X = 3
y = 5
(3,5)
I used substitution because It seemed the easiest.
From the second equation I isolated it for Y to get y=20-5x
I plugged this in to the other equation for the Y value to perform substitution.
-7x + 8 (20-5x) = 19
then it's simple algebra
-7× + 160 - 40x = 19
-47x + 160 = 19
subtract 160 from both side and divide both side by -47 to isolate x.
-47x = -141
x=3
then to find Y, simple plug this into one of the equation above. or simply use this one that we already isolated for Y:
y=20-5x
y=20-5 (3)
y=5
hope that helps
1. 28
2. 2 7/12 or approximately 2.58
3. I believe 580 but I could be wrong.
4. 213.75
Do the ratio of the two sides. To get the area square the two sides.
(9/15) ratio of sides
(9/15)^2 ratio of areas
81/225
Multiply for the known area
90*(81/225) = 162/5 = 32,4 sq. inches (area of corresponding triangle)
Answer:
![\large\boxed{\sqrt{xy^3}\cdot\sqrt[3]{x^2y}=\sqrt[6]{x^7y^{11}}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Csqrt%7Bxy%5E3%7D%5Ccdot%5Csqrt%5B3%5D%7Bx%5E2y%7D%3D%5Csqrt%5B6%5D%7Bx%5E7y%5E%7B11%7D%7D%7D)
Step-by-step explanation:
![\text{Use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\sqrt{xy^3}\cdot\sqrt[3]{x^2y}=(xy^3)^\frac{1}{2}(x^2y)^\frac{1}{3}\\\\\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=x^\frac{1}{2}y^{(3)\left(\frac{1}{2}\right)}x^{(2)\left(\frac{1}{3}\right)}y^\frac{1}{3}\\\\\text{use}\ a^na^m=a^{n+m}\\\\=x^{\frac{1}{2}+\frac{2}{3}}y^{\frac{3}{2}+\frac{1}{3}}\\\\\text{the common denominator is 6}](https://tex.z-dn.net/?f=%5Ctext%7BUse%7D%5C%20a%5E%5Cfrac%7B1%7D%7Bn%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5C%5C%5C%5C%5Csqrt%7Bxy%5E3%7D%5Ccdot%5Csqrt%5B3%5D%7Bx%5E2y%7D%3D%28xy%5E3%29%5E%5Cfrac%7B1%7D%7B2%7D%28x%5E2y%29%5E%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28ab%29%5En%3Da%5Enb%5En%5C%20%5Ctext%7Band%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C%3Dx%5E%5Cfrac%7B1%7D%7B2%7Dy%5E%7B%283%29%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%7Dx%5E%7B%282%29%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%7Dy%5E%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20a%5Ena%5Em%3Da%5E%7Bn%2Bm%7D%5C%5C%5C%5C%3Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B2%7D%7B3%7D%7Dy%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5C%5Ctext%7Bthe%20common%20denominator%20is%206%7D)
![\dfrac{1}{2}=\dfrac{1\cdot3}{2\cdot3}=\dfrac{3}{6}\\\\\dfrac{2}{3}=\dfrac{2\cdot2}{3\cdot2}=\dfrac{4}{6}\\\\\dfrac{3}{2}=\dfrac{3\cdot3}{2\cdot3}=\dfrac{9}{6}\\\\\dfrac{1}{3}=\dfrac{1\cdot2}{3\cdot2}=\dfrac{2}{6}\\\\x^{\frac{1}{2}+\frac{2}{3}}y^{\frac{3}{2}+\frac{1}{2}}=x^{\frac{3}{6}+\frac{4}{6}}y^{\frac{9}{6}+\frac{2}{6}}=x^{\frac{7}{6}}y^{\frac{11}{6}}=\sqrt[6]{x^7y^{11}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%3D%5Cdfrac%7B1%5Ccdot3%7D%7B2%5Ccdot3%7D%3D%5Cdfrac%7B3%7D%7B6%7D%5C%5C%5C%5C%5Cdfrac%7B2%7D%7B3%7D%3D%5Cdfrac%7B2%5Ccdot2%7D%7B3%5Ccdot2%7D%3D%5Cdfrac%7B4%7D%7B6%7D%5C%5C%5C%5C%5Cdfrac%7B3%7D%7B2%7D%3D%5Cdfrac%7B3%5Ccdot3%7D%7B2%5Ccdot3%7D%3D%5Cdfrac%7B9%7D%7B6%7D%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B1%5Ccdot2%7D%7B3%5Ccdot2%7D%3D%5Cdfrac%7B2%7D%7B6%7D%5C%5C%5C%5Cx%5E%7B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B2%7D%7B3%7D%7Dy%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B2%7D%7D%3Dx%5E%7B%5Cfrac%7B3%7D%7B6%7D%2B%5Cfrac%7B4%7D%7B6%7D%7Dy%5E%7B%5Cfrac%7B9%7D%7B6%7D%2B%5Cfrac%7B2%7D%7B6%7D%7D%3Dx%5E%7B%5Cfrac%7B7%7D%7B6%7D%7Dy%5E%7B%5Cfrac%7B11%7D%7B6%7D%7D%3D%5Csqrt%5B6%5D%7Bx%5E7y%5E%7B11%7D%7D)
