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4 years ago

Tell whether the lines for this equation are parallel, perpendicular or neither

Mathematics

1 answer:

Arisa [49]4 years ago

8 0

Answer:

Perpendicular

Step-by-step explanation:

Parallel lines are lines which do not intersect and their equations have the same slope.

Perpendicular lines are lines which intersect at 90 degree angles and their equations have slopes which are the negative reciprocal of each other. If the slope is 2 then the negative reciprocal would be -1/2.

To determine which this pair of equations is compare their slopes from slope intercept form.

y= 7/3 x +3 12x + 28y = 40 becomes y = -3/7 x + 10/7

The slope is 7/3. The slope is -3/7.

These are negative reciprocals of each other. The lines are perpendicular,

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3 years ago

After completing the square, what are the solutions to the quadratic equation

Fiesta28 [93]

Answer:

$x_1= \frac{\sqrt{{29}}}{2} +\frac{7}{2}\\\\x_2= -\frac{\sqrt{{29}}}{2} +\frac{7}{2}$

Step-by-step explanation:

1. Subtract 9 from both sides of the equation:

$x^2 - 7x+9-9 = 4-9\\\\x^2 - 7x= -5$

2. Notice that the coefficient of "x" is 7. Then:

$(\frac{7}{2})^2=\frac{49}{4}$

3. Add $\frac{49}{4}$ to both sides of the equation:

$x^2 - 7x+\frac{49}{4}= \frac{49}{4}-5\\\\x^2 - 7x+\frac{49}{4}= \frac{29}{4}$

4. Completing the square, you get:

$(x -\frac{7}{2})^2= \frac{29}{4}$

5. To find the solutions, you must square-root both sides of the equation, simplify, and solve for "x". Then, you get:

$\sqrt{(x -\frac{7}{2})^2}= \±\sqrt{\frac{29}{4}}\\\\x -\frac{7}{2}=\±\frac{\sqrt{{29}}}{2} \\\\x= \±\frac{\sqrt{{29}}}{2} +\frac{7}{2}\\\\\\x_1= \frac{\sqrt{{29}}}{2} +\frac{7}{2}\\\\x_2= -\frac{\sqrt{{29}}}{2} +\frac{7}{2}$

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3 years ago

Read 2 more answers