Answer:
The graph is positive and decreasing for all real values of x where x < -1
Step-by-step explanation:
we have
The function is a vertical parabola open up
The roots (x-intercepts) are x=3 and x=-1
The vertex is the point (1,-4 ) is a minimum
using a graphing tool
see the attached figure
we know that
In the interval (-∞,-1) ---> the function is positive and decreasing
In the interval (-1,1) ---> the function is negative and decreasing
In the interval (1,3) ---> the function is negative and increasing
In the interval (3,∞) ---> the function is positive and increasing
therefore
The graph is positive and decreasing for all real values of x where x < -1
Answer: 1 million
Step-by-step explanation:
Step-by-step explanation:
I guess method 1 means to deal with whole factors.
x + 5 = (x - 2)(x + 5)
for (x + 5) <> 0 we can divide both sides by this factor :
1 = x - 2
x = 3
for the second solution we deal with
x + 5 = 0
x = -5
so, for x = -5 and x = 3 both functions deliver the same output, and these are the intersection points.
method 2 : we multiply the expression out and solve it then
x + 5 = (x - 2)(x + 5)
x + 5 = x² + 5x - 2x - 10 = x² + 3x - 10
0 = x² + 2x - 15
the general solution to such a square equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -15
x = (-2 ± sqrt(2² - 4×1×-15))/(2×1) =
= (-2 ± sqrt(4 + 60))/2 = (-2 ± sqrt(64))/2 = (-2 ± 8)/2 =
= -1 ± 4
x1 = -1 + 4 = 3
x2 = -1 - 4 = -5
and you get the 2 solutions again. as expected, they are the same as with method 1, of course.
Answer: 
Step-by-step explanation:
By definition, the equation of the line in slope-intercept form of is:
Where m is the slope and b is the y-intercept.
Then, given the slope 2/5 and the point, (-10, -5), you can calculate the value of b by susbtituting and solve for it:
Substitute this value and the slope into the equation. THerefore, you obtain:
Answer:
Step-by-step explanation:
There are two case I used, since we are not give diagram, so I assumed that U can be the right angle and also assume that W can be the right angle so, I used both assumption to solve, check attachment
1. Using Trigonometry
Assuming that U is the right angle
Tan θ = opp / adj
Tan 60 = UW / UV
Tan 60 = UW / 18
UW = 18 × Tan60
UW = 18 × √3
UW = 18√3
UW = 31.18 unit
Also, assume that W is right angle
Using trigonometry
Sinθ = opp / hyp
Sin60 = UW / UV
Sin60 = UW / 18
UW = 18 × sin60
UW = 18 × √3/2
UW = 9√3
UW = 15.59 unit
