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2 years ago

Which equation is graphed in the figure?

Mathematics

2 answers:

rjkz [21]2 years ago

6 0

Answer: B
Hope this helps :)

kenny6666 [7]2 years ago

4 0

Answer: Option B.

Step-by-step explanation:

1. The equation of the line has the following form:

$y=mx+b$

Where m is the slope of the line and b is the y-intercept.

2. Therefore, you must solve for y to write the equation in that form:

$3y-4x=\frac{7}{2}x+\frac{3}{2}y+6\\\frac{3}{2}y=\frac{15}{2}x+6\\y=\frac{30}{6}y+4\\y=5x+4$

3. As you can see, the y-intercept is b=4, therefor, the equation of the option B is the equation graphed in the figure.

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2 years ago

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

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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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