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3 years ago

What is the missing length??

Mathematics

1 answer:

amid [387]3 years ago

4 0

Answer

The missing length is 10

Step-by-step explanation:

Represent the missing length with x

The sides of the given shape are directly proportional.

Mathematically:

(15 + x) to (12 + 8) and x to 7

Represent as a ratio:

$(15 + x) : (12 + 8) = x : 8$

$15 + x : 20= x : 8$

Convert to fraction

$\frac{15 + x}{20} = \frac{x}{8}$

Cross Multiply:

$(15 + x)*8 = 20 * x$

$120 + 8x = 20x$

Collect Like Terms

$20x - 8x = 120$

$12x = 120$

Solve for x

$x = \frac{120}{10}$

$x = 10$

<em>The length of the missing side is 10</em>

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3 years ago

taurus [48]

Answer:

$x^2 - 2x + 10$ , option B

Step-by-step explanation:

Complex numbers:

The most important relation that involves complex numbers is given by:

$i^2 = -1$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

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$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

The solutions are:

$x_1 = 1 - 3i, x_2 = 1 + 3i$

We have to find the polynomial. All option have $a = 1$ . So

$(x - (1 - 3i))(x - (1 + 3i)) = x^2 - x(1 + 3i) - x(1 - 3i) + (1 - 3i)(1 + 3i) = x^2 - x -3ix - x + 3ix + 1^2 - (3i^2) = x^2 - 2x + 1 - 9i^2 = x^2 - 2x + 1 - 9(-1) = x^2 - 2x + 10$

The correct answer is given by option b.

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