12/7 or 1 5/7
Simply multiply things
Mark brainliest please
To solve for x, you need to do inverse operations to both sides. (also, you need to make 2 possibilities for the absolute value)
8 |x+7-3| = 5
Divide both sides by 8 and simplify like terms:
|x+4| = 5/8
Then, you need to separate into 2 different equations like this:
x +4 = 5/8 and
x + 4 = -5/8
Then, solving for x like this:
x = 5/8-4
x = -5/8-4
Which gets you
x = -3.375 and
x = -4.625
Hope this helped!
By the way, I'm getting closer to leveling up, so if you liked my answer, you could reward me with brainliest answer. That'd be great!
Answer:
Tina's height is <em>x</em> inches. She is shorter than her brother, whos height <em>56 </em>inches.
Step-by-step explanation:
Let the height of Tina = x inches
and the height of her brother = 56 inches
if Tina is shorter than her brother then,
<u>x < 56 inches</u>
First you simplify the fraction and variables inside the root. Reduce 126/32 and use exponent rules for dividing variables(subtract the exponents). This will give you,
![\sqrt{ \frac{63 {y}^{5} }{16 {x}^{2} } }](https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7B63%20%7By%7D%5E%7B5%7D%20%7D%7B16%20%7Bx%7D%5E%7B2%7D%20%7D%20%7D%20)
Then move onto the root. Using radical properties you take the root of the numerator and denominator seperately. Since the root of the numerator is not a rational number or perfect square it stays as,
![\sqrt{63 {y}^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%7B63%20%7By%7D%5E%7B5%7D%20%7D%20)
Altogether the new equation will be this,
![\frac{ \sqrt{63 {y}^{5} } }{4x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B63%20%7By%7D%5E%7B5%7D%20%7D%20%7D%7B4x%7D%20)
You can still simplify this further by reducing the radical in the numerator.
You prime factor it to give you 7×9 = 63 which lets you factor out a 3. You can also factor out 4 of the y variables. Breaking down the numerator you get this.
![\sqrt{ {3}^{2} } \sqrt{ {y}^{4} } \sqrt{7y}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%7B3%7D%5E%7B2%7D%20%7D%20%20%5Csqrt%7B%20%7By%7D%5E%7B4%7D%20%7D%20%20%5Csqrt%7B7y%7D%20)
Which simplifies to,
![3 {y}^{2} \sqrt{7y}](https://tex.z-dn.net/?f=3%20%7By%7D%5E%7B2%7D%20%20%5Csqrt%7B7y%7D%20)
Your final simplest form equation is,
Answer:
6
Step-by-step explanation:
Given expression:
![\dfrac{2}{\sqrt[6]{8}} \cdot \sqrt{2}-\left(-\dfrac{18}{\sqrt{81}}-2\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B%5Csqrt%5B6%5D%7B8%7D%7D%20%5Ccdot%20%5Csqrt%7B2%7D-%5Cleft%28-%5Cdfrac%7B18%7D%7B%5Csqrt%7B81%7D%7D-2%5Cright%29)
Rewrite 81 as 9² :
![\implies \dfrac{2}{\sqrt[6]{8}} \cdot \sqrt{2}-\left(-\dfrac{18}{\sqrt{9^2}}-2\right)](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%7D%7B%5Csqrt%5B6%5D%7B8%7D%7D%20%5Ccdot%20%5Csqrt%7B2%7D-%5Cleft%28-%5Cdfrac%7B18%7D%7B%5Csqrt%7B9%5E2%7D%7D-2%5Cright%29)
![\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:](https://tex.z-dn.net/?f=%5Ctextsf%7BApply%20radical%20rule%7D%20%5Cquad%20%5Csqrt%7Ba%5E2%7D%3Da%2C%20%5Cquad%20a%20%5Cgeq%200%3A)
![\implies \dfrac{2}{\sqrt[6]{8}} \cdot \sqrt{2}-\left(-\dfrac{18}{9}-2\right)](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%7D%7B%5Csqrt%5B6%5D%7B8%7D%7D%20%5Ccdot%20%5Csqrt%7B2%7D-%5Cleft%28-%5Cdfrac%7B18%7D%7B9%7D-2%5Cright%29)
![\implies \dfrac{2}{\sqrt[6]{8}} \cdot \sqrt{2}-\left(-2-2\right)](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%7D%7B%5Csqrt%5B6%5D%7B8%7D%7D%20%5Ccdot%20%5Csqrt%7B2%7D-%5Cleft%28-2-2%5Cright%29)
![\implies \dfrac{2}{\sqrt[6]{8}} \cdot \sqrt{2}-\left(-4\right)](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%7D%7B%5Csqrt%5B6%5D%7B8%7D%7D%20%5Ccdot%20%5Csqrt%7B2%7D-%5Cleft%28-4%5Cright%29)
![\implies \dfrac{2}{\sqrt[6]{8}} \cdot \sqrt{2}+4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%7D%7B%5Csqrt%5B6%5D%7B8%7D%7D%20%5Ccdot%20%5Csqrt%7B2%7D%2B4)
![\implies \dfrac{2\sqrt{2}}{\sqrt[6]{8}}+4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B6%5D%7B8%7D%7D%2B4)
Rewrite 8 as 2³ :
![\implies \dfrac{2\sqrt{2}}{\sqrt[6]{2^3}}+4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B6%5D%7B2%5E3%7D%7D%2B4)
![\textsf{Apply radical rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}:](https://tex.z-dn.net/?f=%5Ctextsf%7BApply%20radical%20rule%7D%20%5Cquad%20%5Csqrt%5Bn%5D%7Ba%7D%3Da%5E%7B%5Cfrac%7B1%7D%7Bn%7D%3A)
![\implies \dfrac{2\sqrt{2}}{\left(2^3\right)^{\frac{1}{6}}}+4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%5Csqrt%7B2%7D%7D%7B%5Cleft%282%5E3%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%7D%2B4)
![\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:](https://tex.z-dn.net/?f=%5Ctextsf%7BApply%20exponent%20rule%7D%20%5Cquad%20%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D%3A)
![\implies \dfrac{2\sqrt{2}}{2^{\frac{3}{6}}}+4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%5Csqrt%7B2%7D%7D%7B2%5E%7B%5Cfrac%7B3%7D%7B6%7D%7D%7D%2B4)
![\implies \dfrac{2\sqrt{2}}{2^{\frac{1}{2}}}+4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%5Csqrt%7B2%7D%7D%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%2B4)
![\textsf{Apply radical rule} \quad a^{\frac{1}{2}}=\sqrt{a}, \quad a \geq 0:](https://tex.z-dn.net/?f=%5Ctextsf%7BApply%20radical%20rule%7D%20%5Cquad%20a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Csqrt%7Ba%7D%2C%20%5Cquad%20a%20%5Cgeq%200%3A)
![\implies \dfrac{2\sqrt{2}}{\sqrt{2}}+4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2%5Csqrt%7B2%7D%7D%7B%5Csqrt%7B2%7D%7D%2B4)
Cancel the common factor √2 :
![\implies 2+4](https://tex.z-dn.net/?f=%5Cimplies%202%2B4)
![\implies 6](https://tex.z-dn.net/?f=%5Cimplies%206)
Learn more about radicals here:
brainly.com/question/28106222