The equation that has an infinite number of solutions is ![2x + 3 = \frac{1}{2}(4x + 2) + 2](https://tex.z-dn.net/?f=2x%20%2B%203%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284x%20%2B%202%29%20%2B%202)
<h3>How to determine the equation?</h3>
An equation that has an infinite number of solutions would be in the form
a = a
This means that both sides of the equation would be the same
Start by simplifying the options
3(x – 1) = x + 2(x + 1) + 1
3x - 3 = x + 3x + 2 + 1
3x - 3 = 4x + 3
Evaluate
x = 6 ----- one solution
x – 4(x + 1) = –3(x + 1) + 1
x - 4x - 4 = -3x - 3 + 1
-3x - 4 = -3x - 2
-4 = -2 ---- no solution
![2x + 3 = \frac{1}{2}(4x + 2) + 2](https://tex.z-dn.net/?f=2x%20%2B%203%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284x%20%2B%202%29%20%2B%202)
2x + 3 = 2x + 1 + 2
2x + 3 = 2x + 3
Subtract 2x
3 = 3 ---- infinite solution
Hence, the equation that has an infinite number of solutions is ![2x + 3 = \frac{1}{2}(4x + 2) + 2](https://tex.z-dn.net/?f=2x%20%2B%203%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284x%20%2B%202%29%20%2B%202)
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<u>Complete question</u>
Which equation has infinite solutions?
3(x – 1) = x + 2(x + 1) + 1
x – 4(x + 1) = –3(x + 1) + 1
![2x + 3 = \frac{1}{2}(4x + 2) + 2](https://tex.z-dn.net/?f=2x%20%2B%203%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284x%20%2B%202%29%20%2B%202)
![\frac 13(6x - 3) = 3(x + 1) - x - 2](https://tex.z-dn.net/?f=%5Cfrac%2013%286x%20-%203%29%20%3D%203%28x%20%2B%201%29%20-%20x%20-%202)
Answer:
60 inches
Step-by-step explanation:
s = 15 in
Perimeter of a Square = 4 s
= 4 × 15
= 60 in
∴Chatty needs 60 inches of yarn.
Hope that helps!!
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Answer:
1. 10 in / 3 ft
2. 5 min / 1 h
3. 1 kg / 250 g
Step-by-step explanation:
![h(x) =8x^3-19x^2+14x-3](https://tex.z-dn.net/?f=h%28x%29%20%3D8x%5E3-19x%5E2%2B14x-3)
Step-by-step explanation:
Given functions are:
![f(x) = 8x-3\\g(x) = (x-1)^2](https://tex.z-dn.net/?f=f%28x%29%20%3D%208x-3%5C%5Cg%28x%29%20%3D%20%28x-1%29%5E2)
h(x) is the product of g(x) and f(x)
![h(x) = f(x) * g(x)\\= (8x-3)(x-1)^2\\= (8x-3)(x^2-2x+1)\\= 8x(x^2-2x+1)-3(x^2-2x+1)\\= 8x^3-16x^2+8x-3x^2+6x-3](https://tex.z-dn.net/?f=h%28x%29%20%3D%20f%28x%29%20%2A%20g%28x%29%5C%5C%3D%20%288x-3%29%28x-1%29%5E2%5C%5C%3D%20%288x-3%29%28x%5E2-2x%2B1%29%5C%5C%3D%208x%28x%5E2-2x%2B1%29-3%28x%5E2-2x%2B1%29%5C%5C%3D%208x%5E3-16x%5E2%2B8x-3x%5E2%2B6x-3)
Combining like terms
![=8x^3-16x^2-3x^2+8x+6x-3\\=8x^3-19x^2+14x-3](https://tex.z-dn.net/?f=%3D8x%5E3-16x%5E2-3x%5E2%2B8x%2B6x-3%5C%5C%3D8x%5E3-19x%5E2%2B14x-3)
Hence,
![h(x) =8x^3-19x^2+14x-3](https://tex.z-dn.net/?f=h%28x%29%20%3D8x%5E3-19x%5E2%2B14x-3)
Keywords: Functions, product
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