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3 years ago

Find the measure of <_A. (show work if possible).

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

Answer:

We know that exterior angle of a triangle is equal to the sum of two opposite interior angle.

Step-by-step explanation:

<A = 4y

< B = 3y + 6°

<BCD = 111°

Now

<BCD = <A + <B( exterior angle of a triangle is equal to the sum of two opposite interior angle)

111° = 4y + 3y + 6°

111° - 6° = 7y

105° =7y

Therefore y = 15°

The measure of <A = 4*15°= 60°

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

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3 years ago

The coordinates of three vertices of a rectangle are -2, 3, -2, -1, and 3, -1. what are the coordinates of the fourth vertex

Lera25 [3.4K]

Answer:

(3,-5)

Step-by-step explanation:

We first cal ulate the distance

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3 years ago

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tatiyna

Answer:

Step-by-step explanation:

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A shop has 15% sale. Originally a computer cost £275. How much does the computer cost in the sale?

lutik1710 [3]

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3 years ago

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Kazeer [188]

Answer:

C. quadratic function; quadratic term: −6x^2; linear term: −17x; constant term: −12

Step-by-step explanation:

Answer:

quadratic function; quadratic term: −6x² ; linear term: −17x; constant term: −12

Step-by-step explanation:

The given function is

We need to expand the RHS to get:

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The quadratic term is -6x²

The linear term is -17x

The constant term is -12

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3 years ago