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kondaur [170]
3 years ago
15

Simplify the expression 12c-c

Mathematics
1 answer:
Klio2033 [76]3 years ago
5 0

Answer:

11c

Step-by-step explanation:

Think of it like 12c-1c.

When it is c by itself, then it is just 1c.

Subtract 12-1, get 11.

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Step-by-step explanation:

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(2)^2-4*2+3=-1

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Jeff bicycles 126 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 m
weqwewe [10]

Given Information:

Distance = 160 miles

Required Information:

Rate = r = ?

Answer:

Rate = r = 20 mph

Step-by-step explanation:

Recall that the rate is given by

Rate = distance/time

r = \frac{d}{t} \\\\t = \frac{d}{r} \\\\t = \frac{160}{r} \\\\

It is given that the same trip would have taken 2 hours longer if he had decreased his speed by 4 mph.

Mathematically,

\frac{160}{(r-4)} = \frac{160}{r} + 2 \\\\

Simplify the equation

\frac{160}{(r-4)} - \frac{160}{r} = 2 \\\\\frac{160r - 160(r-4)}{r(r-4)} = 2 \\\\\frac{160r - 160r+640)}{r(r-4)} = 2 \\\\160r - 160r+640 = r(r-4) (2) \\\\640 = r(r-4) (2) \\\\640 = (r^2 - 4r) (2) \\\\640 = 2r^2 - 8r \\\\2r^2 - 8r-640 =0 \\\\2(r^2 - 4r-320) =0 \\\\r^2 - 4r-320 =0 \\\\

Now we are left with a quadratic equation.

We may solve the quadratic equation using the factorization method  

r^2 - 4r-320 =0 \\\\r^2-20r+16r-320=0 \\\\r(r-20)+16(r-20)=0 \\\\(r-20) (r+16)=0 \\\\

So,

(r-20) = 0 \\\\r = 20 \\\\

OR

(r+16)=0 \\\\r = -16 \\\\

Since rate cannot be negative, discard the negative value of r

Therefore, the rate is

r = 20 \: mph

3 0
4 years ago
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