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2 years ago

Match each equivalent expression with the property that it represents.

Mathematics

1 answer:

OlgaM077 [116]2 years ago

6 0

Answer:

Associative Property of Multiplication

[ 3(5) (4) = (3) 5(4)]

Identity Property of Multiplication

5(1) = 5

Identity Property of Addition

(3 + 5) + 0 = (3+5)

Commutative Property of Addition

3 + 5 = 5 + 3

Associative Property of Addition

3 + (5 + 7) = (3 + 5) + 7

Step-by-step explanation:

The associative property states that you can re-group numbers and you will get the same answer and the commutative property states that you can move numbers around and still arrive at the same answer.

The identity property of 1 says that any number multiplied by 1 keeps its identity.

Hoped this helped!

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— 25 — 3х + 5 or – 3х +5 — 31

zysi [14]

Answer:

both should

be equal to hope my work is correct or helps

Step-by-step explanation:

first one

-25<-3x+5 subtract 5 from both sides

-25-5=-30

5-5=0

then divide by -3

-30 divided by -3 =10

x=10

so it is equal to not less than

second one

-3x+5<-31

subtract 5 from both sides 5-5=0

-31 -5=-36

then divide both sides by -3

x=12

6 0

2 years ago

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$