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Answer:
Answer:
y^{2}-5y=750y
2
−5y=750
750-y(y-5)=0750−y(y−5)=0
(y + 25)(y -30) = 0(y+25)(y−30)=0
Step-by-step explanation:
Givens
The area of a rectangular room is 750 square feet.
The width of the room is 5 feet less than the length of the room.
Let's call ww the width and ll the length. According to the problem they are related as follows
w=l-5w=l−5 , because the width is 5 feet less than the lenght.
We know that the area of the room is defined as
A=w\times lA=w×l
Where A=750 ft^{2}A=750ft
2
Replacing the given area and the expression, we have
\begin{gathered}750=(l-5)l\\750=l^{2}-5l \\l^{2}-5l-750=0\end{gathered}
750=(l−5)l
750=l
2
−5l
l
2
−5l−750=0
We need to find two number which product is 750 and which difference is 5, those numbers are 30 and 25.
l^{2}-5l-750=(l-30)(l+25)l
2
−5l−750=(l−30)(l+25)
Using the zero property, we have
\begin{gathered}l=30\\l=-25\end{gathered}
l=30
l=−25
Where only the positive number makes sense to the problem because a negative length doesn't make any sense.
Therefore, the length of the room is 30 feet.
Also, the right answers are the second choice where y=ly=l , the third choice and the last choice
Answer:
y² - 5y = 750
or
750 - y(y - 5) = 0
or
(y + 25)(y - 30) = 0
Step-by-step explanation:
length = y ft
width = y - 5
Area of the rectangular room = 750 square feet
length * width = 750
y*(y-5) = 750
⇒ y² - 5y = 750
y(y-5) = 750
⇒ 0 = 750 - y(y - 5)
⇒ 750 - y(y - 5) = 0
y(y - 5) = 750
y² - 5y -750 = 0
Sum = -5
Product = -750
Factors = 25 , (-30)
y² + 25y - 30y - 750 = 0
y(y + 25) -30(y + 25) = 0
(y + 25)(y - 30) = 0