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3 years ago

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You originally draw a design for an art contest on a 3 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.

2 answers:

bagirrra123 [75]3 years ago

6 0

The answer is 6.3

3 / 5 = x / 10.5
x = 6.3

makvit [3.9K]3 years ago

4 0

Since the drawings are similar, the lengths of the 2 sides are proportional.

Since the largest size is 10.5 for the new drawing, it corresponds to the large side of the former drawing, which is 5.

Similary, the corresponding side of 3 (in the former drawing) in the larger drawing is what we are seeking to find, let's call this x.

So the ratio of 10.5 is to 5 should be equal to the ratio of x is to 3. Setting up the ratio, we have:

$\frac{10.5}{5}= \frac{x}{3}$

Now cross multiply and solve for x, we get:

$\frac{10.5}{5}= \frac{x}{3} \\3*10.5=5x\\31.5=5x\\\frac{31.5}{5} =x\\6.3=x$ .

So the length of the side we are looking for in the former drawing is 6.3 inches.

ANSWER: 6.3 in

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Answer:

Part A) see the explanation

Part B) see the explanation

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Step-by-step explanation:

The complete question in the attached figure

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<u><em>Remember that the price in the table is in thousands</em></u>

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The slope of the Function 2 is two times the slope of the Function 1

Part B) Find and compare the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

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$y=40x+15,000$

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Convert to slope intercept form

isolate the variable y

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A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

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Function 1

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$y=80x$ ----> is a proportional linear equation (the line passes through the origin)

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