Under which of the following operations are the polynomials 3x+2 and 4y-11 not closed
1 answer:
Lets check all the choices:
A. subtraction:
(3x+2)-(4y-11)=3x+2-4y+11=3x-4y+13
similarly, (4y-11)-(3x+2)=-3x+4y-13
both are polynomials (of 2 variables)
B. (3x+2)(4y-11)=12xy-33x+8y-22, which is a polynomial
C. (3x+2)+(4y-11)=3x+2+4y-11=3x+4y-9, which is a polynomial
D.
both
and 
are rational expressions in 2 variables, not polynomials
Answer: D
A. subtraction:
(3x+2)-(4y-11)=3x+2-4y+11=3x-4y+13
similarly, (4y-11)-(3x+2)=-3x+4y-13
both are polynomials (of 2 variables)
B. (3x+2)(4y-11)=12xy-33x+8y-22, which is a polynomial
C. (3x+2)+(4y-11)=3x+2+4y-11=3x+4y-9, which is a polynomial
D.
both
Answer: D
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Part A
We have
. To solve for the x-intercept, we set f(x) equal to 0. That is
Take the square root of both sides,
The x-intercept is (-2,0).
To solve for the y-intercept, we set x=0. That is
The y-intercept is (0, 8)
The coordinates of the optimum point are actually the vertex which can be easily seen from the vertex form equation given above. The minimum point is (-3, -1).
Part B.
We have
.
Factor out -2
Complete the square
Simplify
Part C
We have
.
The maximum height is 12.25 feet after 0.875 seconds from the time of the jump. The dolphin will be back in the water after 1.75 seconds. The graph of the jump is shown in the photo.
We have
Take the square root of both sides,
The x-intercept is (-2,0).
To solve for the y-intercept, we set x=0. That is
The y-intercept is (0, 8)
The coordinates of the optimum point are actually the vertex which can be easily seen from the vertex form equation given above. The minimum point is (-3, -1).
Part B.
We have
Factor out -2
Complete the square
Simplify
Part C
We have
The maximum height is 12.25 feet after 0.875 seconds from the time of the jump. The dolphin will be back in the water after 1.75 seconds. The graph of the jump is shown in the photo.