Use the following function rule to find f(3).

f(x) =
8
x

+ 9

f(3) =

The correct letter that match each summation expression are;

[tex]\displaystyle \sum\limits_{i=1}^n[/tex] is equal to c

[tex]\displaystyle {\sum\limits_{i=1}^n i}[/tex] is equal to b

[tex]\displaystyle \sum_{i=1}^n c[/tex] is equal to d

[tex]\displaystyle\sum_{i=1}^n i^3[/tex] is equal to e

[tex]\displaystyle \sum\limits_{i=1}^n i^2[/tex]is equal to a

The summation expression indicates the sum of all values of a series of a function within a specified limit of values.

The equation for the sum of a constant c and the ith term of an of a sequence of numbers is equivalent to the product of the constant and the sum of the terms of the sequence as follows;

[tex]\sum\limits_{i=1} ^n {c\cdot a_i} = c\cdot \sum\limits_{i=1} ^n {a_i}[/tex] the correct option is c

The sum of ith terms from i = 1 to i = n is an arithmetic series with the formula;

Sₙ = (n/2)·[2·a + (n - 1)·d]

Where; a = The first term = 1

d = The common difference = 1

Therefore;

Sₙ = (n/2)·[2 + (n - 1)] = n + n·(n - 1)/2 = (2·n + n² - n)/2

(2·n + n² - n)/2 = (n² + n)/2 = n·(n + 1)/2

Therefore;

[tex]\sum\limits_{i=1}^n i = \dfrac{n\cdot (n + 1)}{2}[/tex] The correct option is b

The sum of n number of a constant, c is c·n, therefore;

[tex]\sum\limits_{i = 1}^n c = c\cdot n[/tex] The correct option is d

[tex]\sum\limits_{i=1}^n [(1 + i)^3-i^3[/tex] = (2³ - 1³) + (3³ - 2³) + ... + ((n + 1)³ - n³) = (n + 1)³ - 1³

(n + 1)³ - 1³ = n³ + 3·n² + 3·n

[tex]\sum\limits_{i=1}^n [(1 + i)^3-i^3[/tex] = n³ + 3·n² + 3·n

However, we get;'

[tex]\sum\limits_{i=1}^n [(1 + i)^3-i^3[/tex] = [tex]\sum\limits_{i=1}^n [ i^3 + 3\cdot i^2 + 3\cdot i+ 1-i^3][/tex]

[tex]\sum\limits_{i=1}^n [ i^3 + 3\cdot i^2 + 3\cdot i+ 1-i^3][/tex] = [tex]\sum\limits_{i=1}^n [ 3\cdot i^2 + 3\cdot i+ 1][/tex] = 3·S₂ + 3·S₁ + n

Where;

[tex]S_2 = \sum\limits_{i=1}^n i^2[/tex]

[tex]S_1 = \sum\limits_{i=1}^n i[/tex] = n·(n + 1)/2

[tex]\sum\limits_{i=1}^n [ 3\cdot i^2 + 3\cdot i+ 1][/tex] = n³ + 3·n² + 3·n = 3·S₂ + 3·S₁ + n

3·S₂ = n³ + 3·n² + 3·n - (3·S₁ + n) = n³ + 3·n² + 3·n - (3·(n·(n + 1)/2) + n)

n³ + 3·n² + 3·n - (3·(n·(n + 1)/2) + n) = n³ + 3·n²/2 + n/2

3·S₂ = n³ + 3·n²/2 + n/2

S₂ = n³/3 + 3·n²/6 + n/6 = (2·n³ + 3·n² + n)/6

S₂ = (2·n³ + 3·n² + n)/6 = n·(2·n² + 3·n + 1)/6

S₂ = n·(2·n² + 3·n + 1)/6 = n·(2·n + 1)·(n + 1)/6

S₂ = n·(2·n + 1)·(n + 1)/6

[tex]S_2 = \sum\limits_{i=1}^n i^2 = \dfrac{n\cdot (2\cdot n + 1)\cdot (n + 1)}{6}[/tex] The correct option is; a

(n + 1)⁴ - n⁴ = 4·n³ + 6·n² + 4·n + 1

Therefore;

(n + 1)⁴ - 1⁴ = 4·S₃ + 6·S₂ + 4·S₁ + n

4·S₃ = (n + 1)⁴ - 1⁴ - (6·S₂ + 4·S₁ + n)

(n + 1)⁴ - 1⁴- (6·(n·(2·n + 1)·(n + 2)/6) + 4·(n·(n + 1)/2) + n) = (n + 1)·(3·n² - n + 1)

