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Dennis_Churaev [7]
3 years ago
11

Apply the communitive property to 13x7x21 to rearrange the terms and still get the same solution

Mathematics
1 answer:
Snezhnost [94]3 years ago
5 0
The commutative porperty states that numbers can be swapped over , they can change their place in the equation and the result will still be the same.
In our case 13 x 7 x 21, the commutative property means that the numbers can be rearranged
13x7x21=13x21x7=7x21x13=7x13x21
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Dada la ecuacion 25x2 + 4y2 = 100, determina las coordenadas de los vertices, focos, las longitudes de los respectivos ejes mayo
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The given equation is

25x^{2} +4y^{2}=100

Which represents an elipse.

To find its elements, we need to divide the equation by 100

\frac{25x^{2} +4y^{2} }{100} =\frac{100}{100} \\\frac{x^{2} }{4} +\frac{y^{2} }{25} =1

Where a^{2} =25 and b^{2}=4. Remember that the greatest denominator is a, and the least is b. So, we extract the square root on each equation.

a=5 and b=2.

In a elipse, we have a major axis and a minor axis. In this case, the major axis is vertical and the minor axis is horizontal, that means this is a vertical elipse.

The length of the major axis is 2a=2(5)=10.

The length of the minor axis is 2b=2(2)=4.

The vertices are (0,5);(0,-5) and (2,0);(-2,0).

Now, the main parameters of an elipse are related by

a^{2}=b^{2} +c^{2}, which we are gonna use to find c, the parameter of the focus.

c=\sqrt{a^{2}-b^{2} }=\sqrt{25-4}=\sqrt{21}

So, the coordinates of each focus are (0,\sqrt{21}) and (0,-\sqrt{21})

The eccentricity of a elipse is defined

e=\frac{c}{a}=\frac{\sqrt{21} }{5}  \approx 0.92

The latus rectum is defined

L=\frac{2b^{2} }{a}=\frac{2(4)}{5} =\frac{8}{5} \approx 1.6

Finally, the graph of the elipse is attached.

7 0
3 years ago
Factor completely 4u^2-28u+49
aleksandrvk [35]

Assignment: \bold{Factor \ 4u^2-28u+49}

<><><><><>

Answer: \boxed{\bold{\left(2u-7\right)^2}}

<><><><><>

Explanation: \downarrow\downarrow\downarrow

<><><><><>

[ Step One ] Rewrite \bold{4u^2-28u+49}

\bold{\left(2u\right)^2-2\cdot \:2u\cdot \:7+7^2}

[ Step Two ] Apply perfect square formula

Note: Perfect Square Formula: \bold{\left(a-b\right)^2=a^2-2ab+b^2}

\bold{a=2u,\:b=7}

\bold{\left(2u-7\right)^2}

<><><><><><><>

\bold{\rightarrow Rhythm \ Bot \leftarrow}

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