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4 years ago

8

Rewite the expression in exponential form

1 answer:

Anastaziya [24]4 years ago

5 0

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt[6]{k^5}\implies k^{\frac{5}{6}}$

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AB is a line of symmetry of this arrow shape. A)Calculate The Perimeter of the shape.

maw [93]

Answer:

A)58cm

B) $h=4\sqrt{5}cm$

C)125.55square cm

Step-by-step explanation:

AB is a line is symmetry

Total length of left half part=12cm+9cm+3cm+5cm

Total length of left half part=29 cm

Length of left half part=Length of right half part

Therefore, length of right half part=29 cm

A) Perimeter of the shape=29cm+29cm=58cm

B)

Pythagoras theorem

$(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

Hypotenuse=12 cm

Base=5+3=8cm

In triangle ADC

Now, using Pythagoras theorem

$(12)^2=8^2+h^2$

$144=64+h^2$

$h^2=144-64=80$

$h=\sqrt{80}=4\sqrt{5}cm$

C)

Area of shape=Area of triangle+ area of rectangle

Area of shape= $\frac{1}{2}\times b\times h+l\times b$

Where l=9cm

breadth=3+3=6cm

h= $4\sqt{5}cm$

base=2(5)+3(2)=16cm

Area of shape= $\frac{1}{2}\times\times 16\times 4\sqrt{5}+9\times 6$

Area of shape=125.55 square cm

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Here is the answer worked out step by step. Hope this helps!

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