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3 years ago

3 to the 10th power = 3 to the 7th power times x to the 3rd power (solve for x)

Mathematics

1 answer:

bixtya [17]3 years ago

3 0

Answer:

Step-by-step explanation:

Rewriting this sentence as an algebraic equation, we get:

3^10 = 3^7 * x^3.

Dividing both sides by 3^7 simplifies the problem:

3^3 = x^3

Here this x corresponds to the 3 in 3^3. Thus, the solution is x = 3.

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3 years ago

What two numbers multiply to 54 and add up to 7

k0ka [10]

Xy = 54
x + y = 7

$xy = 54$
$\frac{xy}{x} = \frac{54}{x}$
$y = \frac{54}{x}$

$x + y = 7$
$x + \frac{54}{x} = 7$
$\frac{x^{2}}{x} + \frac{54}{x} = 7$
$\frac{x^{2} + 54}{x} = 7$
$x^{2} + 54 = 7x$
$x^{2} - 7x + 54 = 0$
$x = \frac{-(-7) \± \sqrt{(-7)^{2} - 4(1)(54)}}{2(1)}$
$x = \frac{7 \± \sqrt{49 - 216}}{2}$
$x = \frac{7 \± \sqrt{-167}}{2}$
$x = \frac{7 \± i\sqrt{167}}{2}$
$x = \frac{7 \± 12.9i}{2}$
$x = 3.5 \± 6.45i$
$x = 3.5 + 6.45i$ $or$ $3.5 - 6.45i$

x + y = 7
3.5 + 6.45i + y = 7
- (3.5 + 6.45i) - (3.5 + 6.45i)
y = 3.5 - 6.45i
  (x, y) = (3.5 + 6.45i, (3.5 - 6.45i)

  or

  x + y = 7
3.5 - 6.45i + y = 7
- (3.5 - 6.45i)   - (3.5 - 6.45i)
y = 3.5 + 6.45i
(x, y) = (3.5 - 6.45i, 3.5 + 6.45i)

The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.

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3 years ago