4·S₃ = n²·(n + 1)²

S₃ = n²·(n + 1)²/4

[tex]S_3 = \sum\limits_{i=1}^n i^3 = \dfrac{n^2\cdot (n+1)^2}{4}[/tex] The correct option is e

Learn more about the sum of a series of values here: https://brainly.com/question/28586583

#SPJ1

Answer:

117π=367.38

Step-by-step explanation:

r=d/2=3

V=πr2h=π·3²·13=117π=367.38

Step-by-step explanation:

Since bx can be defined for all real numbers r, the domain of an exponential function is all real numbers. The range of bx is all real numbers greater than 0. ... If b > 1, then f is an increasing function. I.e. f(x) increases in value as x increases.

Answer:

36 games won ...............

Answer:

y=1.06x-6

36

Step-by-step explanation:

Answer:

m<1 = 48°

m<2 = 132°

m<3 = 132°

m<5 = 48°

Step-by-step explanation:

Given:

m<4 = 48°

Required:

m<1, m<2, m<3, and m<5

Solution:

m<1 = m<4 (alternate exterior angles are congruent)

m<1 = 48° (substitution)

m<2 = 180° - (m<1) (linear pair theorem)

m<2 = 180° - 48° (substitution)

m<2 = 132°

m<3 = m<2 (alternate interior angles are congruent)

m<3 = 132° (substitution)

m<5 = m<4 (corresponding angles are congruent)

m<5 = 48° (substitution)

Answer:

Step-by-step explanation:

The answer is x= 7/2

decimal form 3.5

Answer:

x = 3, JL = 17, MN = 13

Step-by-step explanation:

Given 2 intersecting chords in a circle , then

The product of the parts of one chord is equal to the product of the parts of the other chord, that is

14x = 7 × 6 = 42 ( divide both sides by 14 )

x = 3

Then

JL = x + 14 = 3 + 14 = 17

MN = 6 + 7 = 13

Answer:

B. √x.

Step-by-step explanation:

That would be B - the square root of x.

Answer:600

Step-by-step explanation:

Answer:

20

___ x X = 120

100

x100       x 100

20x = 120

divide by 20 on both sides.

x = 6

Answer:

180 Degrees minus 117= sixty three

answer is x is 63

Where did I get the 180?

- straight Angles have 180

- 117 is a part of 180

-so that is why you had to subtract

I hope this Helps You!!

Answer:

Step-by-step explanation:

Translation:

A: (1.2)

B: (2,2)

C: (2,4)

Answer:

I think it's c.

Step-by-step explanation:

Answer:

-20 2/5 (2/5 as fraction)

Answer: Find the length of A

3) Find the scale factor.

Step-by-step explanation:

Answer:

x= -18 y=-5/3

Step-by-step explanation:

Answer:

x = -10

y = -3

Step-by-step explanation:

When combining the equations, we must ensure that one of the two variables will cancel out. The easiest way to do this will be to multiply one of the equations by -1, such that the x will cancel out once they are added together. This can be done with either equation, but I will do it for the first one.

This gives us the system:

[tex]\left \{ {{-x-2y=16} \atop {x+6y=-28}} \right.[/tex]

We can then add the two equations by combining each of the terms:

[tex](x - x) + (6y - 2y) = (-28 + 16)\\(0) + (4y) = (-12)\\4y = -12\\y = -3[/tex]

Now that we have the value for y, we substitute it back into any of the original equations and solve for x:

[tex]x + 2y = -16\\x + 2(-3) = -16\\x - 6 = -16\\x = -10[/tex]

To check our work, we substitute both x and y into the other original equation:

[tex]x + 6y = -28\\(-10) + 6(-3) = -28\\-10 - 18 = -28\\-28 = -28[/tex]

Answer:

wbv wncwic wndv envne jcsid ejshf vuia csiubc wcbu

Answer:

64[tex]\pi[/tex] mm² or approximately 201.06 mm²

Step-by-step explanation:

If the diameter is 16 mm, the radius will be 8 mm.

Use the circle area formula, A = [tex]\pi[/tex]r², where r is the radius. Plug in 8 as r:

A = [tex]\pi[/tex]r²

A = [tex]\pi[/tex](8²)

A = 64[tex]\pi[/tex]

So, the area of the circle is 64[tex]\pi[/tex] mm² or approximately 201.06 mm²

If the diameter of the circle above is 16 mm, what is the area of the circle ?

