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3 years ago

How is this problem simplified? I'm confused on how they got 11 and I'm assuming they got 12 by adding 2+10?

Mathematics

1 answer:

Natalka [10]3 years ago

4 0

We can show that this is true by doing this

2√3+10√3-1√3
undistribute √3
(√3)(2+10-1)
(√3)(12-1)
(√3)(11)
11√3

yah, that's what they did, but I just showed that it works

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If n and k are positive integers, is n divisible by 6 ? (1) n = k(k + 1)(k – 1) (2) k – 1 is a multiple of 3.

xz_007 [3.2K]

Answer: yes, it is

Step-by-step explanation:

A number is divisible by 6 if it is divisible by 2 and 3 simultaniously.

n = k(k+1)(k-1)

If k-1 is a multiple of 3, n is divisible by 3, so one of the requirements is ok.

Now, if k-1 is a multiple of 3, it can be even or odd.

if k-1 is even, then it is divisible by 2 and as it is divisible by 3 as well, n is divisible by 6

if k-1 is odd, then k and k+1 is even, hence, divisible by 2.

As n = k(k+1)(k-1), n is also divisible by 6.

4 0

3 years ago

Please help! I will give points for helpng.

xenn [34]

I think 19 i pretty sure

4 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B19%7D%20%20%3D%206" id="TexFormula1" title=" \frac{x}{19} = 6" alt=" \fra

Alex17521 [72]

[ Answer ]

$\boxed{X \ = \ 114}$

[ Explanation ]

$\frac{x}{19}$ = 6

Multiply Both Sides By 19

$\frac{x}{19}$ = 6 · 19

Simplify:

X = 114

Check Your Work:

$\frac{114}{19}$

Simplify:

= 6

$\boxed{[ \ Eclipsed \ ]}$

5 0

3 years ago

A 50-gallon rain barrel is filled to capacity. It drains at a rate of 10 gallons per minute. Write an equation to show how much

makvit [3.9K]

Answer:

The quantity of water drain after x min is 50 $(0.9)^{x}$

Step-by-step explanation:

Given as :

Total capacity of rain barrel = 50 gallon

The rate of drain = 10 gallon per minutes

Let The quantity of water drain after x min = y

Now, according to question

The quantity of water drain after x min = Initial quantity of water × $(1-\dfrac{\textrm rate}{100})^{\textrm time}$

I.e The quantity of water drain after x min = 50 gallon × $(1-\dfrac{\textrm 10}{100})^{\textrm x}$

or, The quantity of water drain after x min = 50 gallon × $(0.9)^{x}$

Hence the quantity of water drain after x min is 50 $(0.9)^{x}$ Answer

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3 years ago

Read 2 more answers

5 Practice

Vladimir79 [104]

Answer:

Given - A rectangle of length 18 feet and wide 14 feet

To find - Area

Solution -

Area of rectangle = Length * Breadth

$18 \times 14$

$252$ square feet

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3 years ago