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Arte-miy333 [17]
3 years ago
14

Find the length of the third side to the nearest tenth.

Mathematics
1 answer:
Grace [21]3 years ago
6 0

Answer:

Hypotenuse=2 units

Step-by-step explanation:

The given triangle is a right angled triangle:

The length of the third side of a right angled triangle can be find by using the Pythagorean Theorem:

Where,    

          Hypotenuse^2=Perpendicular^2+Base^2

Perpendicular= 2 units

Base=2 units

Hypotenuse^2=2^2+2^2\\\\Hypotenuse^2=4+4\\\\Hypotenuse^2=4\\\\Hypotenuse=\sqrt{4} \\\\Hypotenuse=2

The hypotenuse of the triangle is also equals '2'

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2 years ago
What are the roots of the polynomial equation x^3-5x+5=2x^2-5? Use a graphing calculator and a system of equations. Round nonint
leonid [27]

The right answer is c. –2.24, 2, 2.24


This question needs to be solved in two ways. First, using a graphing calculator. Next, using a system of equations.


1. Using a graphing calculator.


We have the following polynomial equation:

x^3-5x+5=2x^2-5


By ordering this equation we have:

x^3-2x^2-5x+10=0


So, we can say that this equation comes from a function given by:

f(x)=x^3-2x^2-5x+10


Thus, by plotting this function, we have that the graph of this function is indicated in Figure 1. By zooming, we can see, in Figure 2, that the roots of the polynomial equation are the x-intercepts of f(x) which are:


x_{1}=-2.236 \\ \\ x_{2}=2 \\ \\ x_{3}=2.236


Finally, rounding noninteger roots to the nearest hundredth we have:


\boxed{Root_{1}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=2.24}


2. Using a system of equations.


The ordered equation is:

x^3-2x^2-5x+10=0


By arranging to factor out we have:

x^3-5x-2x^2+10=0


Then, by factoring:

x(x^2-5)-2(x^2-5)=0


Term (x^2-5) is a common factor, thus:


(x-2)(x^2-5)=0 \\ \\ (x-2)(x-\sqrt{5})(x+\sqrt{5})=0 \\ \\ Finally: \\ \\ \boxed{Root_{1}=-\sqrt{5}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=\sqrt{5}=2.24}

6 0
3 years ago
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Does the distance Ella runs vary directly with the time. (How do you know?
Kazeer [188]

No because she can run slow and waste time and not get that far and it will be 3 min. But if you go fast and stop at the same distance it won’t take as long because of your SPEED.

4 0
3 years ago
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Are 5.5 + 2.1x + 3.8x - 4.1 and 1.4 5.9x equivalent
Marat540 [252]

5.5 + 2.1x + 3.8x - 4.1

5.5-4.1 +x(2.1+3.8)

1.4 +x(5.9)

5.9x+1.4

these are equivalent if there is a plus sign between  1.4 5.9x


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Factor completely x2 + 25
Ganezh [65]

Answer:

(x - 5i)(x + 5i)

Step-by-step explanation:

Write this as x^2 + 25.  Solving for x^2, we get x^2 = -25.

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In factored form, the given expression is (x - 5i)(x + 5i).

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