Answer:
The parallelogram is a "Square" ⇒ (a)
Step-by-step explanation:
In a parallelogram
- Every two opposite sides are parallel
- Every two opposite sides are equal
- Every two opposite angles are equal
- Its diagonals bisect each other
- If the diagonals of a parallelogram are equal, then it is a rectangle
- If the diagonals of a parallelogram are perpendicular to each other, then it is a rhombus
- If the diagonals of a parallelogram are equal and perpendicular, then it is a square
∵ In a parallelogram, its diagonals bisect each other at right angles
∴ Its diagonals are perpendicular
∵ Its diagonals are equal
→ By using rule 3 above
∴ The parallelogram is a square
Answer:
Step-by-step explanation:
11x + 23 = 8x + 35
3x + 23 = 35
3x = 12
x = 4
11(4) + 23 = 44 + 23 = 67 for m<CBD
8(4)+35 = 32 + 35 = 67 for m<ABD
Answer:
a. 1620-x^2
b. x=810
c. Maximum value revenue=$656,100
Step-by-step explanation:
(a) Total revenue from sale of x thousand candy bars
P(x)=162 - x/10
Price of a candy bar=p(x)/100 in dollars
1000 candy bars will be sold for
=1000×p(x)/100
=10*p(x)
x thousand candy bars will be
Revenue=price × quantity
=10p(x)*x
=10(162-x/10) * x
=10( 1620-x/10) * x
=1620-x * x
=1620x-x^2
R(x)=1620x-x^2
(b) Value of x that leads to maximum revenue
R(x)=1620x-x^2
R'(x)=1620-2x
If R'(x)=0
Then,
1620-2x=0
1620=2x
Divide both sides by 2
810=x
x=810
(C) find the maximum revenue
R(x)=1620x-x^2
R(810)=1620x-x^2
=1620(810)-810^2
=1,312,200-656,100
=$656,100