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miss Akunina [59]
2 years ago
15

6x-4(3x-5)=2 solve for x.

Mathematics
1 answer:
jeka57 [31]2 years ago
5 0

Answer:

x = 3

Step-by-step explanation:

6x -4(3x-5) = 2

6x - 12x + 20 = 2

-6x = 2 - 20

-6x = -18

x = 3

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A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t
Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be F=L+2W.

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

LW=80,000...(1)

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be C=20L+5(2W)\Rightarrow 20L+10W.

From equation (1), we will get:

L=\frac{80,000}{W}

Upon substituting this value in cost equation, we will get:

C=20(\frac{80,000}{W})+10W

C=\frac{1600,000}{W}+10W

C=1600,000W^{-1}+10W

To minimize the cost, we need to find critical points of the the derivative of cost function as:

C'=-1600,000W^{-2}+10

-1600,000W^{-2}+10=0

-1600,000W^{-2}=-10

-\frac{1600,000}{W^2}=-10

-10W^2=-1,600,000

W^2=160,000

\sqrt{W^2}=\pm\sqrt{160,000}  

W=\pm 400

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

C''=-2(-1600,000)W^{-3}

C''=3200,000W^{-3}

C''=\frac{3200,000}{W^3}

Now, we will substitute W=400 in 2nd derivative as:

C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05

Since 2nd derivative is positive at W=400, therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting W=400 in L=\frac{80,000}{W}, we will get:

L=\frac{80,000}{400}\\\\L=200

Therefore, the side parallel to the river will be 200 feet.

4 0
3 years ago
PLEASE HELP ME!!!!!!!
Sidana [21]
He has come from the hole in the roof because the text states that he did not come from a door, a window, or a chimney, and that is the only answer that was left.
4 0
3 years ago
What is the lcm of 81 and 17?​
algol [13]

Answer:

1377

Step-by-step explanation:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

3 0
2 years ago
A car travels 6 miles in 5 minutes. How fast is it going in miles per hour? How fast is it going in meters per second?
belka [17]

Answer:

72 m\ p.h.

Step-by-step explanation:

we have 60 minute in one hour

we must divide 60 by 5=12

then 6*12=72!!!

it is very easy

5 0
2 years ago
Read 2 more answers
What is the answer of this question ?
fgiga [73]

Answer:

the answer is B

Step-by-step explanation:

hoped I helped:)

6 0
2 years ago
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