A washer and dryer cost $652 combined. The washer cost $48 less than the dryer. What is the cost of the dryer?
1 answer:
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Discussion
1. Put brackets around the first two terms
y = (-x^2 + 6x) + 5
2. Take out the common factor of -1
y = -(x^2 - 6x) + 5
3. Inside the brackets, take 1/2 of - 6 and square it
y = -(x^2 - 6x + ( - 6 / 2)^2 ) + 5
y = -(x^2 - 6x + (- 3)^2 ) ) + 5
y = -(x^2 - 6x + 9 ) + 5
Note: Step 3 is very long. Make sure you work your way through it
4. You have added 9 inside the brackets. <em><u>It is actually - 9. So add 9 outside to balance the equation out. </u></em> This is the key step. Make sure you understand it.
y = - (x^2 - 6x + 9) + 5 + 9
5. Express the brackets as a square.
y = - (x + 3)^2 + 14
Discussion
The equation is now in vertex form. The minus tells you that the equation is a maximum. The maximum is located at ( - 3, 14 )
A graph follows to show the results.
<h2>Answer:</h2>
<em><u>People who didn't travel by any mode = 45</u></em>
<h2>Step-by-step explanation:</h2>In the question,
Total number of people included in survey = 250
People who traveled by plane but not by train = 70
i.e.
a + e = 70
People who traveled by train but not by plane = 70
i.e.
c + d = 70
People who traveled by Bus but not by Plane or Train = 20
i.e.
f = 20 ..........(1)
People who traveled by bus and plane both = 45
i.e.
e + g = 45
People who traveled by all three = 20
i.e.
g = 20
People who traveled by Plane or Train = 185
i.e.
a + b + c + d + e + g = 185 ........(2)
So,
e = 45 - g = 45 - 20 = 25
e = 25
Now, on putting in eqn. (2) we get,
a + b + c + d + 25 + 20 = 185
a + b + c + d = 140 .......(3)
Now,
We need to find out,
Number of people travelling with any of these three is,
a + b + c + d + e + f + g
So,
On putting from eqn. (3) and (1), we get,
a + b + c + d + e + f + g = 140 + 25 + 20 + 20 = 205
So,
Number of people who didn't travel by any mode =Total people - Number of people travelling by any three
<em><u>People who didn't travel by any mode = 250 - 205 = 45</u></em>