Answer:
k > 12
Step-by-step explanation:
If a quadratic equation has no real roots the values of b^2 - 4ac
( for the general form ax^2 + bx + c = 0) is negative,
So we have the inequality:
(-12)^2 - 4*3* k < 0
144 - 12k < 0
12k > 144
k > 12
The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7
Step-by-step explanation:
The parallel lines have:
- Same slopes
- Different y-intercepts
The form of the linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept
∵ The equation of the given line is y = 5x + 4
∴ m = 5 and b = 4
∵ The two lines are parallel
∴ Their slopes are equal
∴ The slope of the parallel line = 5
- Substitute the value of the slope in the form of the equation
∴ y = 5x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ The parallel line passes through point (-1 , 2)
∴ x = -1 and y = 2
∵ 2 = 5(-1) + b
∴ 2 = -5 + b
- Add 5 to both sides
∴ 7 = b
- Substitute the value of b in the equation
∴ y = 5x + 7
The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7
Learn more:
You can learn more about the equations of the parallel lines in brainly.com/question/9527422
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Answer
The expression is equivalent to sin^{2}x
The first step is to multiply the two expressions between parentheses :
(II)
There is a trigonometric identity that states :
Working with this expression :
⇒
(I)
Using the equation (I) in (II) :
⇒
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