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2 years ago

Ms. Nailor's daughter received $25

Mathematics

1 answer:

IrinaK [193]2 years ago

7 0

The correct answer is $35

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Write the standard form of the equation of the circle with the given characteristics. Center: (3, 5); Solution point: (−2, 17)

Angelina_Jolie [31]

$\text{we know that the general equation of the circle is }\\
\\
(x-h)^2+(y-k)^2=r^2\\
\\
\text{where, (h,k) is the center of the circle and r is the radius.}\\
\\
\text{Given that the centered of the circle is at }(h,k)=(3,5)\\
\text{and a solution point on circle is (-2,17).}\\
\\
\text{so the radius of the circle will be the distance between center and the }$

$\text{solution point. so using the distance formula, we have}\\
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\text{Radius, }r=\sqrt{(-2-3)^2+(17-5)^2}\\
\\
\Rightarrow r=\sqrt{25+144}\\
\\
\Rightarrow r=\sqrt{169}\\
\\
\Rightarrow r=13\\
\\
\text{Hence using the standard for of circle, equation of circle with center}\\
(h,k)=(3,5) \text{ and radius r=13 is}\\
\\
(x-3)^2+(y-5)^2=(13)^2\\
\\
\Rightarrow (x-3)^2+(y-5)^2=169$

3 0

2 years ago

Caleb bought groceries and paid

lutik1710 [3]

Answer:

Price of Caleb's groceries before tax= $6.4

Step-by-step explanation:

Let price of groceries before tax be = $ $x$

Sales tax % = 2.5%

Sales tax applied = $2.5\% \ of\ x = \frac{25}{100}\times x = \frac{25}{100} x$

Actual sales tax paid = $1.60

∴ $\frac{25}{100}x=1.60$

Multiplying both sides by 100.

$100\times \frac{25}{100}x=1.60\times 100$

$25x=160$

Dividing both sides by 25.

$\frac{25x}{25}=\frac{160}{25}$

$x=6.4$

∴ Price of groceries before tax= $6.4

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Since there are 6 possible results when rolling a die, each number has a 1 in 6 chance that it will be rolled.
1 and 2 are two possible results, so there is a 2 in 6 chance they will be rolled. As a fraction:
2/6
simplified:
1/3

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