Which pairs of polygons are congruent?
2 answers:
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Remember that to find the zeroes of a quadratic expression of the form 
we could either factor it or use the quadratic formula. When 
, like in our case, is often way easier and faster factor the expression than using the quadratic formula. The only thing we need to do to factor the expression is find tow number whose product is 48 and its sum is 14; those numbers are 6 and 8. 
and 
. Now we can factor our quadratic like follows:
Since we are trying to find the zeroes of the function, we are going to set each one of our factored binomial equal to zero and solve for x:
and
We can conclude that the zeroes of the function
are and .
Since we are trying to find the zeroes of the function, we are going to set each one of our factored binomial equal to zero and solve for x:
and
We can conclude that the zeroes of the function
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!