The answer is (b² + 5b + 4).
The volume of a rectangular prism (V) is:
V = l · w · h (l - length, w - width, h - height)
The base of the rectangular prism is the product of length and width, so the area of the base is:
A = l · w
Since V = l · w · h and A = l · w, then:
V = A · h
It is given:
V = b³ + 8b² + 19b + 12
h = b + 3
⇒ b³ + 8b² + 19b + 12 = A · (b + 3)
⇒ A = (b³ + 8b² + 19b + 12) ÷ (b + 3)
Now, we have to present the volume as multiplication of factors. One of the factors is b+3. So:
b³ + 8b² + 19b + 12 = (b · b² + 3b²) + (5b² + 15b) + (4b + 3·4) =
= b²(b + 3) + 5b(b + 3) + 4(b + 3) =
= (b + 3)(b² + 5b + 4)
A = (b³ + 8b² + 19b + 12) ÷ (b + 3) = (b + 3)(b² + 5b + 4) ÷ (b + 3)
(b + 3) can be cancelled out:
A = (b² + 5b + 4)
Step-by-step explanation:
5x+2y=29
5x-2y=41
add the equations
10x=70
divide both sides by ten
x=7
substitute 7 in the first equation
5(7)+2y=29
simplify
35+2y=29
subtract 35 from both sides
2y=-6
simplify
y=-3 x=7
3x+2y=9
5x+2y=12
subtract the equations
-2x=-3
simplify
x=1.5
substitute
3(1.5)+2y=9
simplify
4.5+2y=9
subtract 4.5 from both sides
2y=4.5
simplify
y=2.25 x=1.5
5x+2y=-9
2x-3y=4
multiply first equation by three and second by two
15x+6y=-27
4x-6y=8
add equations
19x=-19
simplify
x=-1
substitute
15(-1)+6y=-27
simplify
-15+6y=-27
add 15 to both sides
6y=-12
simplify
y=-2 x=-1
Since ABCD is a rectangle, AB and CD are parallel sides. This means that you can set AB equal to CD to solve for x. It would be:
1/2x+6=5/2x-2.
6=4/2x-2
8=2x
4=x
So the answer would be e. 4.
Hope this helps!
Step-by-step explanation:
a (-infinite , -3) U (3 , infinite)
b + 5 , - 5
