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!
Step-by-step explanation:
-7/2 = -28
-7 = -28 × 2
-7 = -56
Answer:
Step-by-step explanation:
(x+1)(x-3)(x-4) = (x+1)(x²-7x+12) = x³-6x²+5x+12
:::::
(x+3)(x-0)(x-0)(x-5) = (x+3)(x²)(x-5) = (x²-2x-15)x² = x⁴-2x³-15x²
:::::
(x+2)³ = x³ + 3·x²·2 + 3·x·2² + 2³ = x³ + 6x² + 12x + 8
:::::
(x+3)²(x+1) = (x²+6x+9)(x+1) = x³ + 7x² + 15x + 9
Answer:
x=14/6
Step-by-step explanation:
Complementary angles add up to 90.
Say the complementary angle is A.
Angle A + Angle B = 90
Angle A + 60 = 90
Angle A = 30 degrees
Hope this helps :)
