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What are the solutions to the quadratic equation 4(x + 2)2 = 36

Marysya12 [62]

Answer:

x=5/2

Step-by-step explanation:

3 0

3 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.

8 0

3 years ago

Please help! Im so dumb (　-̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷄ ω-̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷅ )

klio [65]

ANSWER:

For the first picture, it is the first answer. This is because of the Exterior Angle Theorem.

For the second picture, use the Exterior Angle Theorem again, but this time, solve for x.

$132 = x + (3x-24)\\132 = 4x - 24\\156=4x\\x=39$

The m∡B = 39°

3 0

3 years ago

Write 10 feet and 4 yards as a fraction in simplest form

S_A_V [24]

⅚. You first find out how many feet are in a yard (three). Then you write the fraction- 10/12. Then you reduce. The number two can evenly go into both of those numbers. Ten divided by two is five. Twelve divided by two is six. So, your final answer is ⅚.

5 0

3 years ago

Plz show work ☺ and plz explain

dolphi86 [110]

You HAVE to use Pemdas.
2[3(4^2+1)]-2^3
2(3(16+1))-2^3
2(3(17))-2^3
2*51-2^3
102-8
94.

Explanation: you use Pemdas P-parenthesis
E-exponents
M-multiplication
D-division
A-addition
S-subtraction

3 0

3 years ago

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