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2 years ago

Which of the following are true statements about the expression 5 + (-5)?

Mathematics

2 answers:

Julli [10]2 years ago

5 0

Answer:

y= -1/4x

Step-by-step explanation:

krok68 [10]2 years ago

4 0

Answer:

Step-by-step explanation:

the expression equals 0. 5-5 is 0...

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Answer:

1/5

Step-by-step explanation:

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2 years ago

Given that 'n' is a natural number. Prove that the equation below is true using mathematical induction.

LenaWriter [7]

<h3>To ProvE :- </h3>

1 + 3 + 5 + ..... + (2n - 1) = n²

Method :-

If P(n) is a statement such that ,

P(n) is true for n = 1
P(n) is true for n = k + 1 , when it's true for n = k ( k is a natural number ) , then the statement is true for all natural numbers .

$\sf\to \textsf{ Let P(n) : 1 + 3 + 5 + $\dots$ +(2n-1) = n$^{\sf 2}$ }$

Step 1 : Put n = 1 :-

$\sf\longrightarrow LHS = \boxed{\sf 1 } \\$

$\sf\longrightarrow RHS = n^2 = 1^2 = \boxed{\sf 1 }$

Step 2 : Assume that P(n) is true for n = k :-

$\sf\longrightarrow 1 + 3 + 5 + \dots + (2k - 1 ) = k^2$

Add (2k +1) to both sides .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1)=k^2+(2k+1)$

RHS is in the form of ( a + b)² = a²+b²+2ab .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1)= (k +1)^2$

Adding and subtracting 1 to LHS .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1) + 1 -1 = (k +1)^2 \\$

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+2) - 1 = (k +1)^2$

Take out 2 as common .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+\{2(k+1)-1\}= (k +1)^2$

P(n) is true for n = k + 1 .

Hence by the principal of Mathematical Induction we can say that P(n) is true for all natural numbers 'n' .

**Edits are welcomed**

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2 years ago

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Korvikt [17]

Step-by-step explanation:

$(6 {y}^{2} + 2y + 5) - (5 {y}^{2} - 6y - 11) \\ = 6 {y}^{2} + 2y + 5 - 5 {y}^{2} + 6y + 11 \\ = 6 {y}^{2} - 5 {y}^{2} + 2y + 6y + 5 + 11 \\ = {y}^{2} + 8y + 16$

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3 years ago

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Temka [501]

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Which of the following are true statements about the expression 5 + (-5)?​

Which of the following are true statements about the expression 5 + (-5)?