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ladessa [460]
3 years ago
14

Tim has m dollars. Rebecca has $6 less than times the number of dollars that Tim has. Which expression represents the total amou

nt of money that Tim and Rebecca have? If Tim has $70, how much money do Rebecca and Tim have altogether?
Mathematics
1 answer:
Effectus [21]3 years ago
6 0

Answer:

$71

Step-by-step explanation:

Tim has M dollars

Rebecca is having (M/10 - 6)

Then, the amount of money Tim and Rebecca are having

= M + M/10 - 6

= (11M/10) - 6 dollars

The expression representing the total amount of money is [(11X/10) - 6]

If Tim is having $70, then total amount both would have together

= [(11 × 70/10) - 6]

= 77 - 6

= $71

Therefore, the expression for the total amount is [(11M/10) - 6] dollars

The total amount both are having together is $71.

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Answer:

D. 13

Step-by-step explanation:

x = 5

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meaning the side length has to be 13, also.

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3 years ago
Lim x-1 x³-2x²+3x-2/(2x^4-3x+1)
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Since the limit becomes the undetermined form

\displaystyle \lim_{x\to 1} \dfrac{x^3-2x^2+3x-2}{2x^4-3x+1} \to \dfrac{0}{0}

it means that both polynomials have a root at x=1. So, we can fact both numerator and denominator:

x^3-2x^2+3x-2 = (x-1)(x^2-x+2)

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So, the fraction becomes

\dfrac{(x-1)(x^2-x+2)}{(x-1)(2x^3+2x^2+2x-1)} = \dfrac{x^2-x+2}{2x^3+2x^2+2x-1}

Now, as x approaches 1, you have no problems anymore:

\displaystyle \lim_{x\to 1} \dfrac{x^2-x+2}{2x^3+2x^2+2x-1} \to \dfrac{2}{5}

4 0
3 years ago
suppose a farmer encloses a rectangular region of a land next to a river. fencing will be used on 3 sieds, and none is needed al
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Answer:

Dimensions :

x (the longer side, only one side with fence )   =  90  ft

y ( the shorter side two sides with fence )        =  45  ft

Total fence used   45 * 2  +  90    =  180 ft

A(max)  =  

Step-by-step explanation: If a farmer has 180 ft of fencing to encloses a rectangular area with fence in three sides and the river on one side, the farmer surely wants to have a maximum enclosed area.

Lets call "x" one the longer side  ( only one of the longer side of the rectangle will have fence, the other will be along the river and won´t need fence. "y" will be the shorter side

Then we have:

P = perimeter  =  180  =  2y  +  x        ⇒   y  =  ( 180 - x )  / 2        (1)

And   A (r)   =  x * y

A(x)   =  x  *  ( 180 - x ) /2       ⇒   A(x)   = (180/2) *x   -  x² / 2

Taking derivatives on both sides of the equation :

A´(x)   =  90   -  x    

Then if    A´(x)   =  0   ⇒        90   -  x    =  0     ⇒   x  =  90 ft

and from :       y  =  ( 180 - x )  / 2     ⇒     y  =  90/2

y  =  45  ft

And

A(max)  =  90 * 45    =  4050  ft²

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Step-by-step explanation:

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