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3 years ago

Multiply or divide as indicated b^3 x b^-3

Mathematics

1 answer:

Andru [333]3 years ago

7 0

The domain: $b\neq0$

Method 1.

$Use\ a^n\cdot a^m=a^{n+m}\\\\b^3\cdot b^{-3}=b^{3+(-3)}=b^{3-3}=b^0=1$

Method 2.

$Use\ a^{-n}=\dfrac{1}{a^n}\\\\b^3\cdot b^{-3}=b^3\cdot\dfrac{1}{b^3}=\dfrac{b^3}{b^3}=1$

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10) A rhombus has a<br> diagonal 8.6 mm long<br> and an area of 81.7 mm. what is the<br> perimeter?

BaLLatris [955]

Answer:

P=41.72

Step-by-step explanation:

S=ACxDB/2

81.7=8.6xDB/2

81.7=4.3xDB|:4.3

19(mm)=DB

DO=19/2=9.5

OC=8.6/2=4.3

(O is the center of the rhombus, where two diagonals meet)

a²+b²=c² (DO²+OC²=DC²)

9.5²+4.3²=c²

90.25+18,49=c²

√108,74=√c²

c≈10.43

P=4c

P=4x10.43

P=41.72

Hope it helps:)

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2 years ago

five times the difference of twice a number and three, decreased by the sum of the number and eight, equals thirteen

trapecia [35]

5x(2y-3)-(y+8)=13 I believe this is correct

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3 years ago

Jasmine runs 13kilometers and 76 minutes. how long woukd it take to run 1 kilometers

k0ka [10]

Answer:

It would take her 5.85 minutes to run 1 kilometer.

Step-by-step explanation:

76/13= 5.846

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3 years ago

Which of these sets could represent the side lengths of a right triangle?

Jlenok [28]

Answer:

{6, 8, 10} is a set which represents the side length of a right triangle.

Step-by-step explanation:

In a right triangle:

$(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}$

Now, in the given triplets:

(a) {4, 8, 12}

Here, $(4)^{2} + (8)^{2} = 16 + 64 = 80\\\implies H = \sqrt{80} = 8.94$

So, third side of the triangle 8.94 ≠ 12

Hence, {4, 8, 12} is NOT a triplet.

(b) {6, 8, 10}

Here, $(6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10$

So, third side of the triangle 10

Hence, {6, 8, 10} is a triplet.

Here, $(6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10$

So, third side of the triangle 10 ≠ 15

Hence, {6, 8, 15} is NOT a triplet.

(d) {5, 7, 13}

Here, $(5)^{2} + (7)^{2} = 25 + 49 = 74\\\implies H = \sqrt{74} = 8.60$

So, third side of the triangle 8.60 ≠ 13

Hence, {5, 7, 13} is NOT a triplet.

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3 years ago

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Elena L [17]

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Step-by-step explanation:

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