To find the value of x+y, we will first find the sum of all the interior angles of the hexagon.The sum of the interior angles in a hexagon is always equal to 720 degrees.

All the angles in the diagram are in terms of x or y except for angle t. However, we know that the corresponding exterior angle is 30 degrees. The sum of angle t and 30 is 360. We can solve this in an algebraic equation.

t+30=360
Subtract 30 from both sides
t = 330

Now, we can solve for the values of x+y. We can set this up in another algebraic equation.

x+x+x+2y+y+30=720

Combine like terms:
3x+3y+30 = 720

Subtract 30 from both sides:
3x+3y = 690

Divide both sides by 3:
$\frac{3x + 3y}{3} = \frac{690}{3}$
x+y = 230

The sum of x and y is 230.

6 0

4 years ago

The management of Ditton Industries has determined that the daily marginal revenue function associated with selling x units of t

barxatty [35]

Answer:

(a) The daily total revenue realized from the sale of 210 units of the toaster oven is $6,195.

(b) The additional revenue realized when the production (and sales) level is increased from 210 to 310 units is $1,400.

Step-by-step explanation:

The marginal revenue gives the actual revenue realized from the sale of an additional unit of the commodity given that sales are already at a certain level. The derivative <em>R'</em> of the function <em>R</em> measures the rate of change of the revenue function.

We know that the daily marginal revenue function is given by

$R'(x) = -0.1x+40$

(a) To find the the daily total revenue you must:

Integrate the daily marginal revenue function,

$\int R'(x)dx = \int(-0.1x+40)dx\\\\R(x)=-\int \:0.1xdx+\int \:40dx\\\\R(x)=-0.05x^2+40x+C$ ,

where C is a constant.

Find the value of C, using the fact that if you sell 0 units your daily revenue is $0.

$0=-0.05(0)^2+40(0)+C\\C=0$

$R(x)=-0.05x^2+40x$

The daily total revenue realized from the sale of 210 units of the toaster oven is

x = 210 units

$R(210)=-0.05(210)^2+40(210)\\R(210)=-210^2\cdot \:0.05+8400\\R(210)=-2205+8400\\R(210)=6195$

(b) To find the additional revenue realized when the production (and sales) level is increased from 210 to 310 units you must:

Find the daily total revenue realized from the sale of 310 units

$R(310)=-0.05(310)^2+40(310)\\R(310)=-310^2\cdot \:0.05+12400\\R(310)=-4805+12400\\R(310)=7595$

The additional revenue realized when the production (and sales) level is increased from 210 to 310 units is

$R(310)-R(210)=7595-6195=1400$

3 0

4 years ago

Rewrite the expression without using grouping symbol 7(x - 20)

Kitty [74]

7 (x - 20)

use distribution method

7x - 140

6 0

3 years ago