Answer:
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.
(f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
(f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
(f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15x2 – 10x
= –15x2 + 2x + 8
\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(
g
f
)(x)=
g(x)
f(x)
= \small{\dfrac{3x+2}{4-5x}}=
4−5x
3x+2
My answer is the neat listing of each of my results, clearly labelled as to which is which.
( f + g ) (x) = –2x + 6
( f – g ) (x) = 8x – 2
( f × g ) (x) = –15x2 + 2x + 8
\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(
g
f
)(x)=
4−5x
3x+2
Step-by-step explanation:
Answer:
3rd Definition
Step-by-step explanation:
A sphere is a three dimensional and round, and every point on its surface is the same distance from its center.
Answer:
volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( 
x + b )² dx
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)
from the image;
the equation of AB will be;
y-b / b-0 = x-0 / 0-a
(y-b)(0-a) = (b-0)(x-0)
0 - ay -0 + ba = bx - 0 - 0 + 0
-ay + ba = bx
ay = -bx + ba
divide through by a
y = x + ba/a
y = x + b
so R is bounded by y = x + b and y =0, 0 ≤ x ≤ a
The volume of the solid revolving R about x axis is;
dv = Area × thickness
= π( Radius)² dx
= π ( x + b )² dx
V = π ₀∫^a ( x + b )² dx
Therefore, volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( x + b )² dx
Answer:
x = 12
Step-by-step explanation:
x + 3 = 
x + 1
multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions
3x + 18 = 4x + 6 ( subtract 3x from both sides )
18 = x + 6 ( subtract 6 from both sides )
12 = x
Step-by-step explanation:
(Assuming that this triangle is isosceles)
If this triangle is isosceles, then x° is going to be equal to its twin angle; 40°.
We can solve for z now.
180 = 40 + 40 + z
180 = 80 + z
Subtract 80 from both sides.
100 = z
z = 100°
Now that we know z = 100 degrees, we can begin to solve the expression (3x -20)
The expression sits on a 180° line and the angle z (100°) shares the line with the expression (3x - 20)°
180 = 100 + (3x - 20)
Subtract 100 from both sides.
80 = 3x - 20
Add 20 to both sides to isolate 3x
100 = 3x
Divide by 3 on both sides.
100/3 = 3x/3
33.33... = x
