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3 years ago

I need help solving x^2-2=7 by factoring

Mathematics

1 answer:

bonufazy [111]3 years ago

4 0

x^2-2=7

Subtract 7 from both sides

x^2-2-7=7-7

x^2-9=0

x^2-3^2=0

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

Where a=x and b=3

(x-3)(x+3)

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Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

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In April, the Messa family gets 800 text messages included in their plan. Together, Tommy and Mary use half of the messages. Jac

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Answer: See explanation

Step-by-step explanation:

Total number of text messages = 800

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The expression to find the number of messages Cathy uses will be:

= 800 - (1/2 × 800) - 240

Since the expression is 800 - (1/2 × 800) - 240, the number of messages that Cathy will use will be:

= 800 - (1/2 × 800) - 240

= 800 - 400 - 240

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You can solve the problem this way:

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86/138 (Week 1)

92/131 (Week 2)

98/124 (Week 3)

104/117 (Week 4)

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Answer:

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Step-by-step explanation:

1/3 times 1/2 = 1/6

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Answer:

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Step-by-step explanation:

Have a nice day/night lol

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