23.455 = 890 * (2x - 1) + 925x
23.455 = 1780x - 890 + 925x
23.455 = 2705x - 890
24.345 = 2705x
x = 9
Answer:
![\dfrac{\sqrt[3]{95^2}}{17\cdot95^4}=\dfrac{\sqrt[3]{9\,025}}{1\,384\,660\,625}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B3%5D%7B95%5E2%7D%7D%7B17%5Ccdot95%5E4%7D%3D%5Cdfrac%7B%5Csqrt%5B3%5D%7B9%5C%2C025%7D%7D%7B1%5C%2C384%5C%2C660%5C%2C625%7D)
Step-by-step explanation:
The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)/(a^c) = a^(b-c)
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![\dfrac{190^3}{68^2}\times\dfrac{34}{95^{\frac{19}{3}}}=\dfrac{(2\cdot 95)^3}{(2\cdot 34)^2}\cdot\dfrac{34}{95^6\cdot 95^{\frac{1}{3}}}=2^{3-2}95^{3-6-\frac{1}{3}}34^{1-2}\\\\=2\cdot 95^{-3\frac{1}{3}}\cdot 34^{-1}=2\cdot 95^{-4+\frac{2}{3}}\cdot 34^{-1}\\\\=\dfrac{2\sqrt[3]{95^2}}{95^4\cdot 34}=\dfrac{\sqrt[3]{95^2}}{17\cdot95^4}\\\\=\dfrac{\sqrt[3]{9\,025}}{1\,384\,660\,625}](https://tex.z-dn.net/?f=%5Cdfrac%7B190%5E3%7D%7B68%5E2%7D%5Ctimes%5Cdfrac%7B34%7D%7B95%5E%7B%5Cfrac%7B19%7D%7B3%7D%7D%7D%3D%5Cdfrac%7B%282%5Ccdot%2095%29%5E3%7D%7B%282%5Ccdot%2034%29%5E2%7D%5Ccdot%5Cdfrac%7B34%7D%7B95%5E6%5Ccdot%2095%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%3D2%5E%7B3-2%7D95%5E%7B3-6-%5Cfrac%7B1%7D%7B3%7D%7D34%5E%7B1-2%7D%5C%5C%5C%5C%3D2%5Ccdot%2095%5E%7B-3%5Cfrac%7B1%7D%7B3%7D%7D%5Ccdot%2034%5E%7B-1%7D%3D2%5Ccdot%2095%5E%7B-4%2B%5Cfrac%7B2%7D%7B3%7D%7D%5Ccdot%2034%5E%7B-1%7D%5C%5C%5C%5C%3D%5Cdfrac%7B2%5Csqrt%5B3%5D%7B95%5E2%7D%7D%7B95%5E4%5Ccdot%2034%7D%3D%5Cdfrac%7B%5Csqrt%5B3%5D%7B95%5E2%7D%7D%7B17%5Ccdot95%5E4%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%5Csqrt%5B3%5D%7B9%5C%2C025%7D%7D%7B1%5C%2C384%5C%2C660%5C%2C625%7D)
Answer:
The angle of the figure is 90°
9514 1404 393
Answer:
11 cm by 33 cm
Step-by-step explanation:
You can solve this problem mentally as follows.
Consider the rectangle as 3 squares, side-by-side. Then the area of each of those squares is 363/3 = 121 cm^2. From your knowledge of the squares of numbers, you know that 121 = 11^2. So, the width of the rectangle is 11 cm, and the length is 3 times that, or 33 cm.
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Using variables, we can let w represent the width. Then 3w can represent the length, and the area is ...
A = LW
A = (3w)(w) = 3x^2 = 363
w^2 = 363/3 = 121
w = √121 = 11
3w = 3·11 = 33
The width is 11 cm; the length is 33 cm.
Answer:
The second option, 3x^2(x+3)(4x+1)
Step-by-step explanation:
Factor out the common term, which is 3x^2
This then becomes 3x^2(4x^2+13x+3)
Factor the inside term and it becomes
(3x^2)(x+3)(4x+1)
