Answer:
![\frac{-17}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B-17%7D%7B6%7D)
Step-by-step explanation:
Let x be the number we want to find.
First we analyze the given informations
Info 1 : <u><em>Two times the sum of four times a number plus six</em></u>
We translate this statement (info 1) mathematically as : 2×(4x + 6)
Info 2 : <u><em>five less than twice the same number</em></u>
We translate this statement (info 2) mathematically as : 2x - 5
Info 1 <u><em>is the same as</em></u> Info 2 ⇔ 2×(4x + 6) = 2x - 5
2×(4x + 6) = 2x - 5
⇔ 8x + 12 = 2x - 5
⇔ 8x - 2x = -5 - 12
⇔ 6x = - 17
⇔ x = -17/6
In a given radioactive nuclide, we can easily find the mass number, mass of proton and neutron by subtracting the mass of proton from the mass number. The mass number, mass of proton and mass of neutron of the radioactive nuclide are 131, 56 and 75 respectively.
<h3>Properties of an atom</h3>
Data;
- Mass Number = 131
- Atomic Number = 56
In a given atom, the mass number of an atom comprises of the mass of proton and mass of neutron. The atomic number of the element or atom is equal to the mass of the proton.
In this case,
mass number = mass of proton + mass of neutron.
![131=56 + neutron\\neutron = 131 - 56\\neutron = 75](https://tex.z-dn.net/?f=131%3D56%20%2B%20neutron%5C%5Cneutron%20%3D%20131%20-%2056%5C%5Cneutron%20%3D%2075)
From the calculation above, the mass number, mass of proton and mass of neutron of the radioactive nuclide are 131, 56 and 75 respectively.
Learn more on mass of an element here;
brainly.com/question/496676
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Your answer is negative 2 I took the test and I got it
Answer:
![g^{-1}(x)=-\frac{3}{2}x-\frac{15}{2}](https://tex.z-dn.net/?f=g%5E%7B-1%7D%28x%29%3D-%5Cfrac%7B3%7D%7B2%7Dx-%5Cfrac%7B15%7D%7B2%7D)
Step-by-step explanation:
Given function,
![g(x) = -\frac{2}{3}x-5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-%5Cfrac%7B2%7D%7B3%7Dx-5)
Step 1 : Replace g(x) by y:
![y = -\frac{2}{3}x-5](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B2%7D%7B3%7Dx-5)
Step 2 : Swap x and y:
![x = -\frac{2}{3}y-5](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B2%7D%7B3%7Dy-5)
Step 3 : Solve the equation for y ( isolate y in the left side ):
![x +\frac{2}{3}y=-5](https://tex.z-dn.net/?f=x%20%2B%5Cfrac%7B2%7D%7B3%7Dy%3D-5)
![\frac{2}{3}y=-5-x](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dy%3D-5-x)
![y=\frac{3}{2}(-5-x)](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7D%28-5-x%29)
![y=-\frac{15}{2}-\frac{3}{2}x](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B15%7D%7B2%7D-%5Cfrac%7B3%7D%7B2%7Dx)
![y=-\frac{3}{2}x-\frac{15}{2}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B2%7Dx-%5Cfrac%7B15%7D%7B2%7D)
Step 4: Replace y by
:
![g^{-1}(x)=-\frac{3}{2}x-\frac{15}{2}](https://tex.z-dn.net/?f=g%5E%7B-1%7D%28x%29%3D-%5Cfrac%7B3%7D%7B2%7Dx-%5Cfrac%7B15%7D%7B2%7D)
Hence, the inverse of the function g(x) is
.
![\qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star](https://tex.z-dn.net/?f=%20%5Cqquad%20%5Cqquad%20%20%5Cbf%20%5Chuge%5Cstar%20%5C%3A%20%20%5C%3A%20%20%5Clarge%7B%20%20%5Cunderline%7BAnswer%7D%20%7D%20%20%5Chuge%20%5C%3A%20%20%5C%3A%20%5Cstar)
[ b ] is the Correct one
![\textsf{ \underline{\underline{Steps to solve the problem} }:}](https://tex.z-dn.net/?f=%5Ctextsf%7B%20%20%5Cunderline%7B%5Cunderline%7BSteps%20to%20solve%20the%20problem%7D%20%7D%3A%7D)
![\qquad❖ \: \sf \:4 \: log_{3}(y) - 6 \: log_{3}(x) + 7 \: log_{3}(z)](https://tex.z-dn.net/?f=%20%5Cqquad%E2%9D%96%20%5C%3A%20%20%5Csf%20%5C%3A4%20%20%5C%3A%20log_%7B3%7D%28y%29%20%20-%206%20%5C%3A%20%20log_%7B3%7D%28x%29%20%20%2B%207%20%5C%3A%20%20log_%7B3%7D%28z%29%20)
![\qquad❖ \: \sf \: \: log_{3}(y {}^{4} ) - \: log_{3}(x {}^{6} ) +\: log_{3}(z {}^{7} )](https://tex.z-dn.net/?f=%20%5Cqquad%E2%9D%96%20%5C%3A%20%20%5Csf%20%5C%3A%20%5C%3A%20log_%7B3%7D%28y%20%7B%7D%5E%7B4%7D%20%29%20%20-%20%20%5C%3A%20%20log_%7B3%7D%28x%20%7B%7D%5E%7B6%7D%20%29%20%20%2B%5C%3A%20%20log_%7B3%7D%28z%20%7B%7D%5E%7B7%7D%20%29%20)
![\qquad❖ \: \sf \: \: log_{3}(y {}^{4} ) + \: log_{3}(z{}^{7} ) - \: log_{3}(x {}^{6} )](https://tex.z-dn.net/?f=%20%5Cqquad%E2%9D%96%20%5C%3A%20%20%5Csf%20%5C%3A%20%5C%3A%20log_%7B3%7D%28y%20%7B%7D%5E%7B4%7D%20%29%20%20%20%2B%20%20%5C%3A%20%20log_%7B3%7D%28z%7B%7D%5E%7B7%7D%20%29%20%20%20-%20%5C%3A%20%20log_%7B3%7D%28x%20%7B%7D%5E%7B6%7D%20%29%20)
(
)
![\qquad❖ \: \sf \: log_{3}( {y}^{4} {z}^{7} ) - log_{3}( {x}^{6} {}^{} )](https://tex.z-dn.net/?f=%20%5Cqquad%E2%9D%96%20%5C%3A%20%20%5Csf%20%5C%3A%20log_%7B3%7D%28%20%7By%7D%5E%7B4%7D%20%7Bz%7D%5E%7B7%7D%20%20%29%20%20-%20%20log_%7B3%7D%28%20%7Bx%7D%5E%7B6%7D%20%7B%7D%5E%7B%7D%20%20%29%20)
(
)
![\qquad❖ \: \sf \: log_{3} \bigg( \dfrac{y {}^{4} {z}^{7} }{ {x}^{6} } \bigg )](https://tex.z-dn.net/?f=%20%5Cqquad%E2%9D%96%20%5C%3A%20%20%5Csf%20%5C%3A%20%20%20%20log_%7B3%7D%20%5Cbigg%28%20%5Cdfrac%7By%20%7B%7D%5E%7B4%7D%20%7Bz%7D%5E%7B7%7D%20%20%7D%7B%20%7Bx%7D%5E%7B6%7D%20%7D%20%5Cbigg%20%29%20)
(
)
![\qquad \large \sf {Conclusion} :](https://tex.z-dn.net/?f=%20%5Cqquad%20%5Clarge%20%5Csf%20%7BConclusion%7D%20%20%3A%20)
[ b ] is the Correct choice