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4 years ago

Last summer, Betty earned $4200 by painting houses. She invested

Mathematics

1 answer:

Musya8 [376]4 years ago

3 0

x*(1.035) + (4,200-x)*(1.045) = 4,374.00

1.035x + 4,389.00 -1.045x = 4,374.00

15.00 = .01x

x = 1,500 so x (1,500) invested at 3.5% and

(4,200 - 1,500) (or 2,700) invested at 4.5%

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Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

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$$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

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Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Here, $x_1=-6, y_1=-10, x_2=-8, y_2=-6$

$r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}$

$r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}$

$r=\sqrt{(-2)^{2}+(4)^{2}}$

$r=\sqrt{20}$ units

The standard form of the equation of a circle is

$(x-a)^{2}+(y-b)^{2}=r^{2}$ , where (a, b) are center and r is the radius.

Here, center = (–6, –10) and $r=\sqrt{20}$

$(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}$

$(x+6)^{2}+(y+10)^{2}=20$

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