Answer:
see explanation
Step-by-step explanation:
Let u = x² ( choice of variable is flexible ), then
4u² - 21u + 20 = 0 ← expressed as a quadratic
This can now be solved for u and converted back into terms of x
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:
3
Step-by-step explanation:
Note the general factorisation of a difference of 2 squares is
a² - b² = (a + b)(a + b)
Given
(- 5x - 3)(- 5x + ?)
Then ? = 3 so that the complete factors are
(- 5x - 3)(- 5x + 3)
11/2 divided by $0.99 is $<span>1.51</span>
Answer:
they are equal so what one shows that they rise 2 run 2
Step-by-step explanation:
