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zhannawk [14.2K]
3 years ago
11

(

id="TexFormula1" title=" (\frac{2}{3} x^{-3} y^{4} z^{2})^{3} " alt=" (\frac{2}{3} x^{-3} y^{4} z^{2})^{3} " align="absmiddle" class="latex-formula"> 
Mathematics
1 answer:
kobusy [5.1K]3 years ago
7 0
\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad 
a^n\implies \cfrac{1}{a^{-n}}
\\\\
-------------------------------

\bf \left(\cfrac{2}{3}x^{-3}y^4z^2  \right)^3\implies \stackrel{\textit{distributing the exponent}}{\left[\left( \cfrac{2}{3} \right)^3x^{^{-3\cdot 3}}y^{4\cdot 3}z^{2\cdot 3}  \right]}\implies \cfrac{2^3}{3^3}x^{-9}y^{12}z^6
\\\\\\
\cfrac{8}{27}\cdot \cfrac{1}{x^9}y^{12}z^6\implies \cfrac{8y^{12}z^6}{27x^9}
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What is the measure of 0 ?
MrRissso [65]

Answer:

Option A. 4 radians

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

C=2\pi r

we have

r=5\ cm

substitute

C=2\pi (5)

C=10\pi\ cm

step 2

Find the measure of angle \theta

we know that

The circumference of the circle subtends a central angle of 2π radians

so

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Find out the central angle by an arc length of 20 cm

\frac{10\pi}{2\pi}=\frac{20}{x}\\\\x=2\pi (20)/10\pi\\\\x=4\ radians

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3 years ago
Consider the following polynomial.
vfiekz [6]

Answer:

The equivalent factored form of this equation is (x² + 49)(x - 6)

Step-by-step explanation:

<em>x³ - 6x² + 49x - 294</em>

First, group the first and second terms together and group the last two terms together.

<em>(x³ - 6x²) + (49x - 294)</em>

Find the greatest common factor of both parentheses and factor them.  

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Now, since the two terms in the parentheses are the same, then we have factored the equation correctly.

So, the factored form of the equation is (x² + 49)(x - 6)

3 0
2 years ago
Read 2 more answers
Dennis is cutting construction paper into rectangles for a project he needs to cut one rectangle that is 12 inches times 15 1/4
Nataly_w [17]

Answer:

Dennis need 288.91 square inches of construction paper for his project.

Step-by-step explanation:

Dennis is cutting construction paper into rectangles for a project.

He needs to cut one rectangle that is 12 inches times 15 1/4 inches

First convert the mixed fraction to improper fraction

15\frac{1}{4} = \frac{(15\times4) + 1}{4} = \frac{61}{4}

So the area of 1st rectangle is

A_1 = 12\times \frac{61}{4} = 183 \: in^{2}

He needs to cut another rectangle that is 10 1/3"" x 10 1/4""

The symbol " means inches

First convert the mixed fraction to improper fraction

10\frac{1}{3} = \frac{(10\times3) + 1}{3} = \frac{31}{3}

10\frac{1}{4} = \frac{(10\times4) + 1}{4} = \frac{41}{4}

So the area of 2nd rectangle is

A_2 = \frac{31}{3}\times \frac{41}{4} = 105.91 \: in^{2}

The total construction paper needed for this project is

A = A_1 + A_2\\\\A = 183 + 105.91\\\\A = 288.91 \: in^{2}

Therefore, Dennis need 288.91 square inches of construction paper for his project.

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3 years ago
Sara has 4\frac{3}{4}4 4 3 ​ yards of red fleece and 2\frac{2}{3}2 3 2 ​ yards of blue fleece fabric. How many yards of red and
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Step-by-step explanation:

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3 years ago
I need help with number 12 I’ll rate 5 stars if you help
Brrunno [24]

Answer:

0.25in.

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