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CaHeK987 [17]
3 years ago
6

Does the equation 14 - 3x = -4x have one, many or no solution?​

Mathematics
2 answers:
Sonbull [250]3 years ago
6 0

Answer:

One Solution

Step-by-step explanation:

1. Re-arrange the terms:

-3x + 4x = 14

2. Collect Like-Terms:

x=-14

Therefore, the answer is one solution: x = -14.

hope that helps :D

BabaBlast [244]3 years ago
3 0

Answer:

one solution,x=- 14

Step-by-step explanation:

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A fence must be built to enclose a rectangular area of 20,000 ft^2. Fencing material costs $4 per foot for the two sides facing
Marysya12 [62]

The cost of the least expensive fence is $3200

Step-by-step explanation:

The given is:

  • A fence must be built to enclose a rectangular area of 20,000 ft²
  • Fencing material costs $4 per foot for the two sides facing north and south and ​$8 per foot for the other two sides

We need to find the cost of the least expensive fence

Assume that the length of each side opposite to North or South is x feet and the length of each other sides  is y feet

∵ The length of the rectangle = x feet

∵ The width of the rectangle = y feet

∵ The rectangular area is 20,000 ft²

- Area of a rectangle = length × width

∴ x × y = 20,000

- Divide both sides by x to find y in terms of x

∴ y=\frac{20,000}{x}

The fence's length is equal to the perimeter of the rectangular area

∵ Perimeter of the rectangle = 2 length + 2 width

∴ Perimeter of the rectangle = 2x + 2y

∵ Fencing material costs $4 per foot for the two sides facing

   North and South

∴ x costs $4 per foot

∵ The cost of the other two sides is $8 per foot

∴ y costs $8 per feet

The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y

∵ The cost of the fence (C) = 4(2x) + 8(2y)

∴ C = 8x + 16y

- Substitute y by its value above

∴ C=8x+16(\frac{20,000}{x})

∴ C=8x+\frac{320,000}{x}

To find the least expensive differentiate C with respect to x and equate the answer by 0 to find the value of x

∵ \frac{320,000}{x} can be written as 320,000x^{-1}

∴ C=8x+320,000x^{-1}

∵ \frac{dC}{dx}=8(1)x^{1-1}+320,000(-1)x^{-1-1}

∴ \frac{dC}{dx}=8-320,000x^{-2}

- Equate \frac{dC}{dx} by zero

∴ 8-320,000x^{-2}=0

∵ -320,000x^{-2}=-\frac{320,000}{x^{2}}

∴ 8-\frac{320,000}{x^{2}}=0

- Subtract 8 from both sides

∴ -\frac{320,000}{x^{2}}=-8

- Multiply both sides by x²

∴ - 320,000 = - 8x²

- Divide both sides by -8

∴ 40,000 = x²

- Take √  for both sides

∴ 200 = x

Substitute x in the equation of C to find the least cost of fence

∵ C=8(200)+\frac{320,000}{(200)}

∴ C = 1600 + 1600

∴ C = 3200

The cost of the least expensive fence is $3200

Learn more:

You can learn more about the differentiation in brainly.com/question/4279146

#LearnwithBrainly

5 0
2 years ago
In a pre algebra class containing 40 students, there are 18 freshmen, 19 sophomores, and 3 juniors. What fraction of the class a
dezoksy [38]

\frac{9}{20} of the class consists of freshmen.

Step-by-step explanation:

Given,

Total number of students = 40

Number of freshmen = 18

Number of sophomores = 19

Number of juniors = 3

Fraction of freshmen = \frac{Number\ of\ freshmen}{Total\ number\ of students}

Fraction of freshmen = \frac{18}{40}

Fraction of freshmen = \frac{9}{20}

\frac{9}{20} of the class consists of freshmen.

Keywords: fraction, division

Learn more about fractions at:

  • brainly.com/question/10712420
  • brainly.com/question/10744457

#LearnwithBrainly

7 0
3 years ago
Please answer correctly !!!! Will mark brainliest !!!!!!
Musya8 [376]

Answer:

h(r) = 6(r+1)+10

Step-by-step explanation:

Just solve for q. Because that's the output. h(r) = q

3 0
2 years ago
Read 2 more answers
Round 18366 to the nearest thousand
hodyreva [135]
184,000 can be rounded by underlining the 3 in the thousands place and look to the right. if, it is more than 5 add 1 to the left, 184.... then replace the numbers behind the rounded number, will be 0. 184,000
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5 0
3 years ago
Directed line segment DE has endpoints D(-4,-2) and E(1,8). Point F divides DE such that DF:FE is 3:2What are the coordinates of
VMariaS [17]

The Solution.

The given points are

D(-4,-2)\text{ and E(1,8)}

The formula is

\frac{mx_2+nx_1}{m+n}_{},\frac{my_2+ny_1}{m+n}

In this case,

m=3,n=2

Therefore,

\begin{gathered} (\frac{mx_2+nx_1}{m+n}_{},\frac{my_2+ny_1}{m+n}) \\ =(\frac{3(1)+_{}2(-4)_{}}{3+2}_{},\frac{3(8)_{}+2(-2)_{}}{3+2}) \\  \end{gathered}=(\frac{3-8}{5},\frac{24-4}{5})=(-\frac{5}{5},\frac{20}{5})=(-1,4)

Hence, the correct answer is (-1, 4) (option 3)

3 0
10 months ago
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