Answer:
Plot the graph and the points.
You can see B, C and E belong to the graph,
Answer:
![(\sqrt{30}-2\sqrt{5})\ m](https://tex.z-dn.net/?f=%28%5Csqrt%7B30%7D-2%5Csqrt%7B5%7D%29%5C%20m)
Step-by-step explanation:
we know that
The length of the side, s, of a cube with a surface area, SA is equal to the formula
![s=\sqrt{\frac{SA}{6}}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7BSA%7D%7B6%7D%7D)
Step 1
Find the length of the side, s, of a cube with a surface area of ![180\ m^{2}](https://tex.z-dn.net/?f=180%5C%20m%5E%7B2%7D)
we have
![SA=180\ m^{2}](https://tex.z-dn.net/?f=SA%3D180%5C%20m%5E%7B2%7D)
substitute in the formula
![s=\sqrt{\frac{180}{6}}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7B180%7D%7B6%7D%7D)
![s=\sqrt{30}\ m](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B30%7D%5C%20m)
Step 2
Find the length of the side, s, of a cube with a surface area of ![120\ m^{2}](https://tex.z-dn.net/?f=120%5C%20m%5E%7B2%7D)
we have
![SA=120\ m^{2}](https://tex.z-dn.net/?f=SA%3D120%5C%20m%5E%7B2%7D)
substitute in the formula
![s=\sqrt{\frac{120}{6}}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7B120%7D%7B6%7D%7D)
![s=\sqrt{20}=2\sqrt{5}\ m](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B20%7D%3D2%5Csqrt%7B5%7D%5C%20m)
Step 3
Find the difference of the length sides
![(\sqrt{30}-2\sqrt{5})\ m](https://tex.z-dn.net/?f=%28%5Csqrt%7B30%7D-2%5Csqrt%7B5%7D%29%5C%20m)
Answer:
Step-by-step explanation:
The three consecutive integers are
(n+2), (n+3), (n+4).
(n+2)+(n+3)+(n+4) = 3n+9
Answer:
I is clear that, the linear equation
has no solution.
Step-by-step explanation:
<u>Checking the first option:</u>
![\frac{2}{3}\left(9x+6\right)=6x+4](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%5Cleft%289x%2B6%5Cright%29%3D6x%2B4)
![6x+4=6x+4](https://tex.z-dn.net/?f=6x%2B4%3D6x%2B4)
![\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D4%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![6x+4-4=6x+4-4](https://tex.z-dn.net/?f=6x%2B4-4%3D6x%2B4-4)
![6x=6x](https://tex.z-dn.net/?f=6x%3D6x)
![\mathrm{Subtract\:}6x\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D6x%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![6x-6x=6x-6x](https://tex.z-dn.net/?f=6x-6x%3D6x-6x)
![0=0](https://tex.z-dn.net/?f=0%3D0)
![\mathrm{Both\:sides\:are\:equal}](https://tex.z-dn.net/?f=%5Cmathrm%7BBoth%5C%3Asides%5C%3Aare%5C%3Aequal%7D)
![\mathrm{True\:for\:all}\:x](https://tex.z-dn.net/?f=%5Cmathrm%7BTrue%5C%3Afor%5C%3Aall%7D%5C%3Ax)
<u>Checking the 2nd option:</u>
![5x+12=5x-7](https://tex.z-dn.net/?f=5x%2B12%3D5x-7)
![\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D5x%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![5x+12-5x=5x-7-5x](https://tex.z-dn.net/?f=5x%2B12-5x%3D5x-7-5x)
![\mathrm{Simplify}](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D)
![12=-7](https://tex.z-dn.net/?f=12%3D-7)
![\mathrm{The\:sides\:are\:not\:equal}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Asides%5C%3Aare%5C%3Anot%5C%3Aequal%7D)
![\mathrm{No\:Solution}](https://tex.z-dn.net/?f=%5Cmathrm%7BNo%5C%3ASolution%7D)
<u>Checking the 3rd option:</u>
![4x+7=3x+7](https://tex.z-dn.net/?f=4x%2B7%3D3x%2B7)
![\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D7%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![4x+7-7=3x+7-7](https://tex.z-dn.net/?f=4x%2B7-7%3D3x%2B7-7)
![\mathrm{Simplify}](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D)
![4x=3x](https://tex.z-dn.net/?f=4x%3D3x)
![\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D3x%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![4x-3x=3x-3x](https://tex.z-dn.net/?f=4x-3x%3D3x-3x)
![\mathrm{Simplify}](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D)
![x=0](https://tex.z-dn.net/?f=x%3D0)
<u>Checking the 4th option:</u>
![-3\left(2x-5\right)=15-6x](https://tex.z-dn.net/?f=-3%5Cleft%282x-5%5Cright%29%3D15-6x)
![\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D15%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![-6x+15-15=15-6x-15](https://tex.z-dn.net/?f=-6x%2B15-15%3D15-6x-15)
![\mathrm{Simplify}\](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D%5C)
![-6x=-6x](https://tex.z-dn.net/?f=-6x%3D-6x)
![\mathrm{Add\:}6x\mathrm{\:to\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BAdd%5C%3A%7D6x%5Cmathrm%7B%5C%3Ato%5C%3Aboth%5C%3Asides%7D)
![-6x+6x=-6x+6x](https://tex.z-dn.net/?f=-6x%2B6x%3D-6x%2B6x)
![\mathrm{Simplify}](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D)
![\mathrm{Both\:sides\:are\:equal}](https://tex.z-dn.net/?f=%5Cmathrm%7BBoth%5C%3Asides%5C%3Aare%5C%3Aequal%7D)
![\mathrm{True\:for\:all}\:x](https://tex.z-dn.net/?f=%5Cmathrm%7BTrue%5C%3Afor%5C%3Aall%7D%5C%3Ax)
Result:
Therefore, from the above calculations it is clear that, the linear equation
has no solution.
Just move all terms to the left side and set equal to zero. Then, set each factor equal to zero.
a = 5,1