Answer: -4.25 ≤ x ≤ 6.25
Step-by-step explanation:
The midpoint of a segment is located at the same distance of each of the endpoints of the segment.
The midpoint is at x = 1.
The length of the segment is 10.5, if we divide it by two we have:
10.5/2 = 5.25
Now, if we want the endpoints to be at the same distance of the midpoint, then the endpoints will be:
Xmax = midpoint + 5.25
Xmin = midpoint - 5.25
Then the extremes are:
Xmax = 1 + 5.25 = 6.25
Xmin = 1 - 5.25 = -4.25
Then this segment can be written as:
Xmin ≤ x ≤ Xmax
-4.25 ≤ x ≤ 6.25
Answer:
the answer is B
Step-by-step explanation:
The area of the square is 100ft
Answer: depth = 5 ft
width = 10 ft
length = 40 ft
Step-by-step explanation:
d = depth
width = d + 5
length = d + 36
Volume = length x width x depth = 2000 cf
d(d+35)(d+5) = 2000
d(
+ 40d + 175) = 2000
d^3 + 40d^2 + 175d = 2000
rewrite in standard cubic polynomial form : ax3 + bx2 + cx + d = 0
d^3 + 40(d^2) + 175d - 2000 = 0
Find the roots of the cubic polynomial:
factors of 2000 are 1, 5, 10 15, 20, etc.
Try the factor 5 first by plugging it in the equation:
5^3 + 40(5^2) + 175(5) - 2000 = 0
Lucky break! No need to find the other roots because they will be negative, and you can't have a negative value for a pool depth.
So, depth = 5 ft
width = 5 + 5 = 10 ft
length = 5 + 35 = 40 ft
Answer:
The equation of the line that is <em>perpendicular</em> to <em>y = 2x + 2</em> is
<em>y = -1/2x</em>
Step-by-step explanation:
The original equation is y = 2x + 2; it's slope is <em>2</em>
Any line perpendicular to this equation would have to have a slope that is the negative reciprocal of the original slope.
Example:
y = 2x + 2 so,
the perpendicular line's slope must be -1/2
Write a new equation with the new slope:
y = -1/2x + b
We know that this line passes through (8, -4)
Plug these coordinates in the equation to find b, the y-intercept
-4 = -1/2 (8) + b
-4 = -4 + b
0 = b
b = 0
We do not have to write y = -1/2x + 0
So, our final answer is "y = -1/2x is perpendicular to y = 2x+2"
