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andrey2020 [161]
2 years ago
13

What type of triangle has side lengths 9, 10, and √130? A. obtuse B. not a triangle C. acute D. right

Mathematics
1 answer:
EastWind [94]2 years ago
3 0

Answer: Option C.

Step-by-step explanation:

The lengths of our triangle are:

9, 10 and √130.

If the triangle is a triangle rectangle, by the Pitagoream's theorem we have:

A^2 + B^2 = H^2

in this case H is the larger side, this must be √130.

then:

A and B must be 9 and 10.

9^2 + 10^2 = (√130)^2

81 + 100 = 130

This is false, so this is NOT a triangle rectangle, the hypotenuse is shorter than it should be.

Now, we have some kind of rule:

 if A^2 + B^2 = H^2 then we have one angle of 90° and two smaller ones. (triangle rectangle)

 if A^2 + B^2 > H^2 then all the angles are smaller than 90°, this is an acute triangle.

 if A^2 + B^2 < H^2 then we have one angle larger than 90°, this is an obtuse angle.

(H is always the larger side, A and B are the two shorter ones).

In this case:

81 + 100 > 130

Then this must be an acute angle.

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The area of a rectangle is given by the multiplication of its dimensions:

\text{Area} = \text{width} \times \text{length}

In this case, we have an exact value for the area, and two variable expressions for width and length. Let's replace the formula above with what we're given:

285 = (2x-3)(x+4)

If you expand the right hand side, you have

285 =  2 x^2+ 5 x-12

And if you move all terms to the right hand side, this becomes

0 =  2 x^2+ 5 x-297

This is a quadratic equation, since it is in the form ax^2+bx+c=0, where a = 2,\ b=5 \text{ and } c = -297

If you plug these values in the generic formula

x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

you get

x = \dfrac{-27}{2} \text{  or  } x = 11

Let's see which dimensions they yield:

x = \dfrac{-27}{2} \implies 2x-3 = -30,\quad x+4 = \dfrac{-19}{2}

But the dimensions of a rectangle can't be negative, so we can't accept this answer.

The other solution yields

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3 years ago
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Answer:

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Step-by-step explanation:

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If you have 8 cups of berries and it takes 2/3 cup to make a dessert how many desserts can you make?
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To divide by a fraction, multiply the forst number by the reciprocal of the second.
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Step-by-step explanation:

Since we cannot divide by 0, the value of x which results in a denominator that is 0 is a value excluded from the domain;

This value can be found by setting the denominator equal to 0;

In this case, it is very simple as the denominator expression is simply "x", so the exluded value is: x = 0.

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3 years ago
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