Answer:
1. The given equation does not have root at x = - 3.
2. (x - 3) (x + 1) (x² + 4) = 0
This curve will intersect twice the x-axis.
Step-by-step explanation:
1. If the right hand side of the equation 
......... (1) becomes same as the left hand side by putting x = - 3, then only we can conclude that x = - 3 is a root of the equation.
But in this case 
.
Therefore, x = - 3 is not a root of the above equation (1).
2. The equation of the polynomial with roots 3, -1, 2i, and -2i is
(x - 3) (x + 1) (x - 2i) (x + 2i) = 0
⇒ (x - 3) (x + 1) (x² + 4) = 0 (Answer)
Therefore, the graph of the above curve will intersect twice the x-axis in a real coordinate plane, at x = 3 and at x = -1. (Answer)
The sales tax is $4.32 -4.00 = $0.32.
The tax rate is
.. $0.32/$4.00 = 0.08 = 8%
Answer/Step-by-step explanation:
A) The temperature in Chicago could be -10*F because -10 is to the right of -13 on the number line.
Higher Temperatures -->
o----------->I
I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I
-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
With a dilation, each dimension increases by the factor. Thus, if we let the dimensions be x and y, the new dimensions are 2x and 2y.
(a): The original perimeter is 2(x+y), but the new one is 2(2x+2y). This is twice the original perimeter, so it is 18*2=36.
(b): The original area is xy, and the new one is (2x)(2y), or 4xy. This is four times the original area, or 20*4=80.
(c): As it's given that the side lengths are integers, the intended solution is most likely to divide by 2 in the perimeter to see that the sum of the side-lengths is 9 and their product is 20. Guessing/checking values for each side, we see that 4 and 5 work for the smaller rectangle. Multiplying by two, the larger one has lengths 8 and 10.
Alternatively, we set them to x and y and use the equations:
x+y=9
xy=20
Dividing by y, we see that x=20/y. Substituting, we have that y+20/y=9. Subtracting 9 and multiplying by y, we have:
y^2-9y=20
Factoring, we have (y-5)(y-4)=0. The solutions to this equation are 4 and 5, which result in x=5, y=4 or x=4, y=5 respectively. Thus, we see that 4 and 5 are the side-lengths. Note that this solution did not require the assumption that the side-lengths are integers!
Answer:
30 for the first one
Step-by-step explanation:
