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3 years ago

The surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²? What is the scale factor of the smaller

Mathematics

1 answer:

max2010maxim [7]3 years ago

7 0

Answer:

scale factor of the smaller prism to the larger prism is B. 21/23

Step-by-step explanation:

Given

surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²?

scale factor is ratio of sides of two similar objects

thus scale factor for given prism will be = side of smaller prism / side of larger prism

in general rule

If shape of solid has scale factor of k

scale factor of area = k²

scale factor of volume = k³

_____________________________

Given in the problem area of two prism is given

we know area = side^2

scale factor of area = k²

k^2 = area of smaller prism / area of larger prism

$k^2 = 882 / 1058 = 441/529\\k = \sqrt{ 441/529} \\k = 21/23$

Thus, correct option is B 21/23.

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$\boxed{\sf x=-2}$

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Step-by-step explanation:

First, Let's solve for x in -2x+2y=-4:

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Subtract 2y from both sides:

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Divide both sides by -2:

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$\sf 3x+3y=-18$

→ let x=2+y

$\sf 3\bold{(2+y)}+3y=-18$

Simplify:

$\sf 6+6y=-18$

Now, let's solve for y in 6+6y=-18

$\sf 6+6y=-18$

Subtract 6 from both sides:

$\sf 6+6y-6=-18-6$

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Divide both sides by 6:

$\sf \cfrac{6y}{6}=\cfrac{-24}{6}$

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→ let y = -4

$\sf x=2+\bold{-4}$

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Therefore, x=-2 and y=-4.

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