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Black_prince [1.1K]

2 years ago

12

Two whole numbers have a least common multiple of 60. Each number is lesss than or equal to 12. The greatest common factor of th

e two numbers is 2. What are the two numbers?

1 answer:

blsea [12.9K]2 years ago

6 0

Answer:

10 and 6

Step-by-step explanation:

2 can go into both 6 and 10 and 6 and 10 are multiples of 60

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A hemisphere has an area of 256 pi cm^2. What is its volume?

Amanda [17]

$\bf \begin{array}{llll}
\textit{surface area of a sphere}\\\\
A=4\pi r^2
\\\\\\
\textit{a hemisphere is half that}\\\\
A=\cfrac{4\pi r^2}{2}\implies A=2\pi r^2
\end{array}\qquad r=radius
\\\\\\
\textit{now, we know the area is }256\pi \implies 256\pi =2\pi r^2
\\\\\\
\cfrac{256\pi }{2\pi }=r^2\implies \sqrt{128}=r\implies \boxed{8\sqrt{2}=r}
\\\\
-----------------------------\\\\$

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad r=radius
\\\\\\
\textit{a hemisphere is half that}\\\\
V=\cfrac{\frac{4}{3}\pi r^3}{2}\implies V=\cfrac{\frac{4\pi r^3}{3}}{\frac{2}{1}}\implies V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}
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V=\cfrac{2\pi r^3}{3}
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V=\cfrac{2\pi (8^3\sqrt{2^3})}{3}\implies V=\cfrac{2\pi \cdot 512\cdot 2\sqrt{2}}{3}
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\boxed{V=\cfrac{2048\pi \sqrt{2}}{3}}$

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3 years ago

What is the solution of log 2 (3x-7) = 3

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$\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_2(3x-7)=3\implies 2^{\log_2(3x-7)}=2^3\implies 3x-7=2^3\implies 3x-7=8 \\\\\\ 3x=15\implies x=\cfrac{15}{3}\implies x=5$

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3 years ago

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Alexandra's gross annual salary is $38,556. The maximum amount of rent she can afford to pay can be determined by first solving for her monthly gross salary.

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3 years ago

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Which strategy uses place value to correctly solve for 321 x 4?

Dmitry_Shevchenko [17]

Answer:

300x4 =1200

20x4 = 80

1x4 =8

1288

Step-by-step explanation:

Break apart 321 = 300+20+ 1

This is the hundreds, tens, and ones

Then multiply each by 4

Add all together to get answer

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2 years ago

b) If a shopkeeper allows 20% discount and sells an article for Rs 200, find the marked price of the article.

zzz [600]

Answer:

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Step-by-step explanation:

mp=sp+d%of mp

x = 200+20÷100×x

100x-20x = 20000

x= 250

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1 year ago