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9514 1404 393
Answer:
y +2 = -1/2(x -7)
Step-by-step explanation:
The line PQ has a rise of 6 units for a run of 3 units, so its slope is ...
m = rise/run = 6/3 = 2
A line perpendicular to PQ will have a slope that is the opposite reciprocal of that, so ...
-1/m = -1/2
We have the slope of the desired line, and a point it needs to pass through, so we can use the point-slope form of the equation of a line.
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
An equation for the desired line is ...
y +2 = -1/2(x -7)
__
This can be rearranged to other forms.
y = -1/2x +3/2 . . . . . slope-intercept form
x +2y = 3 . . . . . . . . . standard form
roots of the equation x^2- 4x = - 7 are 2+3i and 2-3i
What are the natures of root of quadratic equation?
Case I:
The roots of the quadratic equation are real and unequal when a, b, and c are real numbers, a 0, and the discriminant is positive.
Situation II: =0
The roots and of the quadratic equation are real and equal when a, b, and c are real numbers, a 0, and the discriminant is zero.
Case III: <0
The quadratic equation has roots when a, b, and c are real numbers, a 0, and the discriminant is negative, but these roots are not equal and are not real. We refer to the roots in this instance as fictitious.
Case IV: Perfect square and
The roots of the quadratic equation are real, rational, and unequal when a, b, and c are real numbers, a 0, and the discriminant is positive and perfect square.
Quadratic Formula
Here a = 1 , b = -4 , c = 7
using quadratic formula
Learn more about quadratic equation from the link below
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