<span>Let x be the amount of hot dog and let y be the amount of water. So you will pay for it 1.50*x+0.80*y. Since you do not want to spend more than 20$, it should satisfy the inequality 1.50*x+0.80*y<=20.</span>
Answer:
Direct Variation
Step-by-step explanation:
The relationship between two variables such that y = kx if k is a nonzero number. Also, as one quantity increases, the second quantity increases or as one quantity decreases, the second quantity decreases. Therefore ac=5 is a direct variation
C.
$100 <span>so you will take 500*.04 and then times it by 5 (5 years) and that will be your answer :)</span>
We have:
Method 1.
Use:
and the vertex form
(h, k) - the coordinates of a vertex
Answer: (-3, 8)
Method 2.
For the coordinates of a vertex (h, k) are equal
We have:
Substitute:
Answer: (-3, 8)
Answer:
Step-by-step explanation:
Known fact: all roots of quadratic equation are real if and only if
discriminant
We know that all roots of are real. We can derive from this condition that
. (<----------- HERE)
Let's do some simplification of second equation:
So we want according to Known fact prove that discriminant of equation
is greater or equal zero.
.
To prove that , we can view D as polynomial of a:
.
Known fact #2: if quadratic polynomial have positive greatest coefficient and it's discriminant then polynomial always positive.
So remains to prove that
lets divide both side by :
divide by 3
transfer terms to the other side:
But we know that from "(<----------- HERE)"!!!
So Q.E.D.