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3 years ago

Simplify 5m-2(6m-5)+2a. -7m-8b. -7m+12c. 17m+12d. 17m-8

Mathematics

1 answer:

fgiga [73]3 years ago

7 0

The answer is B. -7m+12.

First distribute the -2 to 6m and -5.

5m-2(6m-5)+2

5m+(-2*6m)+(-2*-5)+2

5m+-12m+10+2

After that, combine the like terms.

5m+-12m+10+2

-5m+-12m=-7m

10+2=12

The simplified expression is -7m+12.

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Prove the formula that:

azamat

Step-by-step explanation:

Given: [∀x(L(x) → A(x))] →

[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for

arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof

technique.

Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

We need to show that the above expression is unsatisfiable (False).

¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))

∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))

E.I with respect to x,

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))

E.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b

U.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Since P ∧ Q is P, drop L(a) from the above expression.

(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Apply distribution

(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))

Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to

(L(b) ∧ H(a, b) ∧ ¬A(b))

U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace

¬A(b) in the above expression with ¬L(b). Thus, we get,

(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.

This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows

from the premise.

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3 years ago

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3 years ago

I WILL MARK FIRST BRAINLIEST! I leave a thanks too! 0 = -2x^2 - 7x -1 Solve using quadratic formula PLEASEEEEEE I need the answe

slamgirl [31]

Here,

2x^2 + 7x + 1 = 0

given,

a = 2

b = 7

and c = 1

From formula,

x = (-b+-√b^2-4ac) / 2a.

We get,

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3 years ago

What is the answer a, b, c, or d

podryga [215]

Answer: Choice B

(-2, 5)

==================================================

Explanation:

The original system is

$\begin{cases}-4x+3y = 23\\ x-y = -7\end{cases}$

Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations

$\begin{cases}-4x+3y = 23\\ 3x-3y = -21\end{cases}$

Now add straight down

The x terms add to -4x+3x = -1x = -x

The y terms add to 3y+(-3y) = 0y = 0

The terms on the right hand sides add to 23+(-21) = 2

We end up with the equation -x = 2 which solves to x = -2

Now use this to find y. You can pick any equation with x,y in it

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-4x+3y = 23

-4(-2)+3y = 23

8+3y = 23

3y = 23-8

3y = 15

y = 15/3

y = 5

x-y = -7

-2-y = -7

-y = -7+2

y = -5

y = 5

Either way, we get the same y value.

So that's why the solution is (x,y) = (-2, 5)

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3 years ago

Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents

ANEK [815]

-24

Step-by-step explanation:

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3 years ago

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