3 consecutive positive integers : x, x + 1, x + 2
x^2 = x + 2
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x + 1 = 0
x = -1....this is an extraneous solution that does not work
x - 2 = 0
x = 2
check...
square of the first = third
x^2 = x + 2
2^2 = 2 + 2
4 = 4 (correct)
so ur 3 integers are 2,3, and 4
1/5 gallon 1 hour
7/8 gallon x hour
x=(7/8)/(1/5)=(7/8)*5=35/8 hour =4 3/8 hour
Use double angle identity

We can relate '6x' to '3x' in the same way since 6 is 2*3.

Now sub into left side of identity. Simplify until it equals right side.
<u>Given</u>:
Given that the angles of the kite.
The opposite angles of the kite measures (3y + 14)° and (y + 50)°
We need to determine the value of y.
<u>Value of y:</u>
We know the property that the opposite angles are equal.
Thus, applying the property, we have;

Subtracting both sides of the equation by y, we have;

Subtracting both sides of the equation by 14, we get;

Dividing both sides of the equation by 2, we get;

Thus, the value of y is 18.
First let's find the factors of each number:
19: 1,19
21: 1,3,7,21
23: 1,23
25: 1,5,25
21 has 4 factors, 25 has 3 and 23 and 19 are both prime numbers (with two factors). 21 has the most factors.