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Nostrana [21]
3 years ago
5

Does anyone know this answer??

Mathematics
2 answers:
Aleonysh [2.5K]3 years ago
8 0

For this case we have the following equation:

(2x + 3) ^ 2 + 8 (2x + 3) + 11 = 0

Let u = 2x + 3

We have:

u ^ 2 + 8u + 11 = 0

By definition, given an equation of the form ax ^ 2 + bx + c = 0

The quadratic formula, to find the solution can be written as:

x = \frac{-b+/-\sqrt{b ^ 2-4 (a) (c)} }{2(a)}

In this case we have:

a = 1\\b = 8\\c = 11

Substituting in the quadratic formula we have:

See attached image

Answer:

Option B

Andru [333]3 years ago
4 0

x = (- 7 ± √5) / 2

use the substitution u = 2x + 3

equation can now be written as

u² + 8u + 11 = 0

solve for u using the quadratic formula with a = 1, b = 8 and c = 11

u = ( - 8 ± √( 64 - 44 ) )/2

  = ( - 8 ± √20 )/2 = ( - 8 ± 2√5 ) / 2 = - 4 ± √5

change the variable back into terms of  x

2x + 3 = - 4 ± √5 ( subtract 3 from both sides )

2x = - 7 ± √5 ( divide both sides by 2 )

x = ( - 7 ± √5 ) / 2

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[ Refer to the attached file ]

( Slide to refer all files )

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Both lines are equal (they are the same)

<em></em>

Step-by-step explanation:

Given

3y - 8 = -5x

6y = -10x + 16

Required

What is true about graph of both lines

<em>Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check  if both lines are either parallel or perpendicular</em>

<em />

To do this,

The first thing to do is to calculate the slope of both lines

3y - 8 = -5x

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3y = -5x + 8

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y = -\frac{5x}{3} + \frac{8}{3}

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y = 0 + \frac{8}{3}

y = \frac{8}{3}

Solve for the x intercept; <em>Let y = 0</em>

0 = -\frac{5x}{3} + \frac{8}{3}

Subtract \frac{8}{3} from both sides

0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}

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-\frac{3}{5}*- \frac{8}{3} = x

\frac{3}{5} * \frac{8}{3} = x

\frac{8}{5} = x

x = \frac{8}{5}

------------------------------------------------------------------------------------------------------

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y = -\frac{10x}{6} + \frac{16}{6}

Simplify fractions to lowest term

y = -\frac{5x}{3} + \frac{8}{3}

The slope of the line is the coefficient of x;

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Solve for the y intercept; <em>Let x = 0</em>

y = -\frac{5 * 0}{3} + \frac{8}{3}

y = 0 + \frac{8}{3}

y = \frac{8}{3}

Solve for the x intercept; <em>Let y = 0</em>

0 = -\frac{5x}{3} + \frac{8}{3}

Subtract \frac{8}{3} from both sides

0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}

- \frac{8}{3} = -\frac{5x}{3}

Subtract both sides by -\frac{3}{5}

-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}

-\frac{3}{5}*- \frac{8}{3} = x

\frac{3}{5} * \frac{8}{3} = x

\frac{8}{5} = x

x = \frac{8}{5}

-------------------------------------------------------------------------------------------------------

By comparing the slope, x intercept and y intercept of both lines;

It'll be observed that they have the same slope, x intercept and y intercept

<em>This implies that both lines are equal; in other words, they are the same.</em>

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