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BigorU [14]
2 years ago
6

If 100 treats will feed 15 dogs (each dog is given the same number of treats), how many dogs can be fed with 40 treats?

Mathematics
1 answer:
Lisa [10]2 years ago
4 0

Answer: 6 dogs

Step-by-step explanation:

If 100 treats will feed 15 dogs, then that means that the number of treats that each dog requires is:

= 100/15

= 6.67 treats

If 6.67 treats will feed one dog then the number of dogs that will be fed by 40 is:

= 40 / 6.67

= 6 dogs

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2. The polynomial 3x3 – 2x2 – 12x + 8 is denoted by f(x).
prohojiy [21]

Answer:

<h2>see below</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • factor theorem
  • PEMDAS
<h3>given:</h3>
  • f(x)=3x³-2x²-12x+8
  • -a×-b=ab
  • -a×b=-ab
  • a²-b²=(a+b)(a-b)
<h3>to do:</h3>
  • use factor theorem to show that (x+2) is a factor of f(x)
<h3>tips and formulas:</h3>
  • When f(c)=0 then x−c is a factor of f(x)
<h3>let's solve:</h3>

according to the question

x+2=0

x=-2

  1. \sf substitute \: the \: value \: of \: x \:  :  \\ \sf 3 {( - 2)}^{3} - 2( { - 2)}^{2}  - 12( - 2) + 8
  2. \sf simplify \: exponets :  \\ 3( - 8) - 2(4) - 12( - 2) + 8
  3. \sf \: multiply :  \\ \tt  - 24 - 8 + 24 + 8
  4. \sf simplify :  \\   \sf- 32 + 32 \\  \sf0

therefore

we have proven that x+2 is a factor of 3x³-2x²-12x+8

let's factorise 3x³-2x²-12x+8

  1. factor out x²: x²(3x-2)-12x+8
  2. factor out -4: x²(3x-2)-4(3x-2)
  3. group: (x²-4)(3x-2)
  4. use a²-b² = (a+b)(a-b):
  • (x+2)(x-2)(3x-2)

and

we are done

8 0
2 years ago
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