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4 years ago

Solve the compound inequality.

Mathematics

2 answers:

Temka [501]4 years ago

7 0

Answer:

Option 4

Step-by-step explanation:

8 < x + 2 《 16

6 < x 《 14

-Dominant- [34]4 years ago

3 0

Answer:

Step-by-step explanation:

hello :

2 < (x+2)/4 ≤4

multiply by 4 : 8 < x+2 ≤16

Subtract 2 : 6 < x ≤14

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weeeeeb [17]

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4 years ago

a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar

xenn [34]

The constraint for the maximum enclosed area is the amount the farmer is

willing to spend on fencing.

The width of the plot that will give the most area, y = 83. $\underline{\overline 3}$ feet

The length of the plot that will give the most area, y = 125 feet

Reasons:

The given parameters are;

The cost of fencing per foot = $20

The maximum amount the farmer is willing to spend = $5000

Number of sides of fencing = 3 sides

Cost of the west side of the = Split with neighbor

Solution:

Let, y, represent the length of the fence, and let x represent the width of

the fence, we have;

Length of fence required = y + 2·x

Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x

Therefore;

Maximum amount to be spent on the fence, 5000 = 20·y + 30·x

$\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x$

$y = \mathbf{250 - \dfrac{3}{2} \cdot x}$

Area of a rectangle = Length × Width

The enclosed rectangular area of the fencing, A = y × x

$\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2$

$\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}$

The leading coefficient of the quadratic function of the area is negative,

therefore, the function only has a maximum point.

At the point of the most area, the slope, $\dfrac{dA}{dx} = 0$

Finding the value of x at the maximum point, we get;

$\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0$

Therefore;

$\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}$

$\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125$

The length of the plot that will give the most area, y = 125 feet

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6 0

3 years ago

I need help now :) ...........

vaieri [72.5K]

Step-by-step explanation:

-2x² + 5x - 3 - (-7 - 9x + 5x²)

= -2x² + 5x - 3 + 7 + 9x - 5x²

= -7x² + 14x + 4.

Hence the coefficient of the x term is 14.

3 0

3 years ago

What is the reciprocal of -13/8 ? A. 13/8 B.-8/13 C.-13/8 D.8/13

erastovalidia [21]

The reciprocal is -8/13

8 0

3 years ago