Answer:
2√35
Step-by-step explanation:
Answer:
1. x = 39.67
2. x = 15
3. x = 49.29
4. x = -12.8
5. x = 96
6. x = 42
7. x = 36
8. x = 0
9. x = 78
Step-by-step explanation:
Just remember to always isolate the unknown. Here are the solutions to your problem. I will explain each step for the first for you to give you an idea how the others were worked out.
1.
Add 2 to both sides to get rid of -2 on the left side.
![\dfrac{3x}{7}-2+(2)=15+(2)///dfrac{3x}{7}=17](https://tex.z-dn.net/?f=%5Cdfrac%7B3x%7D%7B7%7D-2%2B%282%29%3D15%2B%282%29%2F%2F%2Fdfrac%7B3x%7D%7B7%7D%3D17)
Multiply both sides by 7 to get rid of 7 on the left side.
![\dfrac{3x}{7}\times 7 = 17\times 7\\\\3x = 119](https://tex.z-dn.net/?f=%5Cdfrac%7B3x%7D%7B7%7D%5Ctimes%207%20%3D%2017%5Ctimes%207%5C%5C%5C%5C3x%20%3D%20119)
Divide both sides by 3 to get rid of 3 on the left side.
![\dfrac{3x}{3} = \dfrac{119}{3}\\\\x = 39.67](https://tex.z-dn.net/?f=%5Cdfrac%7B3x%7D%7B3%7D%20%3D%20%5Cdfrac%7B119%7D%7B3%7D%5C%5C%5C%5Cx%20%3D%2039.67)
You could also transpose everything by the x to the other side of the equation. Just remember that whatever OPERATION used on the original side, must be opposite on the other side. I'll use the second problem to show this.
![\dfrac{2x}{5}+1=7](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B5%7D%2B1%3D7)
Transpose 1 on the left to the right. It is addition on the left, then it would be subtraction on the other side.
![\dfrac{2x}{5}+1=7\\\\\dfrac{2x}{5}=7-1\\\\\dfrac{2x}{5}=6](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B5%7D%2B1%3D7%5C%5C%5C%5C%5Cdfrac%7B2x%7D%7B5%7D%3D7-1%5C%5C%5C%5C%5Cdfrac%7B2x%7D%7B5%7D%3D6)
Transpose 5 from the left side to the right. It is division on the left, then it would be multiplication on the right.
![\dfrac{2x}{5}=6\\\\2x=6\times 5\\\\2x=30](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B5%7D%3D6%5C%5C%5C%5C2x%3D6%5Ctimes%205%5C%5C%5C%5C2x%3D30)
Transpose 2 from the left side to the right. It is multiplication on the left, then it would be division on the right.
![2x=30\\\\x=\dfrac{30}{2}\\\\x=15](https://tex.z-dn.net/?f=2x%3D30%5C%5C%5C%5Cx%3D%5Cdfrac%7B30%7D%7B2%7D%5C%5C%5C%5Cx%3D15)
Let's move on with the rest now.
3.
![\dfrac{7x}{15}-1=22\\\\\dfrac{7x}{15}=22+1\\\\\dfrac{7x}{15}=23\\\\7x=23\times15\\\\7x=345\\\\x=\dfrac{345}{7}\\\\x=49.29](https://tex.z-dn.net/?f=%5Cdfrac%7B7x%7D%7B15%7D-1%3D22%5C%5C%5C%5C%5Cdfrac%7B7x%7D%7B15%7D%3D22%2B1%5C%5C%5C%5C%5Cdfrac%7B7x%7D%7B15%7D%3D23%5C%5C%5C%5C7x%3D23%5Ctimes15%5C%5C%5C%5C7x%3D345%5C%5C%5C%5Cx%3D%5Cdfrac%7B345%7D%7B7%7D%5C%5C%5C%5Cx%3D49.29)
4.
