To effectively determine the correct answer, it would be helpful to write this into an algebraic expression. We let x as the number. We do as follows:
<span>Four times the square of a certain number increased by 6 times the number equals 108.
4x^2 + 6x = 108
The numbers can be either of the following since the equation generated was a quadratic equation which has two roots.
x = 4.5
x = -6 </span>
Given:
The two points are (-5,8) and (-3,1).
To find:
The distance between the given two points in simplest radical form.
Solution:
Distance formula: The distance between two points is
Using distance formula, the distance between (-5,8) and (-3,1) is
Therefore, the distance between two points (-5,8) and (-3,1) is 
units.
Count change of signs to tell positive roots
then replace x with -x and evaluate, then count change in sign for negative roots
initially
+, -, -, +, +, -
3 changes
3 or 1 positive roots
replacing x with -x
-,-,+,+,-,-
2 changes
2 or 0 negative roots
B is answer
Combine like terms to simplify an expression. For example, all terms with the variable x can be combined into one term. All constants can also be combined.
1) -4x - 10x = -14x
2) -r - 10r = -11r
3) -2x + 11 +6x = 4x + 11
4) 11r - 12r = -r
5) -v + 12v = 11v
6) -8x - 11x = -19x
7) 4p + 2p = 6p
8) 5n + 11n = 16n
9) n + 4 - 9 - 5n = -4n - 5
10) 12r + 5 + 3r - 5 = 15r (the 5 and -5 cancel each other out)
11) -5 + 9n + 6 = 9n + 1
Answer:
-2
Step-by-step explanation:
because the slope is 2, a perpendicular line must be the inverse
the equation for y1 is y=2x+1
y2= -2y+1
