Answer:
Real values of x where x < -1
Step-by-step explanation:
Above the x-axis, the function is positive.
The function is decreasing when the gradient is negative.
The function has a positive
coefficient, therefore the vertex is a local minimum;
This means the gradients are negative before the vertex and positive after it;
To meet the conditions therefore, the function must be before the vertex and above the x-axis;
This will be anywhere before the x-intercept at x = -1;
Hence it is when x < -1.
Answer:
The correct answer is 2.912 cm.
Step-by-step explanation:
A company is designing a new cylindrical water bottle.
Volume of a cylinder is given by π × 
× h, where h is the height of the cylinder and r is the radius of the cylinder.
The volume of each bottle will be 211 
.
The height (h) of the water bottle be 7.9 cm.
Let the radius of the bottle be r cm.
∴ π × × h = 211 ; (π = 3.15)
⇒ × 24.885 = 211
⇒ r = 2.912
The radius of the water bottle is 2.912 cm.
Answer:
8/27
Step-by-step explanation:
The population starts at 2000, so a=2000.
We also know that the population in 3 hours is 1000, so we can setup the equation:
2000 b^3 = 1000
This gets us:
b^3 = 1/2
And taking the cube root of both sides gives us:
b ≈ 0.7937005259841
Rounding that to 4 places, we have:
f(t) = 2000 (0.7937)^t
The region is in the first quadrant, and the axis are continuous lines, then x>=0 and y>=0
The region from x=0 to x=1 is below a dashed line that goes through the points:
P1=(0,2)=(x1,y1)→x1=0, y1=2
P2=(1,3)=(x2,y2)→x2=1, y2=3
We can find the equation of this line using the point-slope equation:
y-y1=m(x-x1)
m=(y2-y1)/(x2-x1)
m=(3-2)/(1-0)
m=1/1
m=1
y-2=1(x-0)
y-2=1(x)
y-2=x
y-2+2=x+2
y=x+2
The region is below this line, and the line is dashed, then the region from x=0 to x=1 is:
y<x+2 (Options A or B)
The region from x=2 to x=4 is below the line that goes through the points:
P2=(1,3)=(x2,y2)→x2=1, y2=3
P3=(4,0)=(x3,y3)→x3=4, y3=0
We can find the equation of this line using the point-slope equation:
y-y3=m(x-x3)
m=(y3-y2)/(x3-x2)
m=(0-3)/(4-1)
m=(-3)/3
m=-1
y-0=-1(x-4)
y=-x+4
The region is below this line, and the line is continuos, then the region from x=1 to x=4 is:
y<=-x+2 (Option B)
Answer: The system of inequalities would produce the region indicated on the graph is Option B
