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Monica [59]
3 years ago
7

X =

ddle" class="latex-formula">x - 5 WHAT IS X
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
6 0

x = -15

Step-by-step explanation:

x =  \frac{2}{3} x - 5

Collect like terms and simplify

x -  \frac{2}{3} x =  - 5 \\  \frac{1}{3} x =  - 5

Cross multiply

x =  - 5 \times 3 \\  \\ x =  - 15

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Answer:

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3 years ago
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Combine the like terms of the expression (8 + 6x) + (-4 + 9c). Explain how you simplified the expression in each step. * pls hel
Delicious77 [7]

Answer: 6x+9c+4

Step-by-step explanation:  (8 + 6x) + (-4 + 9c)

                                              8+6x-4+9c

                                              6x+9c+8-4

                                              6x+9c+4

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3 years ago
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Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 162 square feet
Gnom [1K]

Answer:

The width and length of rectangle is 12.728 m

Step-by-step explanation:

Let the length of the rectangle = L

let the width of the rectangle = W

The subjective function is given by;

F(p) = 2(L + W)

F = 2L + 2W

Area of the rectangle is given by;

A = LW

LW = 162 ft²

L = 162 / W

Substitute in the value of L into subjective function;

f = 2l + 2w\\\\f = 2(\frac{162}{w} )+2w\\\\f = \frac{324}{w} + 2w\\\\\frac{df}{dw} = \frac{-324}{w^2} +2\\\\

Take the second derivative of the function, to check if it will given a minimum perimeter

\frac{d^2f}{dw^2}= \frac{648}{w^3} \\\\Thus, \frac{d^2f}{dw^2}>0, \ since,\frac{648}{w^3} >0 \ (minimum \ function \ verified)

Determine the critical points of the first derivative;

df/dw = 0

\frac{-324}{w^2} +2 = 0\\\\-324 + 2w^2=0\\\\2w^2 = 324\\\\w^2 = \frac{324}{2} \\\\w^2 = 162\\\\w= \sqrt{162}\\\\w = 12.728 \ m

L = 162 / 12.728

L = 12.728 m

Therefore, the width and length of rectangle is 12.728 m

3 0
2 years ago
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