Answer:
Theorem : Opposite sides of a parallelogram are congruent or equal.
Let us suppose a parallelogram ABCD.
Given: and (According to the definition of parallelogram)
We have to prove that: AB is congruent to CD and BC is congruent to AD.
Prove: let us take two triangles, and
In these two triangles, { By the definition of alternative interior angles}
Similarly,
And, AC=AC (common segment)
By ASA,
thus By the property of congruent triangle, we can say that corresponding sides of are also congruent.
Thus, AB is congruent to CD and BC is congruent to AD.
Step-by-step explanation:
Given:
.
Exponential regression model is

To find:
The exponential regression representing the population of Lazy Town as a function of time in years.
Solution:
Exponential regression model is
...(i)
We have,
.
Substituting
and
in (i), we get.

Therefore, the exponential regression representing the population of Lazy Town as a function of time in years, is
.
Answer:
11/6 or 1.8333333333
Step-by-step explanation:
= 
Cross Multiply:
7 x 6 = 42
9 (2x+1)
42 = 9(2x+1)
42 = 18x + 9
Then, isolate the variable. In order to do so, subtract 9 from both sides.
33 = 18x
Now, divide by 18 (to find x)
33/18 =
1.8333333 or 11/6
Answer:
110.9 feet
Step-by-step explanation:
The function that models the flight of the ball is
where f(x) is the vertical distance in feet and x is the horizontal distance the ball travels
If the ball hits the ground, then f(x)=0

The solution is given by the quadratic formula:

We substitute a=-0.02, b=2.2, and c=2 to get:

This implies that:

Since we are dealing with time,

To one decimal place, we have 110.9 feet
Answer:
110
Step-by-step explanation:
To find the constant of variation, divide the number of km by the number of hours:
165/1.5
= 110
This means that the speed of the train is 110 km per hour.
So, the constant of variation is 110.