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Answer:
d. The equation has one solution and there is not enough information to determine the direction of the parabola.
Step-by-step explanation:
For a general quadratic equation
y = ax² +bx +c
the solution is
The discriminant (D) is the part of the quadratic formula underneath the radical: b² - 4ac.
D tells us whether there are
- two different real solutions
- two identical real solutions ("one solution")
- two complex solutions.
If D= 0,
and there are two identical solutions ("one solution").
The direction of the parabola depends on the sign of a.
That information is not given, so we cannot determine the direction of the parabola.
Answer:
Step-by-step explanation:
We know that Megan can plant 1 garden bed in 8 hours. Let M represent Megan's rate. So:
We know that her mother can plant 2 garden beds in that time (8 hours). Let A represent the mother's rate. So:
We can reduce this to 1 flower bed every 4 hours.
We also know that Megan's father can plant 1 1/3 or 4/3 garden beds in 8 hours. Let D represent the father's rate. So:
We can reduce (4/3)/8 to 1/6.
We know that the three began working together. They worked together for 3 hours. So, after 3 hours, the amount of beds they planted all together is 3 hours times their respective rates. So, we can write the following expression:
We know that at this point, Megan's father left, leaving only Megan and her mother. We know that they worked together for another 30 minutes, or 1/2 of an hour. So, after this, they will have planted:
Garden beds.
Now, Megan's mother leaves, leaving only Megan. Let's let x represent the number of hours. So, we can write the last part of our expression:
We know that in the end, they planted 2 flower beds. So, our entire expression equals 2:
To find out how long it took Megan, we will solve for x.
Let's do each term individually:
First Term:
We have:
Make the fractions with common denominators. Our common denominator here is 24. So:
Add:
Multiply. So, our first term is:
Second Term:
We have:
Again, let's turn the fractions into fractions with common denominators so we can add them. The common denominator here is 8. So:
Add:
Multiply:
So, our equation is now:
Add on the left. Use the common denominator of 48. So:
Add:
Subtract 87/48 from both sides:
Let turn into a fraction with a denominator of 48. So:
Subtract:
Reduce the right using 3:
Multiply both sides by 8:
Reduce using 8. So, the time it will take Megan to finish planting the garden beds by herself is:
And we're done!