Answer: (3x + 11y)^2
Demonstration:
The polynomial is a perfect square trinomial, because:
1) √ [9x^2] = 3x
2) √121y^2] = 11y
3) 66xy = 2 *(3x)(11y)
Then it is factored as a square binomial, being the factored expression:
[ 3x + 11y]^2
Now you can verify working backwar, i.e expanding the parenthesis.
Remember that the expansion of a square binomial is:
- square of the first term => (3x)^2 = 9x^2
- double product of first term times second term =>2 (3x)(11y) = 66xy
- square of the second term => (11y)^2 = 121y^2
=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.
So we can start with the full of possibilities and eliminate them one by one.
The full set is {0,1,2,3,4,5,6,7,8,9}.
Now we know that any prime greater than 2 is odd as otherwise it would have 2 as a factor, so we can eliminate all of these digits that would be an even number, leaving:
{1,3,5,7,9}
We also know that any prime greater than 5 cannot be a multiple of 5 and that all numbers with 5 in the digits are a multiple of 5, so we can eliminate 5.
{1,3,7,9}
We know that 11,13,17 and 19 are all primes, so we cannot eliminate any more of these, leaving the set:
{1,3,7,9} as our answer.
Answer:
f⁻¹(x) = (1/2)x +5
Step-by-step explanation:
In y = f(x), swap the variables, then solve for y. The expression you get is f⁻¹(x).
... y = 2x -10
... x = 2y -10 . . . . . . swapped variables
... x +10 = 2y . . . . . add 10
... (1/2)x + 5 = y . . . . divide by 2
... f⁻¹(x) = (1/2)x + 5 . . . . . . rewrite using function notation
The $50 off was like a coupon after you brought all your merchandise to the counter, so we have to add it back in to determine the number of shirts.
$400+$50=$450 original price of shirts
Original price ÷ price per shirt= quantity purchased
$450 ÷ $15/shirt= 30 shirts purchased
Allison bought 30 shirts.
Hope this helps! :)
Answer:
in confused on what the question is asking is it multiple questions
