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valentinak56 [21]
3 years ago
12

A rectangle has a length of 9 inches and a width of 12 inches. This rectangle is dilated by a scale factor of 3.5 to create a ne

w rectangle. Which figure represents the new rectangle.

Mathematics
2 answers:
Nat2105 [25]3 years ago
8 0
Divide both length and width by the dialtion factor and that will be the dimensions of the new rectangle. 2.5714in by 3.4286in. Round as needed
TiliK225 [7]3 years ago
3 0

Answer : The figure of the new rectangle is shown below.

Step-by-step explanation :

As we are given that:

Length of rectangle = 9 inches

Width of rectangle = 12 inches

When the rectangle is dilated by a scale factor of 3.5 then it create a new rectangle.

Now we have to determine the figure of the new rectangle.

Formula of scale factor is:

\text{Scale factor}=\frac{\text{Larger length}}{\text{Smaller length}}

Given:

Scale factor = 3.5

The length of new rectangle will be:

\text{Scale factor}=\frac{\text{Larger length}}{\text{Smaller length}}

3.5=\frac{\text{Larger length}}{9}

\text{Larger length}=3.5\times 9

\text{Larger length}=31.5 inches

and,

The width of new rectangle will be:

\text{Scale factor}=\frac{\text{Larger width}}{\text{Smaller width}}

3.5=\frac{\text{Larger width}}{12}

\text{Larger width}=3.5\times 12

\text{Larger width}=42 inches

Thus, the figure of the new rectangle is shown below.

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In order to find it, we should divide 12 by 4:-

3

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Hence,

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<h3>note:-</h3>

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The equation of the transformation of the exponential function <em>y</em> = 2ˣ in the form <em>y</em> = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is <em>y</em> = (-2)·2ˣ + 3

<h3>What is an exponential equation?</h3>

An exponential equation is an equation that has exponents that consists of variables.

The given equation is <em>y</em> = 2ˣ

The equation for the transformation is; <em>y</em> = A·2ˣ + k

The points on the graphs are;

(0, 1), (1, -1) and (2, -5)

Plugging the <em>x </em>and <em>y</em>-values to find the value <em>A</em> and <em>k</em> gives  the following simultaneous equations;

When <em>x</em> = 0, <em>y</em> = 1, therefore;

1 = A·2⁰ + k = A + k

1 = A + k...(1)

When <em>x</em> = 1, <em>y</em> = -1, which gives;

-1 = A·2¹ + k

-1 = 2·A + k...(2)

Subtracting equation (1) from equation (2) gives;

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1 = A + k, therefore;

1 = -2 + k

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k = 3

Which gives;

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Learn more about the solutions to simultaneous equations here:

brainly.com/question/26310043

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