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3 years ago

How do I simplify this? With steps please :)

Mathematics

1 answer:

Zigmanuir [339]3 years ago

3 0

Answer:

${ \tt{ = \frac{ {p}^{2} + 8p + 16 }{ {p}^{2} - 16 } }} \\ \\ = { \tt{ \frac{ {(x + 4)}^{2} }{(x - 4)(x + 4)} }} \\ \\ = { \tt{ \frac{(x + 4)}{(x - 4)} }}$

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Help answer question 3

Rufina [12.5K]

Answer:

The answer is the first one. Inside the absolute value symbols it is negative but absolute value answers are always positive. Instead of -30 the answer is 30.

8 0

3 years ago

Simplify (8^4/10^4)^-1/4using rational exponents

Vlad1618 [11]

Answer:

$(\frac{8^4}{10^4} )^{-\frac{1}{4} }$ = $\frac{5}{4}$

Step-by-step explanation:

Explanation

Given

$(\frac{8^4}{10^4} )^{-\frac{1}{4} }$

By using algebra formulas

$(\frac{a}{b} )^{m} = \frac{a^m}{b^n}$

$(\frac{8^4}{10^4} )^{-\frac{1}{4} } = \frac{(8^{4})^{\frac{-1}{4} } }{(10^{4} )^{\frac{-1}{4} } }$

$(a^{m} )^{n} = a^{mn}$

$\frac{(8^{4})^{\frac{-1}{4} } }{(10^{4} )^{\frac{-1}{4} } } = \frac{8^{4X\frac{-1}{4} } }{10^{4 X\frac{-1}{4} } }$

= $\frac{8^{-1} }{10^{-1} }$

$= \frac{10}{8} \\= \frac{5}{4}$

Final answer:-

$(\frac{8^4}{10^4} )^{-\frac{1}{4} }$ = $\frac{5}{4}$

7 0

3 years ago

Tim picked up 20% of the books in the room. If he picked up 8 books, how many were in the room? Explain your answer please, I wi

fenix001 [56]

Answer: 40 books

Step-by-step explanation: 20%=8 Books

100 divided by 20 = 5

8 x 5 = 40

6 0

2 years ago

Read 2 more answers

Which algebraic rule describes the translation of quadrilateral ABCD to quadrilateral A’B’C’D?

Ronch [10]

Answer:

Step-by-step explanation:

The figure moves to the right 8 units which is positive and then up 7 units which is also positive.

8 0

1 year ago

Find (a) the arc length and (b) the area of a sector.

Brut [27]

Answer:

a) 23.56 ft (2 dp)

b) 58.90 ft² (2 dp)

Step-by-step explanation:

Formula

$\textsf{Arc length}=r \theta$

$\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta$

$\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}$

Calculation

Given:

$\theta=\dfrac{3 \pi}{2}$
r = 5 ft

$\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 5\left(\dfrac{3 \pi}{2}\right)\\& = \dfrac{15}{2} \pi \\& = 23.56\: \sf ft\:(2\:dp)\end{aligned}$

$\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(5^2) \left(\dfrac{3 \pi}{2}\right)\\\\& = \dfrac{25}{2}\left(\dfrac{3 \pi}{2}\right)\\\\ & = \dfrac{75}{4} \pi \\\\& = 58.90 \: \sf ft^2\:(2\:dp)\end{aligned}$

6 0

2 years ago