Answer:
Step-by-step explanation:
Given Equation :
![\qquad \sf \dashrightarrow \: 3(4x+3) = 2x - 5(3 - x) + 2](https://tex.z-dn.net/?f=%20%5Cqquad%20%5Csf%20%5Cdashrightarrow%20%5C%3A%203%284x%2B3%29%20%3D%202x%20-%205%283%20-%20x%29%20%2B%202)
Using distribute property:
![\qquad \sf \dashrightarrow \: 12x + 9 = 2x - 15 + 5x + 2](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5Cdashrightarrow%20%5C%3A%2012x%20%2B%209%20%3D%202x%20-%2015%20%2B%205x%20%2B%202)
Adding the like terms we get :
![\qquad \sf \dashrightarrow \: 12x + 9 = 2x + 5x - 15 + 2](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5Cdashrightarrow%20%5C%3A%2012x%20%2B%209%20%3D%202x%20%20%2B%205x%20%20-%2015%20%2B%202)
![\qquad \sf \dashrightarrow \: 12x + 9 = 7x - 13](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5Cdashrightarrow%20%5C%3A%2012x%20%2B%209%20%3D%207x%20%20-%2013)
Transposing the variables on the right side and constant terms on the left side :
![\qquad \sf \dashrightarrow \: 12x - 7x = - 13 - 9](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5Cdashrightarrow%20%5C%3A%2012x%20%20-%207x%20%3D%20%20%20-%2013%20-%209)
![\qquad \sf \dashrightarrow \: 5x = - 22](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5Cdashrightarrow%20%5C%3A%205x%20%3D%20%20%20-%2022)
Dividing both sides by 5 :
![\qquad \sf \dashrightarrow \: \dfrac{5x}{5} = \dfrac{ - 22}{5}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5Cdashrightarrow%20%5C%3A%20%20%5Cdfrac%7B5x%7D%7B5%7D%20%20%3D%20%20%5Cdfrac%7B%20-%2022%7D%7B5%7D%20)
![\qquad \bf \dashrightarrow \: x = \dfrac{ - 22}{5}](https://tex.z-dn.net/?f=%5Cqquad%20%5Cbf%20%5Cdashrightarrow%20%5C%3A%20%20x%20%3D%20%20%5Cdfrac%7B%20-%2022%7D%7B5%7D%20)
Each teacher should receive 108 pencils
Answer: option <span>D) y=x, x-axis, y=x, y-axis</span>.
I first thought it was the option C) and I tried with it but it was wrong. This is how I dit it.
Option C step by step:
<span>1) Reflection over the x - axis => point with coordinates (a,b) is transformed into point with coordinates (a, -b)
2) Reflection over the line y = x => point with coordinates (a, -b) is transformed into point with coordinates (-b,a)
3) New feflection over the x - axis => (-b,a) transforms into (-b, -a)
4) New reflection over the line y = x => (-b,-a) transforms into (-a,-b)
Which shows it is not the option C).
Then I probed with option D. Step by step:
1) Reflection over the line y = x => (a,b) → (b,a)
2) Reflection over the x-axis => (b,a) → (b,-a)
3) Reflection over the line y = x => (b,-a) → (-a,b)
4) Reflection over the y-axis => (-a,b) → (a,b).
So, this set of reflections, given by the option D) transforms any point into itself, which proofs that the option D) is the right answer.
</span>
Answer:
Step-by-step explanation:
(27)^2/3=∛27²=∛3³*3³=3*3=9
√36³=√36*36*36=√6²*6²*6²=6*6*6=216
(-243)^3/5=5√2-42³=-27
Given that <span>work hours in new zombie are 200 in year 1 and productivity is $8
per hour worked.
The new zombie's real gdp in year 1 is given by 200 x $8 = $1,600
If work hours increase
to 210 in year 2 and productivity rises to $10 per hour.
The new zombie's real gdp in year 2 is given by 210 x $10 = $2,100
The new
zombie's rate of economic growth is given by
![\frac{\$2,100-\$1,600}{\$1,600} \times 100\%= \frac{\$500}{\$1,600} \times100\%=31.25\%](https://tex.z-dn.net/?f=%5Cfrac%7B%5C%242%2C100-%5C%241%2C600%7D%7B%5C%241%2C600%7D%20%5Ctimes%20100%5C%25%3D%20%5Cfrac%7B%5C%24500%7D%7B%5C%241%2C600%7D%20%5Ctimes100%5C%25%3D31.25%5C%25)
</span>