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Ilia_Sergeevich [38]

2 years ago

7

The closest chicken shack to the city of portales is more than 125 miles away. Which two inequalities represent d the distance o

f chicken shacks from portales

1 answer:

ExtremeBDS [4]2 years ago

5 0

D > 125 or you could write it backwards 125< d

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Choose the value that will correctly replace the missing part?2(?+5)=6x+10

CaHeK987 [17]

Answer:

? = 3x

Step-by-step explanation:

2(? + 5) = 6x + 10

You must plug in a number that will get the same value on both sides of the equal sign.

2*5 = 10

2*? = 6x

6x/2 = 3x

8 0

2 years ago

The width of a box in the shape of a rectangular prism is 4 inches more than the height h . The length is the difference of 9 in

Doss [256]

Answer:

$(a)$ $V = -H^3+ 5H^2 + 36H$

$(b)$ $Length = 5in; Width = 9in; Height = 5in$ or $Length = 3in; Width = 10in; Height = 6in$

Step-by-step explanation:

Let:

$W=Width; L = Length; H = Height$

Given

$W = 4 + H$

$L = 9 - H$

Solving (a): The polynomial for the volume in terms of height

Volume (V) is calculated using:

$V = L * W * H$

$V = (9 - H) * (4 + H) * H$

Expand

$V = (9 - H) * (4H + H^2)$

Open brackets

$V = 36H + 9H^2 - 4H^2 - H^3$

$V = 36H + 5H^2 - H^3$

Rewrite as:

$V = -H^3+ 5H^2 + 36H$

Solving (b): The dimensions when Volume = 180

Substitute 180 for V in: $V = -H^3+ 5H^2 + 36H$

$180 = -H^3+ 5H^2 + 36H$

Rewrite as:

$H^3 - 5H^2 - 36H + 180 = 0$

Factorize:

$H^2(H - 5) - 36(H - 5) = 0$

$(H^2 - 36)(H - 5) = 0$

Express $H^2 - 36$ as difference of two squares

$(H - 6)(H + 6)(H - 5) =0$

This gives:

$H - 6 =0==> H = 6$

$H + 6 =0==> H = -6$

$H - 5 =0==> H = 5$

Since the height can not be negative, then H = 5 or H = 6

Recall that:

$W = 4 + H$

$L = 9 - H$

When H = 5

$W = 4 + 5 = 9$

$L = 9 - 5 = 4$

When H = 6

$W = 4 + 6 = 10$

$L = 9 - 6 = 3$

Hence, the dimensions of the box are:

$Length = 5in; Width = 9in; Height = 5in$

or

$Length = 3in; Width = 10in; Height = 6in$

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2 years ago

Limitation of -4 to the left of the absolute value of x+4 divided by x+4

timama [110]

I believe you're asking about the one-sided limit,

$\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4}$

Recall the definition of absolute value:

• $|x| = x$ if $x\ge0$

• $|x| = -x$ if $x < 0$

Since we're approaching -4 from the left, we're effectively focusing on a domain of $x$ or $x+4$ . So, by the definition above, we have $|x+4| = -(x+4)$ . Then in the limit, we have

$\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4} = \lim_{x\to-4^-}\frac{-(x+4)}{x+4} = \lim_{x\to-4^-}(-1) = \boxed{-1}$

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2 years ago

Chairs need to be set up for the audience members. You want to use the

kolbaska11 [484]

Answer: 18

Step-by-step explanation: If there were 18 seats in the row, it would be an even amount in each row, the same amount in each row, and would see everybody.

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3 years ago

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