Answer:
See Below
Step-by-step explanation:
The boundary line follows the graph of y = 2x - 4 because it represents the line of maximum or minimum values the graph could take. y = 2x - 4 has a y-intercept of -4 because it is in slope-intercept form. It also has a slope of 2, so to find another point on the line, you can go up two and right one. Also, this inequality has a solid line because it is "less than or equal to" and a solid line represents the values that equal.
The average rate of change is -5 per month
<h3>How to determine the average rate of change?</h3>
The interval is given as:
July to December
From the graph, we have:
July = 110
December = 30
The average rate of a function over the interval (a, b) is calculated as:
Rate = [f(b) - f(a)]/[b - a]
So, we have:
Rate = (30 - 110)/(December- July)
This gives
Rate = (30 - 110)/(12 - 7)
Evaluate
Rate = -16
Hence, the average rate of change is -5 per month
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The standard form: Ax + By = C
y = 90 - 15x <em>add 15x to both sides</em>
<h3>15x + y = 90</h3>
Answer:
c) x = 11
Step-by-step explanation:
Given equation: 7x - 9 = 28 + 4(x - 1)
<u><em>Steps:</em></u>
1. Distribute 4 through the parentheses:
7x - 9 = 28 + 4(x) + 4(-1)
7x - 9 = 28 + 4x - 4 [simplify]
7x - 9 = 24 + 4x
2. Subtract 4x from both sides:
7x - 4x - 9 = 24 + 4x - 4x
3x - 9 = 24
3. Add 9 to both sides:
3x - 9 + 9 = 24 + 9
3x = 33
4. Divide both sides by 3:
3x ÷ 3 = 33 ÷ 3
x = 11
5. Check your work:
7x - 9 = 28 + 4(x - 1) [substitute 11 for x]
7(11) - 9 = 28 + 4(11 - 1) [simplify]
77 - 9 = 28 + 4(10) [simplify]
68 = 28 + 40 [add]
68 = 68 ✔
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brainly.com/question/27844321
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Answer:
![\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}}\rightarrow\frac{2x}{3y}\\\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} \rightarrow\frac{3y}{2x}\\\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}}\rightarrow\frac{4x^2}{5y}\\\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}}\rightarrow\frac{3x^2}{2y}\\\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} \rightarrow\frac{2xy}{3}\\\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}}\rightarrow\frac{x}{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E6y%5E4%7D%7B81x%5E2y%5E8%7D%7D%5Crightarrow%5Cfrac%7B2x%7D%7B3y%7D%5C%5C%5Csqrt%5B4%5D%7B%5Cfrac%7B81x%5E2y%5E%7B10%7D%7D%7B81x%5E6y%5E6%7D%7D%20%5Crightarrow%5Cfrac%7B3y%7D%7B2x%7D%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7B64x%5E8y%5E7%7D%7B125x%5E2y%5E%7B10%7D%7D%7D%5Crightarrow%5Cfrac%7B4x%5E2%7D%7B5y%7D%5C%5C%5Csqrt%5B5%5D%7B%5Cfrac%7B243x%5E%7B17%7Dy%5E%7B16%7D%7D%7B32x%5E7y%5E%7B21%7D%7D%7D%5Crightarrow%5Cfrac%7B3x%5E2%7D%7B2y%7D%5C%5C%5Csqrt%5B5%5D%7B%5Cfrac%7B32x%5E%7B12%7Dy%5E%7B15%7D%7D%7B243x%5E7y%5E%7B10%7D%7D%7D%20%5Crightarrow%5Cfrac%7B2xy%7D%7B3%7D%5C%5C%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E%7B10%7Dy%5E%7B9%7D%7D%7B256x%5E2y%5E%7B17%7D%7D%7D%5Crightarrow%5Cfrac%7Bx%7D%7B2y%7D)
Step-by-step explanation:
