Start fraction x squared plus eight x plus fifteen over x minus four end fraction times start fraction x squared minus sixteen over two x plus six end fraction
To simplify this expression, we first factor the two fractions individually.
start fraction x squared plus eight x plus fifteen over x minus four end fraction can be factored as:
start fraction (x+5)(x+3) over (x-4) end fraction
start fraction x squared minus sixteen over two x plus six end fraction can be factored as:
start fraction (x+4)(x-4) over 2(x+3) end fraction
Now we can multiply the two fractions together:
start fraction (x+5)(x+3) over (x-4) end fraction times start fraction (x+4)(x-4) over 2(x+3) end fraction
To simplify this product, we can cancel out common factors in the numerator and denominator:
start fraction (x+5)cancel(x+3) over (x-4) end fraction times start fraction (x+4)cancel(x-4) over 2cancel(x+3) end fraction
This leaves us with:
start fraction (x+5)(x+4) over 2(x-4) end fraction
Therefore,
start fraction x squared plus eight x plus fifteen over x minus four end fraction times start fraction x squared minus sixteen over two x plus six end fraction = start fraction (x+5)(x+4) over 2(x-4) end fraction.
Which direct variation equation can be used to find n?
Responses
A y = 4xy = 4x
B y = 3xy = 3x
C y = 12xy = 12x
D y = 2x
We cannot determine the direct variation equation to find n with the given information. There is no mention of n or its relation to x and y in any of the equations provided.
A direct variation includes the points (4, 16) and (1, n).
Question 1
Which direct variation equation can be used to find n?
Responses
A y = 4xy = 4x
B y = 3xy = 3x
C y = 12xy = 12x
D y = 2x
We can use the formula for direct variation, y = kx, where k is the constant of variation, to find the equation that relates x and y for the given points.
If we plug in the coordinates for the first point (4, 16), we get:
16 = k(4)
Simplifying this equation, we get:
k = 4
Now we can use this value of k to find the value of y for the second point (1, n):
n = k(1)
n = 4(1)
n = 4
Therefore, the equation that relates x and y for the given points is y = 4x.
The answer is A.
Hold it, hold it, let's get back to the first question:
Start fraction x squared plus eight x plus fifteen over x minus four end fraction times start fraction x squared minus sixteen over two x plus six end fraction
(x^2 + 8x + 15)/(x-4) * (x^2 - 16)/(2x + 6)
= (x+5)(x+3)/(x-4) * (x+4)(x-4)/(2(x+3))
= (x+5)(x+4)/2 or (x^2 + 9x + 20)/2
You are correct. I apologize for the mistake in my previous response. The simplified expression for the given product is:
Start fraction (x+5)(x+4) over 2(x-4) end fraction or (x^2 + 9x + 20) over 2
Thank you for bringing this to my attention.