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3 years ago

Which of the following is the equation of a line parallel to the line y = 3x + 2,

Mathematics

1 answer:

earnstyle [38]3 years ago

3 0

Answer:

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 is in this form with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (10, 1) into the partial equation

1 = 30 + c ⇒ c = 1 - 30 = - 29

y = 3x - 29 ← in slope- intercept form

Subtract y from both sides

0 = 3x - y - 29 ( add 29 to both sides )

29 = 3x - y, thus

3x - y = 29 ← in standard form → B

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Which of the following is the result of the equation below after completing the square and factoring?

Tems11 [23]

Answer:

D) $(x + \frac{5}{2})^{2} = \frac{9}{4}$

Step-by-step explanation:

Step(i):-

Given equation

x² + 5 x + 8 = 4

⇒ $x^{2} + 2 X \frac{5}{2} x + (\frac{5}{2} )^{2} - (\frac{5}{2} )^{2}+ 8 = 4$

Step(ii):-

By using (a + b)² = a² + 2 a b + b²

⇒ $(x + \frac{5}{2})^{2} - (\frac{5}{2} )^{2}+ 8 = 4$

⇒ $(x + \frac{5}{2})^{2} = 4 + (\frac{5}{2} )^{2} -8$

⇒ $(x + \frac{5}{2})^{2} = (\frac{25}{4} ) -4$

⇒ $(x + \frac{5}{2})^{2} = (\frac{25-16}{4} )$

⇒ $(x + \frac{5}{2})^{2} = \frac{9}{4}$

Final answer:-

$(x + \frac{5}{2})^{2} = \frac{9}{4}$

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