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katovenus [111]
3 years ago
9

You originally draw a design for an art contest on a 2 in. x 5 in. card. The second phase of the contest requires the drawing to

be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.
Mathematics
1 answer:
Licemer1 [7]3 years ago
4 0

Answer:

  the other dimension is 4.2 inches

Step-by-step explanation:

The scale factor from 5 inches to 10.5 inches is ...

  10.5/5 = 2.1

Then the other dimension is 2 inches times that scale factor:

  2.1×(2 in) = 4.2 in

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A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than
ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

  • A cuboid has 6 faces.
  • A cuboid contains 8 vertices.
  • A cuboid contains 12 edges .
  • The total surface area of a cuboid is

           = 2(length×breadth+breadth×height+length×height) square units

  • The dimension of a cuboid is written as length×breadth×height.
  • The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

=[x\times 2x\times (x+2)]   cubic inches

=[2x^2(x+2)]     cubic inches

=(2x^3+4x^2)     cubic inches

According to the problem,

2x^3+4x^2=192

\Rightarrow 2x^3+4x^2-192=0

\Rightarrow 2(x^3+2x^2-96)=0

\Rightarrow (x^3+2x^2-96)=0

\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0

\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0

\Rightarrow (x-4)(x^2+6x+24)=0

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

 length=(2×4) inches=8 inches

 and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

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3 years ago
You are drawing two cards, without replacement, from a standard deck of 52 cards. What is the
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Answer:

Dear student,

Answer to your query is provided below

Probability of drawing a 2 at first is (4/52) = (1/13)

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Step-by-step explanation:

Total no. Of cards = 52

Total no. Of cards of 2 = 4

Prob. Of drawing 2 = 4/52

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I don’t understand this
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Answer: 3:1

Step-by-step explanation:

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