Answer: x=8
Step-by-step explanation:
the sum of the interior angles of a quadrilateral is 360 (number of sides-2 * 180)
so

Answer:
Gina is 12 years old
Step-by-step explanation:
First, we will have to write these statements mathematically and then solve.
Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.
The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)
The next statement "Gina's brother is half Gina's age" can be mathematically written as y =
---------------------------------------(2)
Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)
We can now proceed to solve;
Substitute equation (1) and equation(2) into equation (3)
x + y + z = 42
x +
+ 2x = 42
Multiply through by 2
2x + x + 4x = 84
7x = 84
Divide both-side of the equation by 7
= 
x = 12
Therefore, Gina is 12 years old
Answer: Growth factor will be 0.15 and percent increase will be 15%.
Step-by-step explanation:
Since we have given that
the exponential growth function

1) We need to find the growth factor :
As we know the formula for "Compound Interest ":

If we compare the formula with our given equation, we get

So, the growth factor is at the rate of 0.15.
2) Percent increase will be

Hence, growth factor will be 0.15 and percent increase will be 15%.
Answer:
see explanation
Step-by-step explanation:
Using the Pythagorean identity
sin²θ + cos²θ = 1 ( divide terms by sin²θ )
+
=
, that is
1 + cot²θ = cosec²θ ← as required