express 0·4393939... as a fraction in its lowest term

Answer:

a) [tex]n = 4 + 7\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex], b) [tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

Step-by-step explanation:

a) The sequence is representative for an arithmetic sequence, whose key characteristic is that difference is between two consecutive elements is the same. In particular, the sequence has a difference of 7 between any two consecutive elements and the initial element is 4. Hence, we can derive the following formula:

[tex]n = n_{o} + r\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex] (1)

Where:

[tex]n_{o}[/tex] - Initial element.

[tex]r[/tex] - Difference between two consecutive elements.

[tex]i[/tex] - Index.

If we know that [tex]n_{o} = 4[/tex] and [tex]r = 7[/tex], then the expression for the n-th term of the sequence is:

[tex]n = 4 + 7\cdot i[/tex], [tex]\forall \,i\in\mathbb{N}_{O}[/tex]

b) In this case, we have a geometric sequence described by the following equation:

[tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]  (2)

The constant element ([tex]2[/tex]) represents the two extreme squares, whereas the second order binomial represents the total of squares in the middle ([tex](i+1)^{2}[/tex]) and emulates the area formula of the square.

Answer:

Step-by-step explanation:

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Answer:

1,195,742.25 (final answer since instructions did not include rounding up or anything)

Step-by-step explanation:

n = 4

The given expression is:

9^8 ÷ 9n

USE PEMDAS order of operations and solve:

9^8 ÷ 9n

= 43046721 ÷ 9n

Substitue n with 4 and solve:

43046721 ÷ 9(4)

= 43046721 ÷ 36

= 1,195,742.25

Answer:

9^4

Step-by-step explanation:

We know that a^b ÷ a^c = a^ (b-c)

9^8 ÷ 9^4

9^(8-4)

9^4

Answer:

-6 and - 65

Step-by-step explanation:

X-12x-29, by completing the square we get (x-6)^2-65

Hi there!

[tex]\large\boxed{m = 2}[/tex]

Since the line is increasing (the y-values are increasing as x increases), we can automatically eliminate any answer choice containing a negative slope.

Thus, the only correct answer choice would be m = 2.

We could also solve using the slope formula:

m = y2-y1/x2-x1

Plug in given points:

m = 3-1 / 0 - (-1)

m = 2 / 1 = 2

Answer:

x = [tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

I used the FOIL method

[(2x + 3) (3x + 2)] − [(3x + 2) (2x− 3)] = 0

[tex](6x^{2} +4x+9x+6) - (6x^{2} -9x+4x-6)=0[/tex]

[tex](6x^{2} +13x+6) - (6x^{2} -5x-6)=0[/tex]

[tex](6x^{2} +13x+6) - 6x^{2} +5x+6=0[/tex]

combine like terms

[tex]6x^{2} -6x^{2} = 0[/tex]

[tex]13x+5x=18x[/tex]

[tex]6+6=12[/tex]

so, [tex]18x +12 = 0[/tex]

subtract 12 on both sides

[tex]18x=-12[/tex]

divide by 18 to isolate x

[tex]x=-\frac{12}{18}[/tex]

and simplifies to

[tex]x=-\frac{2}{3}[/tex]

[tex] \sf \: ( - 12 )\times( - 4) + (- 8 )+ (+ 3) \\ \sf \: = (- 12 \times - 4 )+ (- 8 + 3) \\ \sf \: = 48 - 5 \\ = 43[/tex]

Hope it helps.

RainbowSalt2222

Answer:

- 14x²y

Step-by-step explanation:

Given

- 7x² × 2y

= - 7 × 2 × x² × y

= - 14x²y

Answer:

13m

Step-by-step explanation:

volume of sphere = [tex]\frac{4}{3} * pi * r^{3}[/tex] = 3000π

4r^3/3 = 3000

r^3 =2250

r = ∛2250 = 13.10370 = 13

Answer:

Radius of the sphere is 13.1 m.

Step-by-step explanation:

Volume:

[tex]{ \boxed{ \pmb{volume = { \bf{ \frac{4}{3}\pi {r}^{3} }}}}}[/tex]

Substitute:

[tex]{ \tt{3000\pi = \frac{4}{3} \times \pi \times {( {r}^{3}) } }} \\ \\ { \tt{ {r}^{3} = \frac{3000 \times 3}{4} }} \\ \\ { \tt{r = \sqrt[3]{ \frac{3000 \times 3}{4} } }} \\ { \tt{r = 13.1 \: m}}[/tex]

Answer:

x + y = -5

Step-by-step explanation:

2x - x - y + 2y = -1 - 4

x + y = -5

Answer:

T(n) = 4 + 12*n

Step-by-step explanation:

La pregunta completa se puede ver en la imagen de abajo.

En ella, podemos ver que:

La primera figura tiene: 16 palitos

la segunda figura, con n = 2, se añaden 3 palitos en cada extremo, por lo que tendremos 16 palitos + 4*3 palitos = (16 + 12) palitos

De manera similar, en la tercera figura se vuelven a añadir 3 palitos en cada extremo de la cruz, entonces esta figura tendrá:

(16 + 12) palitos + 4*3 palitos = (16 + 12 + 12) palitos.

