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3 years ago

Solve for all values of x in simplest form. 5-3|2x-7|=-31

Mathematics

1 answer:

Artyom0805 [142]3 years ago

5 0

Answer:

x = 9 1/2 x = -2 1/2

Step-by-step explanation:

5-3|2x-7|=-31

Subtract 5 from each side

5-5-3|2x-7|=-31-5

-3|2x-7|=-36

divide by -3

-3/-3|2x-7|=-36/-3

|2x-7|=12

There is a positive and negative solution to the absolute value equation

2x-7 =12 2x -7 = -12

Add 7 to each side

2x-7+7 =12+7 2x-7+7 = -12+7

2x = 19 2x = -5

Divide by 2

2x/2 = 19/2 2x/2 = -5/2

x = 9 1/2 x = -2 1/2

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The area of two similar triangles are 50dm^2 and 32dm^2. The sum of their perimeters is 117dm. What us the perimeters of each of

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Answer:

Perimeter of one triangle is 65 dm

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Step-by-step explanation:

Please remember the concept

If sides are in the ratio of a:b

Then the area in the ratio of $a^{2} :b^{2}$

It is given sum of their perimeter is 117.

Let the small triangle has perimeter as x.

So, perimeter of big triangle is 117-x.

So, we can set up equation as

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Cross multiply

50(117-x)^2 =32x^2

Expand the left side

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Distribute the left side

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Subtract both sides $32x^{2}$ and rewrite it $18x^{2} -11700x+684450=0$

Solve this quadratic for x.

Divide both sides of the equation by 18 to simplify.

$x^{2}$ -650 x+38025=0

Now, if possible let's factor

Find two integers whose multiplication is 38025 but adds to -650.

-65 and -585 works.

So, we can rewrite it as

(x -65)(x-585) =0

Solve them using zero product property

x=65, x=585

So, x=65 works here.

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Answer:

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Step-by-step explanation:

The question is not complete. The complete question should be in the form:

Victor has 2 fraction models. Each is divided into equal sized sections the models are shaded to represent the same fraction. Model A is divided into 6 sections and 3 sections are shaded. Model B is divided into 12 sections. What do you know about the number of sections shaded in Model B? Explain your answer.

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