Gloria goes to the gym every 6 days. Liz goes to the gym every 4 days. Nate goes to the gym every 8 days. If all three go to the
gym on the same day, how many days will they all go to the gym on the same day again?
1 answer:
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Dos rectas cuyas pendientes son m1 y m2, son perpendiculares si y sólo si m1m2 =-1
with a point and the slope you can find the equation
y-y1=m(x-x1)
as the point is given (-1,-4) then substitute it in the equation
y-(-4)= -2[(x-(-1)]⇒y+4= -2x-2⇒y=-2x-2-4⇒y=-2x-6 and this is the equation of the line that must be graphed
second step)
graph the equation y =- 2x-6, with the points of intersection are for x = 0, y = -2(0)-6= -6 , the point is ( 0,-6) and the other point is for y = 0
0= -2x-6, 2x= -6, x = -6/ 2 = -3, the other point is (-3,0) then the graph is the following, you can see in it the points of intersection
Answer:
Option (2)
Step-by-step explanation:
To find the solution set of the given inequality we will follow the following steps.
1). Convert the inequality into an equation.
2). Find the solutions from the equation.
3). Check these solutions and intervals on a number line.
Given inequality is 5(x - 2)(x + 4) > 0
Step 1. Equation for given inequality is,
5(x - 2)(x + 4) = 0
Step 2. Solutions for the given equation will be,
(x - 2) = 0 ⇒ x = 2
(x + 4) = 0 ⇒ x = -4
Step 3. Therefore, there will be two critical points on the number line,
x = 2, x = -4
Now we will check the solutions of the given inequality in the given intervals,
x < -4, -4 < x < 2 and x > 2
For x < -4,
Let the solution is x = -5
5(x + 4)(x - 2) = 5(-5 + 4)(-4 - 2)
= 30 > 0
Therefore, x < -4 will be the solution area of the inequality.
For -4 < x < 2,
Let the solution is x = 0
5(x + 4)(x - 2) = 5(0 + 4)(0 - 2)
= -40 < 0
Therefore, -4 < x < 2 will not be the solution set for the given inequality.
For x > 2,
Let the solution is x = 3
5(x + 4)(x - 2) = 5(3 + 4)(3 - 2)
= 35 > 0
Therefore, x > 2 will be the solution area of the inequality.
Summarizing all steps we find that the solution set of the inequality is,
{x | x < -4 Or x > 2}
Option (2) will be the answer.
