Answer:
<h2>x > 5</h2>Step-by-step explanation:
Use slope to determine if the following lines are parallel, perpendicular, or neither.
1 answer:
Answer:
The lines are parallel, with the same slope of 5.
Step-by-step explanation:
Remember that if slopes are the same, then the lines are parallel. If the slopes are opposite reciprocals, they are perpendicular. If they are neither of those cases, then they would be neither.
1) Since y = 5x + 1 is already in slope-intercept format (y = mx + b, in which m represents the slope) we know that 5 is the slope of that equation.
2) To find the slope of -5x + y = 6, let's just convert it to the slope-intercept format by isolating y on the left side like so:
(All you need to do is move -5x to the right side of the equation.) So, by looking at y = 5x + 6, we can do the same thing we did from step 1 and find that the slope is 5.
3) Since both of the equations' slopes are 5, they share the same slope - therefore, they are parallel.
Hope this helps! Please do not hesitate to ask any questions.
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Answer:
Step-by-step explanation:
Solve Using the Quadratic Formula
4x^2 + 8x − 5 = 0
Use the quadratic formula to find the solutions.
−b ± √b^2 − 4 (ac)
-------------------------
2a
Substitute the values a = 4, b = 8, and c = −5 into the quadratic formula and solve for x.
−8 ± √82 − 4 ⋅ (4 ⋅ −5)
-------------------------
2 ⋅ 4
Simplify the numerator.
Raise 8 to the p ower of 2.
−8 ± √64 − 4 ⋅ 4 ⋅ −5
x= ---------------------------
2 ⋅ 4
Multiply −4 by 4.
−8 ± √64 − 16 ⋅ −5
x = -------------------------
2 ⋅ 4
Multiply −16 by −5.
−8 ± √64 + 80
x = -------------------
2 ⋅ 4
Add 64 and 80.
−8 ± √144
x = --------------
2 ⋅ 4
Rewrite 144 as 12^2.
−8 ± √122
x = ------------
2 ⋅ 4
Pull terms out from under the radical, assuming positive real numbers.
multiply 2 by 4
−8 ± 12
x= ------------
8
simplify
−2 ± 3
x= ---------
2
The final answer is the combination of both solutions.
x= 1/2, -5/2
Hope this helped!