![\dfrac{5x}{8}+10=2\\\\\dfrac{5x}{8}=2-10\\\\\dfrac{5x}{8}=-8\\\\5x=-8\times8\\\\5x=-64\\\\x=\dfrac{-64}{5}\\\\x=-12.8](https://tex.z-dn.net/?f=%5Cdfrac%7B5x%7D%7B8%7D%2B10%3D2%5C%5C%5C%5C%5Cdfrac%7B5x%7D%7B8%7D%3D2-10%5C%5C%5C%5C%5Cdfrac%7B5x%7D%7B8%7D%3D-8%5C%5C%5C%5C5x%3D-8%5Ctimes8%5C%5C%5C%5C5x%3D-64%5C%5C%5C%5Cx%3D%5Cdfrac%7B-64%7D%7B5%7D%5C%5C%5C%5Cx%3D-12.8)
5.
![\dfrac{x}{6}+4=20\\\\\dfrac{x}{6}=20-4\\\\\dfrac{x}{6}=16\\\\x=16\times6\\\\x=96](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B6%7D%2B4%3D20%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B6%7D%3D20-4%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B6%7D%3D16%5C%5C%5C%5Cx%3D16%5Ctimes6%5C%5C%5C%5Cx%3D96)
6.
![\dfrac{x}{3}-4=10\\\\\dfrac{x}{3}=10+4\\\\\dfrac{x}{3}=14\\\\x=3\times14\\\\x=42](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B3%7D-4%3D10%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B3%7D%3D10%2B4%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B3%7D%3D14%5C%5C%5C%5Cx%3D3%5Ctimes14%5C%5C%5C%5Cx%3D42)
7.
![\dfrac{x}{6}+2=8\\\\\dfrac{x}{6}=8-2\\\\\dfrac{x}{6}=6\\\\x=6\times6\\\\x=36](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B6%7D%2B2%3D8%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B6%7D%3D8-2%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B6%7D%3D6%5C%5C%5C%5Cx%3D6%5Ctimes6%5C%5C%5C%5Cx%3D36)
8.
![\dfrac{x}{9}+8=8\\\\\dfrac{x}{9}=8-8\\\\\dfrac{x}{9}=0\\\\x=0\times9\\\\x=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B9%7D%2B8%3D8%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B9%7D%3D8-8%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B9%7D%3D0%5C%5C%5C%5Cx%3D0%5Ctimes9%5C%5C%5C%5Cx%3D0)
9.
![\dfrac{x}{6}+7=20\\\\\dfrac{x}{6}=20-7\\\\\dfrac{x}{6}=13\\\\x=13\times6\\\\x=78](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B6%7D%2B7%3D20%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B6%7D%3D20-7%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B6%7D%3D13%5C%5C%5C%5Cx%3D13%5Ctimes6%5C%5C%5C%5Cx%3D78)
Answer:
y= -3/4x-1
Step-by-step explanation:
The points are (8,-7) and (0,-1)
The slope is the change in Y over the change in X, so you have -3/4 as your slope.
Then, you have y=-3/4x+b
You substitute either (8,-7) or (0,-1) for X and Y in the equation, and solve it, giving you -1 for B
Answer:
Option C) 2=2 is the last step of Naomi and it is the correct answer
Step-by-step explanation:
Given that Naomi solves a system of equation by Substitution method :
The given system has infinite many solutions
Naomi's last step is 2=2
<h3>For : A system of equations after solved then its constant value must be same in both the sides</h3>
Then the system of equations has infinite many solutions
Therefore it must be 2=2
Hence option C) 2=2 is the last step and it is the correct answer
Answer: The price of each small box is $4.8 and the price of each large box is $10.8.
Step-by-step explanation:
Let x = Price of each small box, y= price of each large box.
As per given,
3x+2y= 36 ...(i)
4x+y= 30 ...(ii)
Multiplying 2 to (ii), we get
8x+2y =60...(iii)
Subtract (i) from (iii), we get
5x= 24
x= 4.8
From (ii)
4(4.8)+y= 30
19.2+y=30
y= 10.8
Hence, the price of each small box is $4.8 and the price of each large box is $10.8.