Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, d

Answer:

Detailed explanation:

* Let’s clarify the procedure for solving this problem

- An exponential function can be expressed as , where

 a signifies the starting amount (x = 0), and b denotes the growth factor

- If b > 1, it qualifies as an exponential growth function

- If 0 < b < 1, it is categorized as an exponential decay function

- Horizontal translation to the right by h units results in the new function being

- Conversely, if translated to the left by h units, the function modifies to

- A vertical upward shift by k units alters the function to

- A vertical downward shift by k units means the new function accounts for

* Now, let’s solve the problem

∵ f(x) is an exponential function

∵ The points (0, 1), (1, 10), (2, 100) are points of f(x)

- g(x) is the transformation of f(x)

∵ The points (3, 1), (4, 10), (5, 100) belong to g(x)

∵ The point (0, 1) on f(x) transforms to (3, 1) on g(x)

∵ The point (1, 10) on f(x) transforms to (4, 10) on g(x)

∵ The point (2, 100) on f(x) translates to (5, 100) on g(x)

∵ Notably, all y-coordinates of f(x) match those of g(x)

 indicating no vertical translation

∴ Hence, no vertical translation occurred

∵ The x-coordinates of f(x) are increased by

   3 units to yield the x-coordinates for g(x)

∴ This shows that f(x) is translated 3 units to the right

∵

∴

- Refer to the corresponding graph for greater clarity

# The red curve denotes f(x)

# The blue curve signifies g(x)

Answer:   a)     b)

Step-by-step explanation:

a) To achieve an even total, there are 3 possible combinations:

1) Even, Even, Even, Even    

2) Even, Even, Odd, Odd  

3) Odd, Odd, Odd, Odd  

Order is irrelevant

Summing these yields your final result:

b) If one die shows a 2 and another a 3, while the remaining two can show any digits, there’s only one way to get a 2, one way for a 3, and six potential numbers for each of the other two dice.

Answer:

7.

Detailed explanation:

28 can be expressed as 2^2 * 7.

In order to achieve a perfect square with 28, multiplying by 7 results in 2^2 * 7^2, equaling 14 squared.

x = lowest height

<x+25 highest height

x=55