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3 years ago

20+x=25 so I'm doing addition property of equality so what does this mean

1 answer:

3 0

The addition property of equality is the idea we can add some number to both sides of an equation. You must add the same number to both sides to keep things balanced.

It's asking "what number can we add to both sides of this equation so that we isolate x?"

Think of 20+x as x+20. We can rearrange terms since adding in any order doesn't matter (eg: 2+3 = 3+2 = 5)

So we really have this equation: x+20 = 25

We can add -20 to both sides to cancel out the +20 on the left side

x+20 = 25

x+20+(-20) = 25+(-20) ...... add -20 to both sides

x = 5

This is the exact same as subtracting 20 from both sides. So 5 will go where x is, meaning that 20+x = 20+5 = 25

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The equation of a circle is x2 + y2 + Cx + Dy + E = 0. If the radius of the circle is decreased without changing the coordinates

tatyana61 [14]

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There will be no change in C and D but E must increase.

Step-by-step explanation:

We are given a equation of circle as:

$x^2+y^2+Cx+Dy+E = 0$

it could also be represented in general form of equation of circle as:

$(x+\dfrac{C}{2})^2+(y+\dfrac{D}{2})^2=\dfrac{C^2}{4}+\dfrac{D^2}{4}-E$

( since we add both the side of the equality by $\dfrac{C^2}{4}$ and $\dfrac{D^2}{4}$ )

Hence, on comparing the equation with general form of the equation:

$(x-g)^2+(y-h)^2=r^2$

The center of circle is (g,h) and radius is r.

Here we have the center as:

$(\dfrac{-C}{2},\dfrac{-D}{2})$

and radius is given aS:

$r=\sqrt{\dfrac{C^2}{4}+\dfrac{D^2}{4}-E}\\\\r=\sqrt{\dfrac{C^2+D^2-4E}{4}$

$r=\dfrac{\sqrt{C^2+D^2-4E}}{2}$

As there is no change in the center hence the value of $\dfrac{-C}{2}$ and $\dfrac{-D}{2}$ remains unchanged i.e. the value of C and D remains unchanged.

Now we are given that the radius of the circle is decreased.

that means the change in radius is due to the change in E.

Hence for the quantity $r=\dfrac{\sqrt{C^2+D^2-4E}}{2}\\$ to decrease E must increase so that the total quantity decreases.

Hence there will be no change in C and D but E must increase in order to decrease the radius of circle.

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