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2 years ago

So if you have 1500 ML then how many liters will you have?

Mathematics

1 answer:

Nat2105 [25]2 years ago

7 0

1500ML=1.5 Liters
Move decimal three places to the left, or divide 1500/1000
1000ML=1L

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Step-by-step explanation:

<u>Given expression</u>:

$\dfrac{a^2-64}{a^2-10a+24} \cdot \dfrac{a^2-12a+36}{a^2+4a-32}$

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$\begin{aligned}a^2-10a+24 & =a^2-4a-6a+24\\& = a(a-4)-6(a-4)\\ & = (a-6)(a-4) \end{aligned}$

$\begin{aligned}a^2-12a+36 & =a^2-6a-6a+36\\& = a(a-6)-6(a-6)\\ & = (a-6)(a-6) \end{aligned}$

$\begin{aligned}a^2+4a-32 & =a^2+8a-4a-32\\& = a(a+8)-4(a+8)\\ & = (a-4)(a+8) \end{aligned}$

Therefore:

$\dfrac{(a-8)(a+8)}{(a-6)(a-4)} \cdot \dfrac{(a-6)(a-6)}{(a-4)(a+8)}$

$\textsf{Apply the fraction rule}: \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}$

$\dfrac{(a-8)(a+8)(a-6)(a-6)}{(a-6)(a-4)(a-4)(a+8)}$

Cancel the common factors (a + 8) and (a - 6):

$\dfrac{(a-8)(a-6)}{(a-4)(a-4)}$

Simplify the numerator:

$\dfrac{(a-8)(a-6)}{(a-4)^2}$

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