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larisa86 [58]
3 years ago
13

Simplify: (6x-4) (9x-2)

Mathematics
1 answer:
Vinil7 [7]3 years ago
5 0

Step-by-step explanation:

Hey, there!!

While simplifying the algebraic expression, you must be very careful about the signs.

Here,

(6x-4) (9x-2)

Multiply 2nd expression by 1st expression,

= 6x ( 9x - 2) -4 ( 9x - 2)

= (54 {x}^{2} - 12x)  - (36x  - 8)

Opening brackets,

= 54 {x}^{2}  - 12x - 36x + 8

Simplifying them we get,

= 54 {x}^{2}  - 48x  + 8

Therefore, the answer is 54x^2 - 48x +8.

<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em>

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What is 04.151515... into a fraction
Sergio039 [100]

Answer:

\displaystyle 4.\overline{15} = \frac{137}{33}.

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

4.151515\cdots = 4 + 0.151515\cdots

The most challenging task here is to express 0.151515\cdots as a proper fraction. Once that fraction is found, expressing the original number 4.151515\cdots will be as simple as rewriting a mixed number as an improper fraction.

Let x = 0.151515\cdots. (x + 4) would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in x are shifted to the left by two places, the repeating part will continue to match:

\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}.

Note, that this "shifting" is as simple as multiplying the initial number by 100 (same as 10 raised to the power of the number of digits that needs to be shifted.)

Subtract the original number from the shifted number to eliminate the fraction part completely:

\begin{aligned}&(100\, x) - x \\ &= 15.151515\cdots\\  & \phantom{=}- 0.151515\cdots\\&=15 \end{aligned}.

In other words:

99\, x = 15.

\displaystyle x = \frac{15}{99} = \frac{5}{33}.

Therefore, the original number would be:

\displaystyle x + 4 = \frac{5}{33} = \frac{132 + 5}{33} = \frac{137}{33}.

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