For each parabola, you have to do a system of equation with the line y = x - 5 and find which of them has one real solution.
For that you can solve the systems and find the roots, but you can also use the rule that to have one real solution the discriminant of the quadratiic equation (b^2 - 4ac) has to be zero.
1)
y = x - 5
y = x^2 + x - 4
=> x - 5 = x^2 + x - 4
=> x^2 + 1 = 0
It is easy to tell, by simple inspection, that this equation has not real solutions.
2)
y = x -5
y = x^2 + 2x - 1
=> x - 5 = x^2 + 2x - 1
=> x^2 + x + 4 = 0
discriminant = b^2 - 4ac = 1^2 - 4(1)(4) = 1 - 16 = - 15
A negative discriminant means that there are not real solutions.
3)
y = x - 5
y = x^2 + 6x + 9
x - 5 = x^2 + 6x + 9
=> x^2 + 5x + 14 = 0
=> b^2 - 4ac = 5^2 - 4(1)(14) = 25 - 56 = - 31 => no real solutions
4)
y = x - 5
y = x^2 + 7x + 4
x - 5 = x^2 + 7x + 4
=> x^2 + 6x + 9 = 0
=> b^2 - 4ac = 6^2 - 4(1)(9) = 36 - 36 = 0 => the system has one real solution.
By the way, that solution is easy to find because you can factor the equation as: (x + 3)^2 = 0 => x = - 3
Answer:
-3/5
Step-by-step explanation:
Go down 3 and over 5
Answer:
740
Step-by-step explanation:
185*4=740
Please mark as Brainliest! :)
Have a nice day.
Answer:
A) Positive
B) Positive
C) None
D) Positive
Step-by-step explanation:
:)
Answer:
<h3>Finding averages.</h3><h3>Organizing data.</h3><h3>Estimating.</h3><h3>Data gathering.</h3>
Step-by-step explanation:
When we plan an effective budget, we certainly need to gather some data about the theme, which includes, prices, description of the stuff we need. Once we have the data we need, then we must organize it to set priorities, to make the budget effective.
Additionally, estiamting and finding averages are important skills, because we need to estimate how effective is the budget. In fact, maybe we would desing different budgets to compare them and analyse, using averages, which one is the most effective.