Does a repeating decimal end in repeating zeros

Which is equal to 47 __ 5

Sergeu [11.5K]

D
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5x9= 45 remainder3 which means it 9 3/5

5 0

3 years ago

Meldie made a cube whose side is (3x - 2) inches. Find its volume in cubic inches.

irinina [24]

Answer:

x^2(3x-2) cubic inches OR in^3

OR

3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3

I AM UNAWARE IF YOU ASKED THAT ONE SIDE IS (3X-2) OR ALL. I WILL ANSWER BOTH PARTS

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NOTE: '^' MEANS TO THE POWER OF..

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Volume = v, abc = 3 sides of cube (height, width, length)

Using the formula for volume in a cube,

$v = abc$

We can solve this.

If one side is (3x-2)in,

(3x-2)(x)(x) = v.... x are the other two sides
x^2(3x-2) = v

x^2(3x-2) cubic inches OR in^3

If all sides are (3x-2)in,

Use the formula,

$(a - b) ^{3} = {a}^{3} + 3ab(b - a) - {b}^{3}$

We can solve this.

(3x-2)(3x-2)(3x-2) = v
(3x-2)^3 = v.... 3x = a and -2 = b
(3x)^3 + [(3)(3x)(2)][2-3x] - (2)^3 = v
27x^3 + 18x(2-3x) -8 = v
(27x^3 + 36x - 54x^2) - 8 = v.. Terms inside brackets - take 3x as common and leave out 8
3x(9x^2 -18x +12) = v... Take 3 as common again in the brackets
3x [ 3 ([3x^2 -6x] + 4) -8 = v....Take 3x common in the terms in square brackets
3x [ 3 [ 3x (x-2) + 4 ]] - 8 = v
3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 = v

3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3

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If you have any questions regarding formulas or anything, comment and I will get back to you asap.

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5 0

1 year ago

Find the base of an isosceles triangle whose area is 60 cm² and the length of one of its equal sides is 13 cm.

Kobotan [32]

Answer:

Base = 24 cm or 10cm

Step-by-step explanation:

REMEMBER:
An isosceles triangle ABC with base BC = ‘b' & height AD = ‘h' & its equal sides =13 cm & area = 60 cm²

Using the formulas

$A=\frac{bh_b}{2}$

$h_b=\sqrt{a^2-\frac{b^2}{4} }$

There are 2 solutions for $b$

$b=2\sqrt{2} \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2+\sqrt{13^4-4*60^2} } }$ ≈ $10cm$ $b=2\sqrt{2} \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2-\sqrt{13^4-4*60^2} } }=24cm$

Less complex:

Area of a triangle = 1/2 * b * h = 60

=> h = 120/b

In right triangle ABD

13² = h² + b² /4 ( by Pythagoras law)

=>169 = 120²/b² + b²/4

=>676 b² = 57600 + b^4

=> b^4 - 676 b² + 57600 = 0

=> b² = 676 +- √(676² - 4*57600) / 2

=> b²= 676 +- √(226576) /2

=> b² = (676 +- 476 )/2

=> b² = 1152/2 , 200 /2

=> b² = 576 , 100

=> b = 24, 10

So, Base = 24 cm or 10cm

4 0

2 years ago

A bottle contains 5/9 liters of soda. Keisha has 3 of these bottles.

satela [25.4K]

Answer: 1 2/3 Liters

Step-by-step explanation:

Create the equation

The equation is going to be the amount of soda, multiplied by the amount of bottles Keisha has

5/9 x 3/1 (3/1 is equivalent to having 3 or 1+1+1)

Solve

We are going to multiple the numbers, numerator by numerator, and denominator by denominator since we do not need to add or subtract

Numerator= 5x3=15
Denominator= 9x1=9

Your improper awnser would be 15/9

DO NOT STOP HERE THIS IS NOT THE SIMPLEST FORM

Create the simplest mixed number

15/9 is equal to 15 divided by 9

we can fit 1 9 in 15 without going over

1 ?/15

15-9=6

1 6/9

Simplify

6 and 9 are both divisible by 3

6 divided by 3 = 2

9 divided by 3 = 3

1 6/9=1 2/3

Awnser and add your units

1 2/3 is the simpelest form, this can not be further divided.

1 2/3 Liters of Soda

3 0

3 years ago

Determine the quotient, q(x), and remainder, r(x) when

Vinvika [58]

ANSWER

Quotient:

$q(x) = 4 {x}^{2} + 3x + 2$

Remainder:

$r(x) = 3x + 1$

EXPLANATION

The given functions are

$f(x) = 12 {x}^{4} + 21 {x}^{3} + 31 {x}^{2} + 21x + 9$

and

$g(x) = 3 {x}^{2} + 3x + 4$

We want to find the remainder and quotient when f(x) is divided by g(x).

We perform the long division as shown in the attachment.

The quotient is

$q(x) = 4 {x}^{2} + 3x + 2$

The remainder is

$r(x) = 3x + 1$

5 0

4 years ago