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Tju [1.3M]
3 years ago
10

Augustus ruled the roman empire from 27 BC to AD 14.For how many years did he rule?​

Mathematics
2 answers:
Lyrx [107]3 years ago
8 0

Answer:

41

Step-by-step explanation:

kari74 [83]3 years ago
6 0

Answer:

41 year

s

Step-by-step explanation:

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HELP PLEASE SIMPLIFY !!!
Lelechka [254]

Answer:

=x^{\frac{5}{6}}+2x^{\frac{7}{3}}

Step-by-step explanation:

x^{\frac{1}{3}}\left(x^{\frac{1}{2}}+2x^2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=x^{\frac{1}{3}},\:b=x^{\frac{1}{2}},\:c=2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+x^{\frac{1}{3}}\cdot \:2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\\mathrm{Simplify}\:x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}:\quad x^{\frac{5}{6}}+2x^{\frac{7}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=x^{\frac{5}{6}}

x^{\frac{1}{3}}x^{\frac{1}{2}}\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=\:x^{\frac{1}{3}+\frac{1}{2}}\\=x^{\frac{1}{3}+\frac{1}{2}}\\\mathrm{Join}\:\frac{1}{3}+\frac{1}{2}:\quad \frac{5}{6}\\\frac{1}{3}+\frac{1}{2}\\\mathrm{Least\:Common\:Multiplier\:of\:}3,\:2:\quad 6\\Adjust\:Fractions\:based\:on\:the\:LCM\\=\frac{2}{6}+\frac{3}{6}

\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{2+3}{6}\\\mathrm{Add\:the\:numbers:}\:2+3=5\\=\frac{5}{6}\\=x^{\frac{5}{6}}\\2x^2x^{\frac{1}{3}}=2x^{\frac{7}{3}}\\=x^{\frac{5}{6}}+2x^{\frac{7}{3}}

7 0
3 years ago
The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each
Agata [3.3K]
First compute the area of the square like this: 9^2=81
There is two semi circles here, so the sum of the two white 
spaces equate the area of a circle. 
the radius of the circle is 9/2. 
So compute the area of the like this:  \pi (\frac{9}{2})^2
And the area of the shaded region is the area of the square minus 
the area of the two semi circles, like this:
81-\pi (\frac{9}{2})^2
We are done. 
8 0
4 years ago
A pole that is 3.2m tall casts a shadow that is 1.29m long. At the same time, a nearby tower casts a shadow that is 39.25m long.
pashok25 [27]

Set up a ratio of height over shadow length:

3.2/1.29 = X/39.25

Cross multiply:

1.29x = 3.2 * 39.25

Simplify:

1.29x = 125.6

Divide both sides by 1.29:

x = 97.364 meters

Round to the nearest meter = 97 meters

5 0
3 years ago
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DochEvi [55]

Answer:

r = p(-b/a)

Step-by-step explanation:

Let p(x) = q(x)(ax + b) + r(x) where q(x) is the quotient when p(x) is divided by ax + b and r(x) is the remainder.

Since ax + b is a first degree polynomial, r(x) is one power less than ax + b is is just a constant, r.

So, p(x) = q(x)(ax + b) + r

Now, p(x) = r when q(x)(ax + b) = 0

since q(x) ≠ 0, ax + b = 0 ⇒ ax = -b ⇒ x = -b/a

⇒ p(x) = r when x = -b/a

So, r = p(-b/a)

So, the remainder when a polynomial function p(x) is divided by a first degree polynomial ax + b is p(-b/a)

8 0
3 years ago
Is checking account an asset or liabilitie
photoshop1234 [79]
A checking account is a liability
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3 years ago
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