Answer:
25/4 will have to be added to "complete the square"
Step-by-step explanation:
x² - 5x - 18 = 0
x² - 5x = 18
Find the half of the coefficient of x and square it
(5/2)² = 25/4
Add 25/4 to both sides to complete the square
x² - 5x + 25/4 = 18 + 25/4
x² - 5x + 25/4 = 18(4/4) + 25/4
x² - 5x + 25/4 = 72/4 + 25/4
x² - 5x + 25/4 = (72+25)/4
x² - 5x + 25/4 = 97/4
(x - 5/2)² = 97/4
Find the square root of both sides
√(x - 5/2)² = ±√97/4
x - 5/2 = √97/2
x = √97/2 + 5/2 or x = -√97/2 + 5/2
x = 7.42443 or -2.42443
Answer:
y = 4/3x-7/3
Step-by-step explanation:
Slope intercept form is y=Mx+b; m=slope & b= y intercept
y=-4/3x+b
Now substitute x & y with the point given
(-9)=-4/3(5)+b
-9= -20/3+b
+20/3 +20/3
-7/3=b
Now substitute this into the original equation
y = 4/3x-7/3
Answer:
product A on machine 1 would make 27 units (rounded down) 81 dollars profit.
product A on machine 2 would make 25 units (rounded down) 75 dollars profit.
product b on machine 1 would make 15 units (rounded down) 75 dollars profit.
product b on machine 2 would make 16 units (rounded down) 80 dollars profit.
Step-by-step explanation:
a1 refers to product a on machine 1
a2 refers to product a on machine 2
same rule applies for product b 1 and 2
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Answer:
3 1/3 feets
Step-by-step explanation:
Given that:
Height of aquarium = 1 3/4 feets
Area of aquarium = 5 5/6 ft²
The length of aquarium = x
Aquarium is shaped in the form of a rectangle :
Area of a rectangle = Length * width
5 5/6 = x * 1 3/4
35/6 = 7x/4
Cross multiply :
7x * 6 = 35 * 4
42x = 140
x = 140 / 42
x = 3 14/42
x = 3 1/3 feets
Hence, Length of the back of aquarium is 3 1/3 feets
