keeping in mind that perpendicular lines have negative reciprocal slopes, hmmm what's the slope of the equation above anyway?
so we're really looking for the equation of a line whose slope is -3/2 and runs through (0,0).
Which pair of complex factors results in a real number product? 15(–15i) 3i(1 – 3i) (8 + 20i)(–8 – 20i) (4 + 7i)(4 – 7i)
2 answers:
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Answer:
15<em>y</em> = -28 <em>x</em> + 205.
Step-by-step explanation:
Slope intercept form of equation is <em>y = mx + c</em> where m is slope and c is the y intercept.
Now slope of line passing through points (-5, 23) and (10, -5):
Now equation of line:
<em> y = mx + c</em>
substituting the value of m in above expression,
Now, since the line is passing through the point (-5, 23) therefore, x = -5 and y = 23. By substituting these values in above equation,
So equation of line in slope intercept form:
Further solving,
15<em>y</em> = -28 <em>x</em> + 205.
1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.
2)The solution for b² - 4b + 4 = 0 is x=2.
<u>Step-by-step explanation</u>:
The general form of quadratic equation is ax²+bx+c = 0
where
- a is the coefficient of x².
- b is the coefficient of x.
- c is the constant term.
<u>To find the roots :</u>
- Sum of the roots = b
- Product of the roots = c
1) The given quadratic equation is m² - 5m - 14 = 0.
From the above equation, it can be determined that b = -5 and c = -14
The roots are -7 and 2.
- Sum of the roots = -7+2 = -5
- Product of the roots = -7
2 = -14
The solution is given by (x-7) (x+2) = 0.
Therefore, the solutions are x=7 and x= -2.
2) The given quadratic equation is b² - 4b + 4 = 0.
From the above equation, it can be determined that b = -4 and c = 4
The roots are -2 and -2.
- Sum of the roots = -2-2 = -4
- Product of the roots = -2
The solution is given by (x-2) (x-2) = 0.
Therefore, the solution is x=2.