Answer:
Step-by-step explanation:
Factorise the denominator of the second fraction
y² - 1 = (y - 1)(y + 1) ← difference of squares
To obtain a common denominator
multiply numerator/ denominator of first fraction by (y + 1)
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← subtract numerators leaving the common denominator
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= 
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← cancel common factor (y - 1) on numerator/denominator
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As what I can observe, the pathway can be formed with 2 right triangles. Thus, I'll get the area of the 2 right triangles and multiply its area by the paving cost per square meter.
Area of Right Triangle: ab / 2
a = 6 2/3 m ⇒ 20/3 m; b = 3m
Area of 1 triangle= (20/3 m * 3 m) ÷ 2 = 20 ÷ 2 = 10 m²
Area of 2 triangles = 10m² * 2 = 20 m²
Total cost = $40 * 20m² = $800
Answer: I think it is b
Step-by-step explanation:
First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.
You'll basically complete the square for two equations at the same time. Set it up like this:
(16x^2 + 96x) + (9y^2 - 18y) = 9
Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.
(x^2 + 6x) + (y^2 - 2y) = 9/144
then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.
For instance the first one will be 6/2 = 3^2 = 9
The next one will be 2/2 =1^2 = 1
Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.
(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1
Then find a common denominator on the right side of the equals sign and add them all together to get:
(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144
Factor out the two polynomials
(x+3)^2 + (y-1)^2 = 1449/144
the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17
