Answer: d. AB = CD and BC = AD
Step-by-step explanation:
A parallelogram is defined as a four-sided figure with the following characteristics:-
- Opposite sides are equal (AB = CD and BC = AD
).
- Opposite angles are equal (∠A=∠C and ∠D=∠B).
- Consecutive angles are supplementary (∠A + ∠D = 180°).
- The diagonals bisect one another.
- If one angle is a right angle, then all angles are right angles.
Answer:
Volume = 16 unit^3
Step-by-step explanation:
Given:
- The solid is situated between x = 0 and x = 4.
- Diagonal lines stretch from y = sqrt(x) to y = -sqrt(x)
Find:
Calculate the volume enclosed.
Solution:
- We will begin by finding the area projection of the solid on the plane at x = 0.
A(x) = 0.5*(diagonal)^2
- The diagonal ranges from y = sqrt(x) to y = -sqrt(x), thus
A(x) = 0.5*(sqrt(x) + sqrt(x))^2
A(x) = 0.5*(4x) = 2x
- By utilizing the area function, we will integrate across x from 0 to 4 to determine the solid's volume:
V = integral(A(x)).dx
V = integral(2*x).dx
V = x^2
- Evaluating from 0 to 4:
V= 16 - 0 = 16 unit^3
The price of the goal is $180, while each soccer ball costs $15.
Answer: Lincoln spent 5 hours working while Hunter dedicated 10 hours to their task.
Step-by-step explanation:
Let x denote the hours Lincoln was employed.
Let y signify the hours put in by Hunter.
Lincoln can iron 30 shirts every hour, and Hunter handles 20 shirts per hour. Together, they managed to iron a total of 350 shirts. Therefore, we have the equation:
30x + 20y = 350 - - - - - - - - - - - 1
The total working hours for Lincoln and Hunter combined is 15.
This leads to the equation:
x + y = 15
By substituting x = 15 - y into equation 1, we arrive at:
30(15 - y) + 20y = 350
450 - 30y + 20y = 350
- 30y + 20y = 350 - 450
- 10y = - 100
y = - 100/ - 10
y = 10
x = 15 - y = 15 - 10
x = 5
