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.
Answer:
The slope of the line = m = 2
Step-by-step explanation:
Given
The points
To determine:
The slope of this graph
Determining the slope between (0, 0) and (1, 2)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [2 - 0] / [1 - 0]
= 2 / 1
Thus, the slope of the line = m = 2
For this case we have the following function:
A (t) = P (1 + r / n) ^ nt
Substituting values we have:
A (4) = 500 * (1 + 0.09 / 1) ^ (1 * (4))
A (4) = 705.790805
Rounding we have:
A (4) = 705.79
Answer:
The answer for this case is given by:
A (4) = 705.79
option A
Answer:
3.33×10⁴
Step-by-step explanation:
You can use the hint, or you can use a common exponent. Here is the latter case.
(3.9×10⁴) -(5.7×10³) = (3.9×10⁴) -(0.57×10⁴) = (3.9 -0.57)×10⁴
= 3.33×10⁴
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With a little practice, you can see the effect on exponents of moving the decimal point. Here, we have ...
5.7×10³ = (0.57×10)×10³ = 0.57×(10×10³) = 0.57×10⁴
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When adding or subtracting in scientific notation, all that is required is that the exponents of all the numbers be the same. The hint says make all the exponents be 0. Above, we have chosen to make them all be 4. You could also use 3:
(3.9×10⁴) -(5.7×10³) = (39×10³) -(5.7×10³) = (39 -5.7)×10³
= 33.3×10³ = 3.33×10⁴
It’s 9b it’s just 4+5 with the b