![\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}} =\sqrt[4]{\frac{(2^4)(x^{6-2})(y^{4-8})}{(3^4)}} =\sqrt[4]{\frac{2^4x^4y^{-4}}{3^4}} =\frac{2xy^{-1}}{3}=\frac{2x}{3y}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E6y%5E4%7D%7B81x%5E2y%5E8%7D%7D%20%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B%282%5E4%29%28x%5E%7B6-2%7D%29%28y%5E%7B4-8%7D%29%7D%7B%283%5E4%29%7D%7D%20%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B2%5E4x%5E4y%5E%7B-4%7D%7D%7B3%5E4%7D%7D%20%3D%5Cfrac%7B2xy%5E%7B-1%7D%7D%7B3%7D%3D%5Cfrac%7B2x%7D%7B3y%7D)
![\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} =\sqrt[4]{\frac{(3^4)(x^{2-6})(y^{10-6})}{(2^4)}} =\sqrt[4]{\frac{3^4x^{-4}y^{4}}{2^4}} =\frac{3x^{-1}y^1}{3}=\frac{3y}{2x}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cfrac%7B81x%5E2y%5E%7B10%7D%7D%7B81x%5E6y%5E6%7D%7D%20%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B%283%5E4%29%28x%5E%7B2-6%7D%29%28y%5E%7B10-6%7D%29%7D%7B%282%5E4%29%7D%7D%20%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B3%5E4x%5E%7B-4%7Dy%5E%7B4%7D%7D%7B2%5E4%7D%7D%20%3D%5Cfrac%7B3x%5E%7B-1%7Dy%5E1%7D%7B3%7D%3D%5Cfrac%7B3y%7D%7B2x%7D)
![\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}} =\sqrt[3]{\frac{(4^3)(x^{8-2})(y^{7-10})}{(5^3)}} =\sqrt[3]{\frac{4^3x^6y^{-3}}{5^3}} =\frac{4x^2y^{-1}}{5}=\frac{4x^2}{5y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B64x%5E8y%5E7%7D%7B125x%5E2y%5E%7B10%7D%7D%7D%20%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B%284%5E3%29%28x%5E%7B8-2%7D%29%28y%5E%7B7-10%7D%29%7D%7B%285%5E3%29%7D%7D%20%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%5E3x%5E6y%5E%7B-3%7D%7D%7B5%5E3%7D%7D%20%3D%5Cfrac%7B4x%5E2y%5E%7B-1%7D%7D%7B5%7D%3D%5Cfrac%7B4x%5E2%7D%7B5y%7D)
![\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}} =\sqrt[5]{\frac{(3^5)(x^{17-7})(y^{16-21})}{(2^5)}} =\sqrt[5]{\frac{3^5x^{10}y^{-5}}{2^5}} =\frac{3x^2y^{-1}}{2}=\frac{3x^2}{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B%5Cfrac%7B243x%5E%7B17%7Dy%5E%7B16%7D%7D%7B32x%5E7y%5E%7B21%7D%7D%7D%20%3D%5Csqrt%5B5%5D%7B%5Cfrac%7B%283%5E5%29%28x%5E%7B17-7%7D%29%28y%5E%7B16-21%7D%29%7D%7B%282%5E5%29%7D%7D%20%3D%5Csqrt%5B5%5D%7B%5Cfrac%7B3%5E5x%5E%7B10%7Dy%5E%7B-5%7D%7D%7B2%5E5%7D%7D%20%3D%5Cfrac%7B3x%5E2y%5E%7B-1%7D%7D%7B2%7D%3D%5Cfrac%7B3x%5E2%7D%7B2y%7D)
![\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} =\sqrt[5]{\frac{(2^5)(x^{12-7})(y^{15-10})}{(3^5)}} =\sqrt[5]{\frac{2^5x^{5}y^{5}}{3^5}} =\frac{2x^1y^{1}}{3}=\frac{2xy}{3}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B%5Cfrac%7B32x%5E%7B12%7Dy%5E%7B15%7D%7D%7B243x%5E7y%5E%7B10%7D%7D%7D%20%3D%5Csqrt%5B5%5D%7B%5Cfrac%7B%282%5E5%29%28x%5E%7B12-7%7D%29%28y%5E%7B15-10%7D%29%7D%7B%283%5E5%29%7D%7D%20%3D%5Csqrt%5B5%5D%7B%5Cfrac%7B2%5E5x%5E%7B5%7Dy%5E%7B5%7D%7D%7B3%5E5%7D%7D%20%3D%5Cfrac%7B2x%5E1y%5E%7B1%7D%7D%7B3%7D%3D%5Cfrac%7B2xy%7D%7B3%7D)
![\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}} =\sqrt[4]{\frac{(2^4)(x^{10-2})(y^{9-17})}{(4^4)}} =\sqrt[4]{\frac{2^4x^{8}y^{-8}}{4^4}} =\frac{2x^{1}y^{-1}}{4}=\frac{x}{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E%7B10%7Dy%5E%7B9%7D%7D%7B256x%5E2y%5E%7B17%7D%7D%7D%20%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B%282%5E4%29%28x%5E%7B10-2%7D%29%28y%5E%7B9-17%7D%29%7D%7B%284%5E4%29%7D%7D%20%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B2%5E4x%5E%7B8%7Dy%5E%7B-8%7D%7D%7B4%5E4%7D%7D%20%3D%5Cfrac%7B2x%5E%7B1%7Dy%5E%7B-1%7D%7D%7B4%7D%3D%5Cfrac%7Bx%7D%7B2y%7D)
Thus,
