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Finger [1]
2 years ago
12

Solve: |x+2|=3 Can someone explain how to do this

Mathematics
1 answer:
katovenus [111]2 years ago
6 0

Hey there!

ORIGINAL EQUATION:
|x + 2| = 3

TRANSLATE:

x + 2 = 3 or x + 2 = -3


SOLVING for: x + 2 = 3

SUBTRACT 2 to BOTH SIDES

x + 2 - 2 = 3 - 2

CANCEL out: 2 - 2 because it give you 1

KEEP: 3 - 2 because help solve for the current x-value

NEW EQUATION: x = 3 - 2

SIMPLIFY IT!
x = 1


Thus, your answer is: x = 2

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\


SOLVING for: x + 2 = -3

SUBTRACT 2 to BOTH SIDES

x + 2 - 2 = -3 - 2

CANCEL out: 2 - 2 because it give you 0

KEEP: -3 - 2 because it help solve for the current x-value

NEW EQUATION: x = -3 - 2

SIMPLIFY IT!
x = -5

Thus, your answer is: x = -5

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\


Therefore, your answer is: x = 1 or x = -5


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

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3 years ago
Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.
Flura [38]

Answer:

The inequality that you have is 5^{n}>2^{2n+1}+100,\,n>4. You can use mathematical induction as follows:

Step-by-step explanation:

For n=5 we have:

5^{5}=3125

2^{(2(5)+1)}+100=2148

Hence, we have that 5^{5}>2^{(2(5)+1)}+100.

Now suppose that the inequality holds for n=k and let's proof that the same holds for n=k+1. In fact,

5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.

Where the last inequality holds by the induction hypothesis.Then,

5^{k+1}>(2^{2k+1}+100)\cdot (4+1)

5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100

5^{k+1}>2^{2k+3}+100\cdot 4

5^{k+1}>2^{2(k+1)+1}+100

Then, the inequality is True whenever n>4.

3 0
2 years ago
Please help, thank you!
shutvik [7]
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3 0
3 years ago
Read 2 more answers
a box has a length of 15 centimetres , a width of 22 centimetres, and a height of 9 centimetres.what is the surface area of the
zzz [600]

Answer:

1326 cm²

Step-by-step explanation:

1) Identify the equation of the surface area of a rectangular prism

       A = 2(wl + wh + hl)

2) Input the corresponding values l=15 cm; w=22 cm; and h=9 cm into the equation, and solve for the area

       A=2(wl+wh+hl)\\A=2((22)(15)+(22)(9)+(9)(15))\\A=2(330+198+135)\\A=2(663)\\A=1326 cm^{2}

3) ∴ A=1326cm^2

5 0
1 year ago
What is the quotient in simplified form? State any restrictions on the variable? \frac{x^2-16}{x^2+5x+6} /\frac{x^2+5x+4}{x^2-2x
lora16 [44]
\frac{x^2-16}{x^2+5x+6} / \frac{x^2+5x+4}{x^2-2x-8}

We can begin by rearranging this into multiplication:

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Now we can factor the numerators and denominators:

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Our answer comes out to be:

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Based on the numerator of the second fraction (since we used its inverse), the denominators of both, and the factors we canceled out earlier, the restrictions are x ≠ -4, -3, -2, -1, 4
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