8-2=6
10+6+3=19
I’m not sure if you are allowed to do it that way so I can find other ways if needed
Answer:
9
Step-by-step explanation:
We can use the distance formula
d = sqrt ( ( y2-y1)^2 + ( x2-x1) ^2)
d = sqrt ( ( 4- -3)^2 + ( -4 -2) ^2)
= sqrt ( ( 7^2 + ( -6)^2)
= sqrt( 49+ 36)
= sqrt(85)
9.219544457
Rounding to the nearest whole number
= 9
Answer:
9 represents the initial height from which the ball was dropped
Step-by-step explanation:
Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:

The general formula for the geometric progression modelling this scenario is:

Here,
represents the initial height i.e. the height from which the object was dropped.
r represents the percentage the object covers with respect to the previous bounce.
Comparing the given scenario with general equation, we can write:
= 9
r = 0.7 = 70%
i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.
Given:
Expression is

To prove:
If r is any rational number, then
is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,

It can be written as

Now,
3, -2 and 4 are rational numbers by property 1.
is rational by Property 3.
are rational by Property 3.
is rational by property 2.
So,
is rational.
Hence proved.