Rules of exponents and the distributive property apply.
(x+y)² = (x+y)·(x+y) . . . . . meaning of exponent of 2
= x·(x+y) +y·(x+y) . . . . . . . distributive property
= x·x +x·y +y·x +y·y . . . . . distributive property
= x² +x·y +x·y +y² . . . . . . meaning of exponent of 2, commutative property of multiplication
= x² +(1+1)·x·y +y² . . . . . . distributive property
= x²+2xy+y² . . . . . . . . . the desired form
Thus
(x+y)² = x²+2xy+y²
To find the slope of the line, first find the slope of 3x + y = 5, and then its opposite reciprocal.
3x + y = 5
y = -3x + 5
the slope of 3x + y = 5 is -3.
the slope is -3, so the opposite reciprocal slope is 1/3.
the equation of any line is y = ax + b
to find this line, y = 3, x = -9, and the slope is 1/3.
3 = -9a + b
3 = -9 (1/3) + b
3 = -3 +b
b = 6
substitute a and b into the equation
y = ax + b
y = 1/3x + 6
the equation of the line is y = 1/3x + 6.
Answer: 362880
The exclamation mark means factorial notation. The rule is we start with the given number, then count down til we get to 1, multiplying all along the way. In this case, we start with 9, then multiply with 8, 7, 6, etc til we get to 1, like so...
9! = 9*8*7*6*5*4*3*2*1 = 362880
Some calculators have a factorial button built in. The button should be labeled with an exclamation mark.
34/6. You do 5 x the 6, then add the 4
