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3 years ago

1. Which property is illustrated by the statement 2(-6/7)=(-6/7)2

Mathematics

1 answer:

Ivanshal [37]3 years ago

6 0

(1) it is (C) the commutative property of multiplication: a*b = b*a, so 2*(-6/7) = (-6/7)*2

(2) it is (D) the commutative property of addition: a+b=b+a, so 5*4+3=3+5*4

commutate = "swap around"

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Doesn’t matter what you pick, they are both the same equation.

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The diagram shows a square ABCD with sides of length 20cm. it also shows a semi circle and an arc circle AB is the diameter of t

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Area of Shaded Region $=50\pi$ cm^2$

Area of Semicircle $=50\pi$ cm^2$

$\dfrac{\text{Area of Shaded region}}{\text{Area of Square}}=\dfrac{ \pi}{8}$

Step-by-step explanation:

Area of Shaded Region = Area of Sector - Area of Semicircle

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$=\frac{90}{360}X\pi *20^2\\ =100\pi cm^2$

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Therefore, area of Shaded Region

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3 years ago

Find the sum of 14 + 8 + 2+ ... + ( 274) + (-280).

Musya8 [376]

The sum of the given sequence is -6384.

Step-by-step explanation:

The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).

The first term of the sequence = 14
The last term of the sequence = -280
The common difference ⇒ 14 - 8 = 6

To find the number of terms in the sequence :

The formula used is $n = (\frac{a_{n}-a_{1}} {d})+1$

where,

n is the number of terms.
$a_{n}$ is the late term which is -280.
$a_{1}$ is the first term which is 14.
d is the common difference which is 6.

Therefore, $n =(\frac{-280-14}{6}) +1$

⇒ $n =( \frac{-294}{6}) + 1$

⇒ $n = -49 + 1$

⇒ $n = -48$

⇒ n = 48, since n cannot be negative.

∴ The number of terms, n = 48.

To find the sum of the arithmetic progression :

The formula used is $S = \frac{n}{2}(a_{1} + a_{n} )$

where,

S is the sum of the sequence.
$a_{1}$ is the first term which is 14.
$a_{n}$ is the late term which is -280.

Therefore, $S = \frac{48}{2}(14+ (-280))$

⇒ $S = \frac{48}{2}(-266)$

⇒ $S = 48 \times -133$

⇒ $S = -6384$

∴ The sum of the given sequence is -6384.

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4 years ago