The answer to your question is: Yes, someone undoubtedly can.
Although you haven't asked to be told or shown how to solve it, I'm here
already, so I may as well stick around and go through it with you.
The sheet is telling you to find the solutions to two equations, AND THEN
DO SOMETHING WITH THE TWO SOLUTIONS. But you've cut off the
instructions in the pictures, so all we have are the two equations, and
you'll have to figure out what to do with their solutions.
<u>First equation:</u>
(2/5) x - 6 = -2
Add 6 to each side:
(2/5) x = 4
Multiply each side by 5:
2x = 20
Divide each side by 2 :
<u>x = 10</u>
<u>Second equation:</u>
-3y + 1/4 = 13/4
Subtract 1/4 from each side:
-3y = 12/4
Multiply each side by 4 :
-12 y = 12
Divide each side by -12 :
<u> y = -1</u>
Answer:
![\[3x+\frac{2}{3}\]](https://tex.z-dn.net/?f=%5C%5B3x%2B%5Cfrac%7B2%7D%7B3%7D%5C%5D)
Step-by-step explanation:
![\[f(x)=x-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%28x%29%3Dx-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
![\[g(x)=3x+1\]](https://tex.z-dn.net/?f=%5C%5Bg%28x%29%3D3x%2B1%5C%5D)
Hence, ![\[(f o g)(x)=f(3x+1)\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3Df%283x%2B1%29%5C%5D)
But, ![\[f(3x+1)=(3x+1)-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D%283x%2B1%29-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
Simplifying,
![\[f(3x+1)=3x+(1-\frac{1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%281-%5Cfrac%7B1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{3-1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B3-1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
Hence, ![\[(f o g)(x)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
First we have to distribute the parentheses on the left side, 2*x is 2x and 2*-3 is -6, so now the equation is 4x+2x-6 = 8x+12
Then, we can add together the two x's on the left side,
so now we have 6x-6 = 8x+12 Subtract 12 from both sides and
you get 6x -18 = 8x Then you can subtract 6x from both the sides and get
-18 = 2x Now we can divide both sides by 2, and the final answer is -9 = x
Since they are not the same and the two sides aren't unequal, there is one solution(:
Hope this is helping you(:
Answer: 7 and 8
<u>Step-by-step explanation:</u>
Let x represent the first number, then x + 1 is the other number.
(x)² + (x + 1)² = 113
x² + x² + 2x + 1 = 113 <em>expanded (x + 1)²</em>
2x² + 2x + 1 = 113 <em>added like terms</em>
2x² + 2x - 112 = 0 <em>subtracted 113 from both sides</em>
x² + x - 56 = 0 <em> divided both sides by 2</em>
(x + 8) (x - 7) = 0 <em>factored polynomial</em>
x + 8 = 0 x - 7 = 0 <em>applied zero product property</em>
x = -8 x = 7 <em> solved for x</em>
↓
not valid since the restriction is that x > 0 <em>(a positive number)</em>
So, x = 7 and x + 1 = (7) + 1 = 8
