Answer:
( - 6 , - 1 )
Step-by-step explanation:
Let's find the rule of that transformation:
1 + = 4 ⇒ = 3
9 + = 10 ⇒ = 1
Thus, the rule of given transformation is ( x + 3 , y + 1 )
So, the image of the point ( - 9 , - 2 ) is
( - 9 + 3 , - 2 + 1 ) = ( - 6 , - 1 )
Answer:
- (x - 3y)(3x + y)
Step-by-step explanation:
Given
(x + 2y)² - (2x - y)² ← expand both parenthesis using FOIL
= x² + 4xy + 4y² - (4x² - 4xy + y²) ← distribute
= x² + 4xy + 4y² - 4x² + 4xy - y² ← collect like terms
= - 3x² + 8xy + 3y² ← factor out - 1 from each term
= - 1(3x² - 8xy - 3y²) ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the coefficient of the y² term which sum to give the coefficient of the xy- term.
product = 3 × - 3 = - 9 and sum = - 8
The factors are - 9 and + 1
Use these factors to split the xy- term
3x² - 9xy + xy - 3y² ( factor the first/second and third/fourth terms )
= 3x(x - 3y) + y(x - 3y) ← factor out (x - 3y) from each term
= (x - 3y)(3x + y)
Thus
(x + 2y)² - (2x - y)² = - (x - 3y)(3x + y)
' n ' the 'n'th term
1 4
2 2
3 0
4 -2 .
In general, the 'n'th term of the sequence is A(n) = 6 - 2n .
Answer:
5.61; 8.5 %
Step-by-step explanation:
Tax = $1.87 per $22 meal
For a $66 meal,
Tax = 66 × 1.87/22
Tax = 3 × 1.87
Tax = $5.61
=====
Tax rate = 1.87/22 × 100
Tax rate = 0.085 × 100
Tax rate = 8.5 %
