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
Its most likely to be c if not a because the answer is going to be about 1 dollar sales tax
Answer:
<u>m∠CAD is 100°</u>
Step-by-step explanation:
The angles of a triangle always add up to 180 degrees.
Add...
100+x=180
Subtract 100 from each side...
x=80°
m∠CAB=80
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A line is always 180°... line DB consists of m∠CAB (just solved) and m∠CAD (which the answer asks)
m∠CAB+m∠CAD=DB
Substitute in the information we have.
80°+m∠CAD=180°
Subtract 80 from both sides...
<u>m∠CAD is 100°</u>
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I hope my answer makes sense to you! :)
The object compresses the spring up to 0.8577m.
<h3>What is Potential Energy?</h3>
Potential Energy is the energy possessed by an object at rest.
The object is falling from the rest and it is assumed that the friction on the ramp is zero and the air resistance is also considered to be zero so only the gravitational force acts and the total potential energy gets converted to Kinetic Energy.
The total amount of potential energy at the top of the ramp is given by
Ep=mgh
Ep=3 * 9.81 *5
Ep=147.15 Joules
This is equal to kinetic energy.
From the formula for elastic potential energy
The distance up to which the spring is compressed is determined
The force constant = 400N/m
147.15 =(1/2)k(x²)
294.3=(400)(x²)
0.73575=x²
x=0.8577 m
So, the object compresses the spring up to 0.8577m.
- When the object compresses the spring, the potential energy of the spring is converted into Kinetic Energy so it will push the object back again.
To know more about Potential Energy
brainly.com/question/24284560
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