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ELEN [110]
3 years ago
15

|2x-5|<1 i need help pleaseeeeee

Mathematics
1 answer:
Fofino [41]3 years ago
7 0

Answer:

x < 3 or x < 2

Step-by-step explanation:

|2x-5|<1

Using compound Inequality

(2x - 5) <± 1

Hence,

a) 2x - 5 < -1

2x < -1 + 5

2x < 4

x < 4/2

x < 2

b) 2x - 5 < +1

2x < 1 + 5

2x < 6

x < 6/2

x < 3

Therefore, x < 3 or x < 2

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Find the length of side x in simplest radical form with a rational denominator.
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3 years ago
Question:
aivan3 [116]

Answer:

part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

so

Let

z ----> the scale factor

\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}

The scale factor is equal to

z=\frac{CB}{C'B'}

substitute

z=\frac{4}{8}

simplify

z=\frac{1}{2}

Part B) What is the ratio of the areas (small to large)?

<em>Area of the small triangle</em>

A=\frac{1}{2}(2)(4)=4\ units^2

<em>Area of the large triangle</em>

A=\frac{1}{2}(4)(8)=16\ units^2

ratio of the areas (small to large)

ratio=\frac{4}{16}=\frac{1}{4}

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

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We know how wide the billboard will be. Therefore, to know how much the original image should be enlarged, you must divide the final width of the billboard between the current width of the invoice.

We know both data, then we perform the operation:

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Therefore the correct answer is option D. 1″ = 7.81′

For the bill to cover the billboard, the bill must be expanded by a factor of 7.81 feet long per inch long that has the original image.

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