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g100num [7]
3 years ago
7

AB = 3 + x

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
6 0

The given quadrilateral ABCD is a parallelogram since the opposite sides are of same length AB and DC is 4 and AD and BC is 2.

<u>Step-by-step explanation</u>:

ABCD is a quadrilateral with their opposite sides are congruent (equal).

The both pairs of opposite sides are given as AB = 3 + x , DC = 4x , AD = y + 1 , BC = 2y.

  • AB and DC are opposite sides and have same measure of length.
  • AD and BC are opposite sides and have same measure of length.

<u>To find the length of AB and DC :</u>

AB = DC

3 + x = 4x

Keep x terms on one side and constant on other side.

3 = 4x - x

3 = 3x

x = 1

Substiute x=1 in AB and DC,

AB = 3+1 = 4

DC = 4(1) = 4

<u>To find the length of AD and BC :</u>

AD = BC

y + 1 = 2y

Keep y terms on one side and constant on other side.

2y-y = 1

y = 1

Substiute y=1 in AD and BC,

AD = 1+1 = 2

BC = 2(1) = 2

Therefore, the opposite sides are of same length AB and DC is 4 and AD and BC is 2. The given quadrilateral ABCD is a parallelogram.

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Answer:

1. 27^{\frac{2}{3} } =9

2. \sqrt{36^{3} } =216

3. (-243)^{\frac{3}{5} } =-27

4. 40^{\frac{2}{3}}=4\sqrt[3]{25} =4325

5. Step 4: (\frac{343}{27}) ^{-1} =\frac{27}{343}

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Step-by-step explanation:

Use the following properties:

a^{\frac{x}{y} } =\sqrt[x]{a^{y} }

\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}

a^{-n} =\frac{1}{a^{n} }

(xy)^{z} =x^{z} y^{z} \\\\

(x^{y}) ^{z} =x^{yz}

x^{y} x^{z} =x^{y+z}

So:

1. 27^{\frac{2}{3} } =\sqrt[3]{27^{2}} =\sqrt[3]{729} }=9

2. \sqrt{36^{3} } =\sqrt{36*36*36} =\sqrt{36} \sqrt{36}  \sqrt{36} =6*6*6=216

3. (-243)^{\frac{3}{5} } =\sqrt[5]{-243^{3} } =\sqrt[5]{-14348907} =-27

4. 40^{\frac{2}{3}}=\sqrt[3]{40^{2} } =\sqrt[3]{2^{6} 5^{2} } =\sqrt[3]{2^{6} } \sqrt[3]{5^{2} } =2^{\frac{6}{3} } 5^{\frac{2}{3} } =4 *5^{\frac{2}{3} } =4\sqrt[3]{5^{2} } =4\sqrt[3]{25}=4325

5. (\frac{343}{27}) ^{-1} =\frac{1}{\frac{343}{27} } =\frac{27}{343}

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