3 years ago

A line is represented by the equation 3x+2y=4. what is another way to represent the same line?

1 answer:

7 0

<u>3x + 2y = 4</u>

Here are a few different ways
to represent the same line:

2y = 4 - 3x

y = -1.5x + 2

5y = -7.5x + 10

3x = 4 - 2y

x = -2/3y + 4/3

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Use mathematical induction to show that 4^n ≡ 3n+1 (mod 9) for all n equal to or greater than 0

cestrela7 [59]

When $n=0$ , you have

$4^0=1\equiv3(0)+1=1\mod9$

Now assume this is true for $n=k$ , i.e.

$4^k\equiv3k+1\mod9$

and under this hypothesis show that it's also true for $n=k+1$ . You have

$4^k\equiv3k+1\mod9$
$4\equiv4\mod9$
$\implies 4\times4^k\equiv4(3k+1)\mod9$
$\implies 4^{k+1}\equiv12k+4\mod9$

In other words, there exists $M$ such that

$4^{k+1}=9M+12k+4$

Rewriting, you have

$4^{k+1}=9M+9k+3k+4$
$4^{k+1}=9(M+k)+3k+3+1$
$4^{k+1}=9(M+k)+3(k+1)+1$

and this is equivalent to $3(k+1)+1$ modulo 9, as desired.

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4 years ago

To win a prize in a archery contest,Kenny must score an average of 70 points or above after 3 rounds.Kenny scores 76 points and

LUCKY_DIMON [66]

He must get 70 points in his last round.

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3 years ago

Read 2 more answers

An inequality is a mathematical statement that ________________the relative values of two expressions.

Natali [406]

Answer:

An inequality is a mathematical statement that EXPLAINS the relative values of two expressions.