Answer:
![1\frac{3}{4}](https://tex.z-dn.net/?f=1%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
In order to find the answer, you first need to convert the mixed number (2 1/3) into a improper fraction and then multiply.
![\frac{3}{4} \times2\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes2%5Cfrac%7B1%7D%7B3%7D)
![2\frac{1}{3} =3\times2=6+1=7=\frac{7}{3}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B3%7D%20%3D3%5Ctimes2%3D6%2B1%3D7%3D%5Cfrac%7B7%7D%7B3%7D)
![\frac{3}{4} \times\frac{7}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes%5Cfrac%7B7%7D%7B3%7D)
![3\times7=21](https://tex.z-dn.net/?f=3%5Ctimes7%3D21)
![4\times3=12](https://tex.z-dn.net/?f=4%5Ctimes3%3D12)
![=\frac{21}{12} =\frac{7}{4} =1\frac{3}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B21%7D%7B12%7D%20%3D%5Cfrac%7B7%7D%7B4%7D%20%3D1%5Cfrac%7B3%7D%7B4%7D)
![=1\frac{3}{4}](https://tex.z-dn.net/?f=%3D1%5Cfrac%7B3%7D%7B4%7D)
Hope this helps.
Answer:
Step-by-step explanation:
2x = 128
x = 128/2
x = 64
Answer:
x=2 and y=1
Step-by-step explanation:
Rewrite equations:
y=−x+3;y=x−1
Step: Solve
y=−x+3
Step: Substitute−x+3foryiny=x−1:
y=x−1
−x+3=x−1
−x+3+−x=x−1+−x(Add -x to both sides)
−2x+3=−1
−2x+3+−3=−1+−3(Add -3 to both sides)
−2x=−4−2x−2=−4−2
(Divide both sides by -2)
x=2
Step: Substitute2forxiny=−x+3:
y=−x+3
y=−2+3
y=1(Simplify both sides of the equation)
Hope this Helps you :)
Answer:
SAS
Step-by-step explanation:
Hope this helps :)
Answer:
See explanation
Step-by-step explanation:
1. Given the expression
![\dfrac{\sqrt[7]{x^5} }{\sqrt[4]{x^2} }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B7%5D%7Bx%5E5%7D%20%7D%7B%5Csqrt%5B4%5D%7Bx%5E2%7D%20%7D)
Note that
![\sqrt[7]{x^5}=x^{\frac{5}{7}} \\ \\\sqrt[4]{x^2}=x^{\frac{2}{4}}=x^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Bx%5E5%7D%3Dx%5E%7B%5Cfrac%7B5%7D%7B7%7D%7D%20%5C%5C%20%5C%5C%5Csqrt%5B4%5D%7Bx%5E2%7D%3Dx%5E%7B%5Cfrac%7B2%7D%7B4%7D%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
When dividing
by
we have to subtract powers (we cannot subtract 4 from 7, because then we get another expression), so
![\dfrac{5}{7}-\dfrac{2}{4}=\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{5\cdot 2-1\cdot 7}{14}=\dfrac{3}{14}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B7%7D-%5Cdfrac%7B2%7D%7B4%7D%3D%5Cdfrac%7B5%7D%7B7%7D-%5Cdfrac%7B1%7D%7B2%7D%3D%5Cdfrac%7B5%5Ccdot%202-1%5Ccdot%207%7D%7B14%7D%3D%5Cdfrac%7B3%7D%7B14%7D)
and the result is ![x^{\frac{3}{14}}=\sqrt[14]{x^3}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B3%7D%7B14%7D%7D%3D%5Csqrt%5B14%5D%7Bx%5E3%7D)
2. Given equation ![3\sqrt[4]{(x-2)^3} -4=20](https://tex.z-dn.net/?f=3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20-4%3D20)
Add 4:
![3\sqrt[4]{(x-2)^3} -4+4=20+4\\ \\3\sqrt[4]{(x-2)^3}=24](https://tex.z-dn.net/?f=3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20-4%2B4%3D20%2B4%5C%5C%20%5C%5C3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%3D24)
Divide by 3:
![\sqrt[4]{(x-2)^3} =8](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20%3D8)
Rewrite the equation as:
![(x-2)^{\frac{3}{4}}=8\\ \\(x-2)^{\frac{3}{4}}=2^3](https://tex.z-dn.net/?f=%28x-2%29%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D8%5C%5C%20%5C%5C%28x-2%29%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D2%5E3)
Hence,
![\left((x-2)^{\frac{3}{4}}\right)^{\frac{4}{3}}=(2^3)^{\frac{4}{3}}\\ \\x-2=2^{3\cdot \frac{4}{3}}\\ \\x-2=2^4\\ \\x-2=16\\ \\x-2+2=16+2\\ \\x=18](https://tex.z-dn.net/?f=%5Cleft%28%28x-2%29%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%5Cright%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%3D%282%5E3%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%5C%5C%20%5C%5Cx-2%3D2%5E%7B3%5Ccdot%20%5Cfrac%7B4%7D%7B3%7D%7D%5C%5C%20%5C%5Cx-2%3D2%5E4%5C%5C%20%5C%5Cx-2%3D16%5C%5C%20%5C%5Cx-2%2B2%3D16%2B2%5C%5C%20%5C%5Cx%3D18)