Leezas aquarium holds 55 gallons of water. She is filling the tank and has already put in 22 gallons. Write and solve an inequal
1 answer:
Leeza can put 33 or less gallons of water in aquarium.
Step-by-step explanation:
Given,
Capacity of aquarium = 55 gallons of water
Water already in aquarium = 22 gallons
Let,
x be the number of gallons that can be added in aquarium.
As aquarium can hold 55 gallons of water, therefore, we cannot add more than 55 gallons of water.
Subtracting 22 from both sides
Leeza can put 33 or less gallons of water in aquarium.
Keywords: inequality, subtraction
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Answer:
a). Center of the circle = (-2, 5)
b). Equation of the line ⇒ y =
Step-by-step explanation:
Equation of the circle is,
x² + 4x + y²- 10y + 20 = 30
a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30
[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30
(x + 2)² + (y - 5)²- 29 + 20 = 30
(x + 2)² + (y - 5)²- 9 = 30
(x + 2)² + (y - 5)² = 39
By comparing this equation with the standard equation of a circle,
Center of the circle is (-2, 5).
b). A point (2, 10) lies on this circle.
Slope of the line joining this point to the center (-2, 5),
=
=
Let the slope of the tangent which is perpendicular to this line is ''
Then by the property of perpendicular lines,
Now the equation of the line passing though (2, 10) having slope
y - y' =
y - 10 =
y - 10 =
y =
y =
Therefore, equation of the line will be, y =