Así, tenemos la relación:

T(1) = 16

T(2) = 16 + 12

T(3) = 16 + 12 + 12

Podemos asumir que la forma general será:

T(n) = 16 + 12*(n - 1)

podemos reescribir esto como:

T(n) = (12 + 4) + 12*(n - 1)

      = 4 + 12 + 12*(n - 1)

      = 4 + 12*n

La opción correcta es la primera.

Answer:

x^2 +3x

Step-by-step explanation:

The outer rectangle has an area of

A = l*w = (4x)*(x+2) = 4x^2 +8x

The inner rectangle has an area of

A = (3x+5)*x = 3x^2 +5x

Subtract the inner rectangle from the outer rectangle

Shaded area = 4x^2 +8x - ( 3x^2 +5x)

Distribute the minus sign

                       =4x^2 +8x -  3x^2 -5x

Combine like terms

                       = x^2 +3x

Answer:

[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{x^{5}y}[/tex]

Required

The equivalent expression

We have:

[tex]\sqrt[3]{x^{5}y}[/tex]

Rewrite as an exponent

[tex]\sqrt[3]{x^{5}y} = (x^{5}y)^\frac{1}{3}[/tex]

Open bracket

[tex]\sqrt[3]{x^{5}y} = x^{5*\frac{1}{3}}y^\frac{1}{3}[/tex]

[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]

The sum of the interior angles in a triangle is 180 degrees.

72 + 35 + <1 = 180

107 + <1 = 180

<1 = 73 degrees

Hope this helps!

Answer:

<1 = 73

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

72+ 35+ <1 = 180

Combine like terms

107 + <1 =180

Subtract 107 from each side

<1 = 180-107

<1 = 73

-4-3-2

1

2

3

4

5 6

x

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Answer:

D) 4x +3y = -6

Step-by-step explanation:

paralell lines so m1 and m2 are equal

m = (3 +1 )/ (0 - 3 )

m = -4/ 3

y -2 = -4/3 (x +3)

y =-4x/3 -2

3y = -4x -6

4x +3y = -6

Step-by-step explanation:

hope it helps you and please mark it brainliest answer

Answer:

VOLUME OF RIGHT CIRCULAR CONE=≈74.93136cm^3

VOLUME OF SPHERE: ≈523.6cm^3

Answer:

1 ) 0.023

2 ) 0.1004

Step-by-step explanation:

2 / 100 + 3 / 1000

= 0.02 + 0.003

= 0.020 + 0.003

= 0.023

1 / 10 + 4 / 10,000

= 0.1 + 0.0004

= 0.1000 + 0.0004

= 0.1004

Answer:

z₁ × z₂ = 12·cis(2·π)

Step-by-step explanation:

z₁ = 4·cis(π/2), z₂ = 3·cis(3·π/2)

We have;

z₁ = 4·cis(π/2) = 4·(cos(π/2) + i·sin(π/2))

z₂ = 3·cis(3·π/2) = 3·(cos(3·π/2) + i·sin(3·π/2))

According to De Moivre's Theorem,

z₁ × z₂ = 4×3×(cos(π/2 + 3·π/2) + i·sin(π/2 + 3·π/2)) = 12·(cos(2·π) + i·sin(2·π))

∴ z₁ × z₂ = 12·cis(2·π)

Answer:

2440

Step-by-step explanation:

an=115

a=7

Sn=n/2(a+an) [Where n is no. of terms]

   = 40/2(7+115)

   = 20(122)

   = 2440

Answer:

a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]

Step-by-step explanation:

[tex]a^{2} +b^{2} = 5 ^{2}[/tex]

a = b

[tex]2a^{2} = 5 ^{2}[/tex]

[tex]2a^{2} = 25\\[/tex]

[tex]a^{2} = \frac{25}{5}[/tex]

a = [tex]\frac{5}{\sqrt{5} }[/tex]

must rationalize...

a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]

Step-by-step explanation:

Hello!

In order to graph this, a point would have to go through (-6, 1). Then, since it says it needs a slope of 5 (or, to make things a bit easer, we could see it as 5/1) we'd need the next point to be 5 up and 1 across.

One possible solution:

(-6, 1) -> (-5, 6)

Answer:

$17,000 at 14% and $9,000 at 2%

Step-by-step explanation:

Let x = amount invested at 14%.

Let y = amount invested at 2%.

x + y = 26000

0.14x + 0.02y = 2560

     -0.02x - 0.02y = -520

(+)    0.14x + 0.02y = 2560

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

       0.12x              = 2040

x = 17,000

x + y = 26000

17000 + y = 26000

y = 9000

Answer: $17,000 at 14% and $9,000 at 2%

Answer:

A' (0,20)

B' (30,-20)

C' (-10,-40)

Answered by GAUTHMATH

Answer:

23

Step-by-step explanation:

[tex]2 y + 7[/tex]

Replace y with 8

[tex]= 2 (8) + 7\\= 16+ 7\\= 23[/tex]

Therefore, the value of the expression when y=8 is 23.

I hope this helps!

Answer: [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

tangent of ∠PLM = [tex]\frac{opposite}{adjacent} =\frac{4}{3}[/tex]

Answer:

PLM=4/3

Step-by-step explanation: