is the correct answer.

Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.

Given that, 23.195 <

Here,

A) 23.195 <23.200

B) 23.195 <23.198

C) 23.195 >23.189

D) 23.195 <23.205

Therefore, option C is the correct answer.

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Answer:

[tex]\displaystyle d = 2\sqrt{13}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

Point (2, 1)

Point (6, 7)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

f(3) = 100

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \left \{ {{f(1) = 4} \atop {{f(2) = 25} \atop {f(n) = f(n - 2) \cdot f(n - 1)}} \right.[/tex]

Step 2: Evaluate

=====================================================

Explanation:

The interior angles are consecutive numbers such as 1,2,3,... or 7,8,9... and so on. The gap between any two adjacent neighbors is 1.

For any polygon with n sides, the interior angles add up to 180(n-2)

We have n = 8 sides so the interior angles sum to 180(n-2) = 180(8-2) = 1080 degrees.

Any octagon has its interior angles add up to 1080 degrees.

-----------------------------

Let x be the smallest angle. The next angle up is x+1. After that is x+2 and so on until we reach x+7 as the 8th angle.

Add up those 8 angles, set the sum equal to 1080 and solve for x

x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)+(x+7) = 1080

8x+28 = 1080

8x = 1080-28

8x = 1052

x = 1052/8

x = 131.5

This is the smallest angle. The next angle up or the second smallest angle is x+1 = 131.5+1 = 132.5 degrees  (choice C)

Answer:

10

Step-by-step explanation:

26×3=78

78÷8=9.75

round up to 10 since you can't buy .75 of a pizza

Answer:1000

Step-by-step explanation:

Answer:

[tex]BC=9\sqrt{3}\approx15.59\text{ units}[/tex]

Step-by-step explanation:

Since Segment BOA is a diameter:

[tex]m\angle ACB=90[/tex]

Arc Ac and Arc CB are in a ratio of two to four. Since Segment BOA is a diameter, Arc ACB measures 180°. Letting the unknown value be x, we can write that:

[tex]2x+4x=180[/tex]

Hence:

[tex]x=30[/tex]

Thus, Arc CB = 120°. By the Inscribed Angle Theorem:

[tex]\displaystyle m\angle A=\frac{1}{2}\left(\stackrel{\frown}{CB}\right)=\frac{1}{2}\left(120)=60[/tex]

Therefore, ΔABC is a 30-60-90 triangle. Its sides are in the ratios shown in the image below.

Since AC is opposite from the 30° triangle, let AC = a.

We are given that AC = 9. Hence, a = 9.

BC is opposite from the 60° angle and it is given by a√3. Therefore:

[tex]BC=9\sqrt{3}\approx15.59\text{ units}[/tex]

Answer:

58

Step-by-step explanation:

58/3 gives a remainder of 1

58/4 gives a remainder of 2

58/5 gives a remainder of 3

Answer:

7/16

Step-by-step explanation:

(15/16 - 1/16)

(15 - 1)/16 = 14/16 = 7/8

•°• = 7/8

Answer:

g(2) = -42

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \left \{ {{g(1) = 50} \atop {g(n) = 8 - g(n - 1)}} \right.[/tex]

Step 2: Evaluate

Answer:

TRUE IS THE ANSWER

Step-by-step explanation:

The name of the circle pictured is circle C is True statement.

A circle is a collection of points in a plane that are all equally spaced apart from one another. The radius is the distance from the centre, while the centre is the location of the point. The diameter is defined as twice the radius. A complete angle, which is equal to or radians, is the angle that a circle subtends from its centre.

we have a graph for a circle.

We know a circle many parts such as Center, Radius, Diameter, Chord, etc.

A circle usually know from its Center.

Also, the center of circle shows the point of circle.

Thus, the given statement is True.

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Answer: $17,852.50

Step-by-step explanation:

First find the total cost of the car including the various charges:

Sales tax = 18,500 * 6.5%

= $1,202.50

Total cost = Purchase price + sales tax + Freight charge + Registration fee + Ownership fee

= 18,500 + 1,202.50 + 450 + 155 + 45

= $20,352.50

Subtract the down payment to find out the amount that will be financed:

= 20,352.5 - 2,500

= $17,852.50

Answer:

3.6km/hr

Step-by-step explanation:

What is the conversion for m/s to km/h ?

According to the conversion

1m = 0.001km

1s = 1/3600 hr

m/s to km/hr = 0.001/(1/3600)

= 0.001×3600

= 3.6

Hence the conversion is 3.6km/hr