Answer:
r = {-8, -4}
Step-by-step explanation:
Simplifying
r2 = -32 + -12r
Solving
r2 = -32 + -12r
Solving for variable 'r'.
Reorder the terms:
32 + 12r + r2 = -32 + -12r + 32 + 12r
Reorder the terms:
32 + 12r + r2 = -32 + 32 + -12r + 12r
Combine like terms: -32 + 32 = 0
32 + 12r + r2 = 0 + -12r + 12r
32 + 12r + r2 = -12r + 12r
Combine like terms: -12r + 12r = 0
32 + 12r + r2 = 0
Factor a trinomial.
(8 + r)(4 + r) = 0
Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve:
Simplifying
8 + r = 0
Solving
8 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + r = 0 + -8
Combine like terms: 8 + -8 = 0
0 + r = 0 + -8
r = 0 + -8
Combine like terms: 0 + -8 = -8
r = -8
Simplifying
r = -8
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:
Simplifying
4 + r = 0
Solving
4 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4
Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4
Combine like terms: 0 + -4 = -4
r = -4
Simplifying
r = -4
Solution
r = {-8, -4}
P(7,6), Q(1,6), R(4,2)
We have PQ parallel to the x axis. We'll call that the base,
b = 7 - 1 = 6
The altitude is then the y difference h = 6 - 2 = 4
The area is 
Answer: 12 square units
In general we can use the shoelace formula for the area of any polygon given coordinates. We write the points like this:
(7,6), (1,6), (4,2)
(1,6), (4,2), (7,6)
The area is then half the absolute value of the sum of the cross products:
Answer:
86 ft
Step-by-step explanation:
<em>First method: Logical thinking</em>
Think of the position 34 ft below sea level as -34.
The position above sea level is 52.
You need to find the distance between -34 and 52.
You go from 34 ft below sea level, -34 to 0. That is 34 ft.
Then you go from sea level, 0 ft, to 52 ft above sea level. That is 52 ft.
The total is 34 ft + 52 ft = 86 ft
Answer: 86 ft
<em>Second method: Calculate a distance in math</em>
The distance between two points on a number line is the absolute value of the difference of their coordinates. The coordinates are -34 and 52. Subtract the numbers in either order, and take the absolute value of the difference.
|-34 - 52| = |-86| = 86
If you did it in the other order, you'd get the same answer.
|52 - (-34)| = |52 + 34| = |86| = 86
Answer: 86 ft
Answer:
a)6
b)v^2-u^2/2a
Step-by-step explanation:
a)Given that,
u=12
a= -6
s=9
We know that,
v^2=u^2+2as
or, v^2=(12)^2+2×(-6)×9
or,v^2=144-108
or,v^2=36
or, v=√36
∴v=6
(Ans)
b)If ,v^2=u^2+2as
then, u^2+2as=v^2
or,2as=v^2-u^2
or, s=v^2-u^2/2a
∴s=v^2-u^2/2a
Hope ya find it helpful.. Thanks a lot...
