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Pavlova-9 [17]
3 years ago
14

Which of the following were among the common features of the new state constitutions adopted following our Declaration of Indepe

ndence? (Check all that apply)
State ownership of all property

Civil Liberties and Rights

Separation of powers and Checks and Balances

Unlimited government

Limited Government

Popular Sovereignty
History
1 answer:
kolbaska11 [484]3 years ago
3 0
<span>The state constitutions allowed for civil liberties, a separation of powers (so one branch could not become too powerful compared to the others), checks and balances (for the same reason), and limited government.</span>
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Explanation:

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13.what is the equation of a parabola with the given vertex and focus ?
Slav-nsk [51]
13.

Find the parabola with vertex (-2, 5) and focus (2, 6)

<span>(x-h)^2=4p(y-k), (h,k)=(x,y)

</span><span>coordinates of the vertex axis of symmetry: x=-2

</span><span>p=1 (distance above vertex on the axis of symmetry)

4p=4

</span>(x + 2)^2 = 4 (y - 5)

--------------------------------------------------------------------------------

14. W<span>hat is the center and radius of a circle with the given equation?
</span><span>x2</span>+4x+<span>y2</span>−10y−7=<span>0

</span>Move all variables to the left side and all constants to the right side.<span><span>x2</span>+4x+<span>y2</span>−10y=7+<span>0

</span></span>Add <span>77</span> and <span>00</span> to get <span>77</span>.<span><span>x2</span>+4x+<span>y2</span>−10y=<span>7

</span></span>Complete the square<span> for </span><span><span><span>x2</span>+4x</span><span><span>x2</span>+4x</span></span><span>.
</span><span><span>(x+2)</span>2</span>−<span>4
</span>
Substitute <span><span><span><span>(x+2)</span>2</span>−4</span><span><span><span>(x+2)</span>2</span>-4</span></span> for <span><span><span>x2</span>+4x</span><span><span>x2</span>+4x</span></span> in the equation <span><span><span>x2</span>+4x+<span>y2</span>−10y=7</span><span><span>x2</span>+4x+<span>y2</span>-10y=7</span></span>.<span><span><span>
(x+2)</span>2</span>−4+<span>y2</span>−10y=<span>7

</span></span>Move <span><span>−4</span><span>-4</span></span> to the right side of the equation by adding <span>44</span> to both sides.<span><span><span>(x+2)</span>2</span>+<span>y2</span>−10y=7+<span>4

</span></span>Complete the square<span> for </span><span><span><span>y2</span>−10y</span><span><span>y2</span>-10y</span></span><span>.
</span><span><span>(y−5)</span>2</span>−<span>25

</span>Substitute <span><span><span><span>(y−5)</span>2</span>−25</span><span><span><span>(y-5)</span>2</span>-25</span></span> for <span><span><span>y2</span>−10y</span><span><span>y2</span>-10y</span></span> in the equation <span><span><span>x2</span>+4x+<span>y2</span>−10y=7</span><span><span>x2</span>+4x+<span>y2</span>-10y=7</span></span>.<span><span><span>
(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>−25=7+<span>4

</span></span>Move <span><span>−25</span><span>-25</span></span> to the right side of the equation by adding <span>2525</span> to both sides.<span><span><span>(x+2)</span>2</span><span><span>(y−5)</span>2</span>=7+4+<span>25

</span></span>Add <span>77</span> and <span>44</span> to get <span>1111</span>.<span><span><span>(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>=11+<span>25

</span></span>Add <span>1111</span> and <span>2525</span> to get <span>3636</span>.<span><span><span>(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>=<span>36

</span></span>This is the form of a circle. Use this form to determine the center and radius of the circle.<span><span><span>(x−h)</span>2</span>+<span><span>(y−k)</span>2</span>=<span>r<span>2

</span></span></span>Match the values in this circle to those of the standard form. The variable <span>rr</span> represents the radius of the circle, <span>hh</span> represents the x-offset from the origin, and <span>kk</span> represents the y-offset from origin.<span><span>r=6</span><span>r=6</span></span><span><span>h=−2</span><span>h=-2</span></span><span>k=<span>5

</span></span>These values represent the important values for graphing and analyzing a circle.Center: <span>(−2,5)(-2,5)</span>Radius: 6

6 0
3 years ago
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