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Ede4ka [16]
3 years ago
15

Two lines intersect at a point, forming ​ ∠1 , ∠2 , ∠3 , and​ ​ ∠4 ​ . ∠1 and ∠3 are vertical angles. ∠2 and​ ​ ∠4 are vertical

angles. m∠1=70° What is the measure of ​​ ∠2 ​?
20°
70°
90°
110°
Mathematics
2 answers:
ZanzabumX [31]3 years ago
6 0
Angle 1 and angle 2 are a linear pair, which make a sum of 180
angle 2=180-angle 1=180-70=110
sesenic [268]3 years ago
5 0
< 1 + < 2 = 180.....because they form a linear pair and equal 180
70 + < 2 = 180
< 2 = 180 - 70
< 2 = 110 <==
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aev [14]

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7 0
2 years ago
Which polynomial is written in descending order?
Anarel [89]

The ascending or descending order of a polynomial is determined by the increasing or decreasing power of variable “x” respectively.

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3 years ago
A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t
solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by  

V = V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x

First, we differentiate V(x) with respect to x, to get,

\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450

Equating the first derivative to zero, we get,

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x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2},

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At x =

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Thus, by double derivative test, the maxima occurs at

x = \displaystyle\frac{5(3-\sqrt{3})}{2} for V(x).

Thus, largest volume the box can have occurs when x = \displaystyle\frac{5(3-\sqrt{3})}{2}}.

Maximum volume =

V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}

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shutvik [7]
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Answer:

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