Yes this is correct great job!
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!
Short Answer CRemarkYou may think there is no way to resolve this. Either of the first two look like they might work and you cannot be sure what you will get with the last two unless you know.
The answer is one of the last two. The equation cannot have just one or even a large number of complex numbers. When you are factoring a polynomial, the number of complex numbers must be even.
The complex root you have is x + 2i. Its partner is x - 2i
The complete equation would be
y = (x - 2i)(x + 2i) (x - 2)(x + 4)(x - 4)
I'll edit to add the graph.
Answer:
We cannot infer at the 10% significance level that the assumption of ski centers is wrong
Step-by-step explanation:
The null hypothesis for this question can be stated as
Null hypothesis H0: =4
Alternate hypothesis Ha:
The test is two tailed
Standard Deviation –
= 2
z=(4.84-4)/(2/sqrt(63))
=3.33
Z(0.1/2)=1.645 is less than Z =3.334
Hence, we will reject H0
Hence, the average growth skier ski’s four times a year is not true
<u>Answer:</u>
(i) Total cost of the flat is Rs. 540000.
(ii) Expenditure incurred on labour is Rs. 150000
<u>Step-by-step explanation:</u>
According to the question, cement cost is Rs. 112500, which represents 75° in the pie chart.
(i) The total cost of the flat is represented by the total 360° in the pie chart.
∴ Using unitary method
75° represents Rs. 112500
⇒ 360° represents =
× 360
= Rs. 540000
∴ Total cost of flat = Rs. 540000
(ii) Similarly, to calculate the cost of labour, represented by 100° in the pie chart, we can use the unitary method:
75° represents Rs. 112500
⇒ 100° represents =
× 100
= Rs. 150000
∴ Cost of labour = Rs. 150000