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3 years ago

5

X^2-25=0 Using factoring method

2 answers:

Tema [17]3 years ago

6 0

Hello.

Move <span><span>−25</span><span>-25</span></span> to the right side of the equation by subtracting <span><span>−25</span><span>-25</span></span> from both sides of the equation.<span><span><span>x2</span>=25</span><span><span>x2</span>=25

</span></span>Take the square root of both sides of the equation to eliminate the exponent on the left side.
<span><span>
</span></span>The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite <span>2525</span> as <span><span>52</span><span>52</span></span>.

Pull terms out from under the radical, assuming positive real numbers.The complete solution is the result of both the positive and negative portions of the solution.
<span><span>
</span></span>The complete solution is the result of both the positive and negative portions of the solution.

<span>Answer: x=5,−<span>5

Have a nice day</span></span>

Alexxandr [17]3 years ago

5 0

$x^2 - 25 = 0$

That's the difference of two squares, which has a general factorization

$a^2 - b^2 = (a+b)(a-b)$

Applying it to our case

$0 = x^2 - 25 = (x+5)(x-5)$

Two factors multiply to zero; either must be zero.

$x=-5 \textrm{ or } x=5$

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Ipatiy [6.2K]

m = 16
8 6

Cross multiply:
m * 6 = 8 * 16

Simplifying
m * 6 = 8 * 16

Reorder the terms for easier multiplication:
6m = 8 * 16

Multiply 8 * 16
6m = 128

Solving
6m = 128

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Divide each side by '6'.
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2 years ago

For each of the following, use logic laws to decide whether the statement is a tautology contradiction, or neither. a (a) (A B)

spayn [35]

Answer:

The statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ is a contingency.

The statement $(P\rightarrow \lnot P)\land P$ is a contradiction.

Step-by-step explanation:

A tautology is a proposition that is always true.

A contradiction is a proposition that is always false.

A contingency is a proposition that is neither a tautology nor a contradiction.

a) To classify the statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ , you need to use the logic laws as follows:

$(A\rightarrow \lnot B)\land (B\rightarrow A) \equiv$

$\equiv (\lnot A \lor\lnot B)\land(\lnot B \lor A)$ by the logical equivalence involving conditional statement.

$\equiv (\lnot B\lor \lnot A )\land(\lnot B \lor A)$ by the Commutative law.

$\equiv \lnot B \lor (\lnot A \land A)$ by Distributive law.

$\equiv \lnot B \lor (A \land \lnot A)$ by the Commutative law.

$\equiv \lnot B \lor F$ by the Negation law.

Therefore the statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ is a contingency.

b) To classify the statement $(P\rightarrow \lnot P)\land P$ , you need to use the logic laws as follows:

$(P\rightarrow \lnot P)\land P \equiv$

$\equiv (\lnot P \lor \lnot P)\land P$ by the logical equivalence involving conditional statement.

$\equiv P \land (\lnot P \lor \lnot P)$ by the Commutative law.

$\equiv (P \land \lnot P) \lor (P \land \lnot P)$ by Distributive law.

$\equiv F \lor F \equiv F$ by the Negation law.

Therefore the statement $(P\rightarrow \lnot P)\land P$ is a contradiction.

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3 years ago