<h3>
Answer:</h3>
42. 29°
43. 3x³ +2x² -3x +10
44. 20a² +68a
<h3>
Step-by-step explanation:</h3>
42. The right-angle corner tells you the two marked angles are complementary — they sum to 90°.
(-3x +20)° + (-2x +55)° = 90°
-5x +75 = 90 . . . . . . . . . . collect terms, divide by °
-5x = 15 . . . . . . . . . . . . . . . subtract 75
x = -3 . . . . . divide by the coefficient of x
The angle of interest is (-3x+20)°. Filling in the found value for x, we have ...
(-3·(-3) +20)° = 29° = m∠BDC
___
43. The distributive property is useful for multiplying polynomials.
(x +2)(3x² -4x +5) = x(3x² -4x +5) +2(3x² -4x +5)
= 3x³ -4x² +5x +6x² -8x +10 . . . . . eliminate parentheses
= 3x³ +2x² -3x +10
___
44. Area is the product of length and width, so this becomes a problem in multiplying polynomials.
area = (5a +17)(4a) = 20a² +68a . . . . area in square feet
<span>12.3
Volume function: v(x) = ((18-x)(x-1)^2)/(4pi)
Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x.
The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is
v(x) = (18-x)pi((x-1)/(2pi))^2
v(x) = (18-x)pi((x-1)^2/(4pi^2))
v(x) = ((18-x)(x-1)^2)/(4pi)
The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative:
v'(x) = (x-1)(3x - 37) / (4pi)
Convert to quadratic equation.
(3x^2 - 40x + 37)/(4pi) = 0
3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0
Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi)
The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>
Answer:
f(x) + g(x) = 3x + 7
Step-by-step explanation:
f(x) = 2x + 2, g(x) = x + 5
f(x) + g(x) = 2x + 2 +x + 5
f(x) + g(x) = 2x +x + 5 +2
f(x) + g(x) = 3x + 7
Answer:
B. 
- 4x - 5
Step-by-step explanation:
(p о n) (x) is the same thing as (p(n(x))
We know n(x) = x - 5, so let's input that into our expression
(p(x - 5))
Since we know p(x) = x^2 + 6x, let's replace the x with the new value x-5. Now our expression is:
p(x) = (x - 5)^2 + 6(x - 5)
Now all we have to do is simplify.
(x - 5)^2 is the same as: (x - 5)(x - 5)
Using the foil method, it simplifies to: x^2 - 10x + 25
6 (x - 5) = 6x - 30
Now our expression is: x^2 - 10x + 25 + 6x - 30
Combine like terms: x^2 - 4x - 5
The expression is: - 4x - 5
5.3 minutes.
First, let's calculate the volume of the tank. That will be the area of the base multiplied by it's length. And since it's base is a circle, the area is pi*r^2. So:
V = l*pi*r^2
V = 3.5 * pi * (2.2/2)^2
V = 3.5 * pi * (1.1)^2
V = 3.5 * pi * 1.21
V = 4.235 * pi
V = 13.30464489
So the tank has a volume of about 13.3 ft^3. Now simply divide that volume
by the rate of incoming fluid. So
13.3 / 2.5 = 5.32
Rounding to 2 significant figures gives a time of 5.3 minutes.
