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3 years ago

Which is the completely factored form of 12x^3-60x^2+4x-20

Mathematics

1 answer:

Shkiper50 [21]3 years ago

6 0

Answer:

(12x²+4)(x-5)

Step-by-step explanation:

To factor the expression factor by grouping.

(12x³ - 60x²) + (4x - 20)

12x²(x - 5) 4(x-5)

(12x²+4)(x-5)

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Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table shows

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The value of cement mixer after t year is $f(t) = 54,205(0. 87)^{t}$

Given to us

The value of cement mixer when bought, $P$ = $ 54,205

the value of cement mixer after 1 year, $P_1$ = $ 47,158. 35

the value of cement mixer after 2 year, $P_2$ = $ 41,027. 76

To find out depreciation we can use the formula for depreciation,

$P_n= P(1-r)^n\\where,\\P_n= Value\ of\ asset\ after\ n\ year\\P= Value\ of\ asset\ when\ bought\\r= rate\ of\ depreciation\\n= number\ of\ years$

By putting the value, in the formula we get,

$P_1= P(1-r)^n\\\\47,158.35= 54,205\times (1-r)^1\\\\\dfrac{47,158.35}{54,205} = (1-r)\\\\0.87=1-r\\\\r=0.13$

Therefore, putting the value of $r$ and $P$ in depreciation formula for $t$ years we get,

$P_n= P(1-r)^n$

$f(t) = 54,205(0. 87)^{t}$

Hence, the value of cement mixer after t year is $f(t) = 54,205(0. 87)^{t}$ .

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Which is the completely factored form of 12x^3-60x^2+4x-20​

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