Diameter of the circle = 16 mm. (Given)

Radius (r) of the circle = 16/2 = 8 mm.

[tex] \bigstar [/tex] To Find the area of the circle.

Since we know,

[tex] \dag [/tex] Area of circle is πr².

So, Area of the circle = 3.14 × (8)²

Area of the circle = 3.14 × 8 × 8

Area of the circle = 200.96 = 201 mm².

The answer is 104°.

.. .. ..

Answer:

Step-by-step explanation:

A line is always equal to 180. So if angle POR is 76, you would do 180-76 which equals 104.

Answer: p(1/2)=11/2p(a)=a.

Step-by-step explanation:

Answer:

       2x3 - 5x2 + 2x - 7

 ——————————————————

       x - 2      

Step-by-step explanation:            2x3 - 5x2 + 2x - 7

Simplify   ——————————————————

                 x - 2      

Checking for a perfect cube :

3.1    2x3 - 5x2 + 2x - 7  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  2x3 - 5x2 + 2x - 7

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  2x - 7

Group 2:  2x3 - 5x2

Pull out from each group separately :

Group 1:   (2x - 7) • (1)

Group 2:   (2x - 5) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

3.3    Find roots (zeroes) of :       F(x) = 2x3 - 5x2 + 2x - 7

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  2  and the Trailing Constant is  -7.

The factor(s) are:

of the Leading Coefficient :  1,2

of the Trailing Constant :  1 ,7

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -16.00    

     -1       2        -0.50        -9.50    

     -7       1        -7.00        -952.00    

     -7       2        -3.50        -161.00    

     1       1        1.00        -8.00    

     1       2        0.50        -7.00    

     7       1        7.00        448.00    

     7       2        3.50        24.50    

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

3.4    Polynomial Long Division

Dividing :  2x3 - 5x2 + 2x - 7

                             ("Dividend")

By         :    x - 2    ("Divisor")

dividend     2x3  -  5x2  +  2x  -  7

- divisor  * 2x2     2x3  -  4x2        

remainder      -  x2  +  2x  -  7

- divisor  * -x1      -  x2  +  2x    

remainder              -  7

- divisor  * 0x0                

remainder              -  7

Quotient :  2x2 - x

Remainder :  -7

so x=-7

Answer:

YOU DONT KNOW HOW TO ROUND SMH

Step-by-step explanation:

LEARN KID LEARN CMON ITS EASY

Answer:

√65/2 square units

Step-by-step explanation:

Find the diagram attached

Area of the triangle = 1/2 * base * height

To get the base and height, we will use the distance formula;

Area of the triangle LMN = 1/2 * LM * MN

For MN

Given the coordinate M(3, 2) and N(1, 3)

MN = √(3-2)²+(1-3)²

MN = √1²+(-2)²

MN = √1+4

MN = √5

For LM;

Given the coordinate L(1, -1) and M(3, 2)

LM = √(2-(-1))²+(3-1)²

LM = √(2+1)²+(2)²

LM = √3²+(2)²

LM = √9+4

LM = √13

Area of the triangle LMN = 1/2 * √13 * √5

Area of the triangle LMN = √65/2 square units

Answer:

-33.

Step-by-step explanation:

[12 -5 x 9]

= 12 - 45

= -33.

Answer:

-36

Step-by-step explanation:

[12-45]=3

-33=3

-33-3=-36

The diagram isn't attached. However, a rated diagram has been found and attached below.

Answer:

0.8611

Step-by-step explanation:

The probability of an event involves taking the ratio of the required measurement and the entire measurement.

Based on information on the attached circle, the shaded region of the circle takes 310° of the entire 360°

Choosing a point at random from which nside the circle ;

P(shaded portion) = shaded section / total measure of circle

P(shaded point) = 310 / 360 = 0.8611

Answer: X=10

Step-by-step explanation:

Answer:

4a + 4b = 10

6a + 6b = 12

Step-by-step explanation:

Putting the equation in a system of linear equation :

We donate, apples and oranges using any preffered letter or alphabet

Let :

Apples = a ; oranges = b

4 apples and 4 oranges equals $10

4a + 4b = 10

6 Apples and 6 oranges equals $12

6a + 6b = 12

Hence, the system of linear equation :

4a + 4b = 10

6a + 6b = 12

Answer:

No Solution

Step-by-step explanation:

It would require different amounts of dollars to fulfill eah equation.

Step-by-step explanation:

given

2x + y = 13

turning to y = ax + b we get

y = - 2x + 13

hope it helps :)❤