1 yard = 3 feet so 1 yard by 1 yard = 3 x 3 = 9 square feet.. This means that 9 squares that are 3 feet by 3 feet will fit into a square that is 1 yard by 1 yard.

4 0

3 years ago

Use mathematical induction to prove that the statement is true for every positive integer n. Show your work.

never [62]

My first reasoning is the fact that the main number is 2
2nd reasoning is that
2 x n = 4
then 4 - 2 = 2
2 + 2 = 4
4 is a factor of 2

3 0

3 years ago

Find the average rate of change of f ( x ) = 9 x 2 − 7 on the interval [ 2 , a ] . Your answer will be an expression involving a

aleksandrvk [35]

Answer:

9a + 18

Step-by-step explanation:

so the first step is to evaluate the value of f(2).

$f(2) = 9(2)^2-7\\f(2)=9(4)-7\\f(2)=36-7\\f(2)=29$

Now that we have this value we can use the slope formula (y2 - y1) / (x2 - x1) where y2 is f(a), y1 is 29, x2 is a, and x1 is 2

$\frac{f(a)-29}{a-2}\\\\\frac{(9a^2-7)-29}{a-2}\\\frac{9a^2-36}{a-2}$

Now from here we can use long division to simplify it further

$9a^2/a = 9a\\9a(a-2)=9a^2-18a\\(9a^2-36)-(9a^2-18a)\\18a-36\\\\18a/a=18\\18(a-2)=18a-36\\(18a-36)-(18a-36)\\0\\\\9a+18$

8 0

2 years ago