Answer: second option y = 2(x + 7/2)^2 + 1/2
Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
Answer:
both 17 and 19 are right triangles because they both have a right angle
Step-by-step explanation:
The answer is 2
Because 2-3=-1
Here, number of periods (years), n=5
Annual interest rate, i=0.05 (compounded yearly)
Present value/deposit, P=100
Future value of deposit = P(1+i)^n=100(1.05^5)=127.63 (to the nearest cent)
Answer: After 5 annual interest payments, Bob will have 127.63 in his account.
Answer:
The statement can be expressed as
There are two different students in your class who have visited the same websites.
Step-by-step explanation:
Given that
- W(x, y) mean that student x has visited website y.
- The domain of x consists of all students in your school
- The domain of y consists of all website.
It would help to know the meaning of the symbols used, this will help understand the statement better.
- ∧ means conjuction
- ∃ means 'there exists'
- ∀ means 'for all'
- ≠ means 'different from'
- ↔ means 'if and only if'
The statement
∃x∃y∀z((x ≠ y) ∧ (W(x, z) ↔ W(y, z)))
can be expressed as:
There are two different students in your class who have visited the same websites.
