Answer: The correct option is (B) 24 : 25.
Step-by-step explanation: Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.
We are to find the ratio of the area of R to the area of S.
Let 2x, 3x be the sides of rectangle R and y be the side of square S.
Then, according to the given information, we have
Therefore, the ratio of the area of R to the area of S is
![\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%5Ctimes3x%7D%7By%5Ctimes%20y%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B5x%5E2%7D%7By%5E2%7D%5C%5C%5C%5C%5C%5C%3D6%5Cleft%28%5Cdfrac%7Bx%7D%7By%7D%5Cright%29%5E2%5C%5C%5C%5C%5C%5C%3D6%5Ctimes%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%5Cright%29%5E2~~~~~~~~~~~%5B%5Ctextup%7BUsing%20equation%20%28i%29%7D%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B24%7D%7B25%7D%5C%5C%5C%5C%3D24%3A25.)
Thus, the required ratio of the area of R to the area of S is 24 : 25.
Option (B) is CORRECT.
Ok so we know that y=1 so we can simply sub in the value of y into the equation :
y = -5x +3
1 = -5x +3
Move the -5x to the LHS ( Left-hand-side ) therefore it changes sign as well move 1 to the RHS ( Right-hand-side ) it also changes sign.
5x = 3 - 1
5x = 2
x = 2/5
x = 0.4
Hope this helps :).
Answer:
Step-by-step explanation:
Answer:
4 GB
Step-by-step explanation:
Let "g" represent the number of gigabytes of data used. Then the phone bill is computed as ...
bill = 65 + 12g
Aurora's bill is 113, so we can put that value into the equation and solve for g.
113 = 65 + 12g
48 = 12g . . . . . . subtract 65 from both sides of the equation
4 = g . . . . . . . . . divide both sides of the equation by 12
Aurora used 4 gigabytes of data in September.
_____
You can also use your mathematical reasoning to solve this problem. The total bill consists of two charges: a fixed charge of 65 and a charge that depends on data. If you subtract the fixed charge from the bill, you find that the charge that depends on data is 113-65 = 48.
The data charge is 12 times the number of gigabytes. The data charge on the bill is 48, which is 12 times 4. Then the number of gigabytes is 4.
48
(5)(9) + 3
45 + 3
Hope this helps!!!!
