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3 years ago

Find the radius of the circle. 6(x – 3)2 + 6(y + 7)2 = 216

Mathematics

1 answer:

Fantom [35]3 years ago

7 0

Answer:

radius=6

Step-by-step explanation:

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A candy company makes boxes of chocolates. Each box has 32 chocolates total. Of those 32 chocolates 14 of them have nuts. If the

Agata [3.3K]

Answer: 266

Step-by-step explanation: This is a ratio problem. If there are 14 chocolates with nuts out of every 32 chocolates, you can use this as a ratio and set it up as a proportion.

(1) 14 chocolates w/ nuts / 32 chocolates = n chocolates / 608 chocolates

(2) Solve for n: 8,512 = 32n; n = 266

7 0

3 years ago

Which expression is equivalent to r to the 9th over r to the 3rd

alisha [4.7K]

Answer:

$r^{6}$

Step-by-step explanation:

To make this a bit easier to see, we'll expand that expression.

R to the 9th is just r times itself 9 times. R to the third is r times itself 3 times.

(excuse my bad formatting)

The expression:

r • r • r • r • r • r • r • r • r • 1

r • r • r • 1

Remember, anything and everything has a coefficient or denominator of 1.

So, we can cancel 3 r's from the numerator and denominator.

r • r • r • r • r • r • 1

Simplify....

$\frac{1r^{6}}{1}$

That just equals $r^{6}$ .

3 0

2 years ago

Eleanor and her little sister Joanna are responsible for two chores on their family’s farm, gathering eggs and collecting milk.

iris [78.8K]

Answer:

4 dozens

Step-by-step explanation:

Find Eleanor and Joanna's ratio of eggs to milk

Eleanor:

Dozen eggs : gallons of milk

9 : 3

3 : 1

Joanna:

Dozen eggs : gallons of milk

2 : 2

1 : 1

They gather one gallon of milk each which means Joanna has 1 dozen eggs and Eleanor has 3 dozens of eggs.

Total dozen of eggs = 3 + 1 = 4

Therefore, total dozen of eggs the family have per week is 4 dozens.

4 0

3 years ago

NEED THE ANSWER PLEASE...

sesenic [268]

Answer:

The correct answer option is D. $\frac { 3 n ^ { 3 } } { 5 m ^ { 2 } }$ .

Step-by-step explanation:

We are given the following expression and we are to simplify it:

$\frac { 3 m ^ { - 2 } } { 5 n ^ { - 3 } }$

Here the variables $m$ and $n$ are having negative powers. So to change these powers from negative to positive, we will take their reciprocals to get:

$\frac { 3 n ^ { 3 } } { 5 m ^ { 2 } }$

7 0

3 years ago

Read 2 more answers

4sin²<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D" id="TexFormula1" title="\frac{x}{2}" alt="\frac{x}{2}" align="absm

raketka [301]

Answer:

$\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}$

Step-by-step explanation:

Hi there!

We want to solve for $x$ in:

$4\sin^2(\frac{x}{2})=3$

Since $x$ is in the argument of $\sin^2$ , let's first isolate $\sin^2$ by dividing both sides by 4:

$\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}$

Next, recall that $\sin^2x$ is just shorthand notation for $(\sin x)^2$ . Therefore, take the square root of both sides:

$\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}$

Simplify using $\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ :

$\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}$

Let $\phi = \frac{x}{2}$ .

<h3>Case 1 (positive root):</h3>

$\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}$

Therefore, we have:

$\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

<h3>Case 2 (negative root):</h3>

$\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

8 0

2 years ago

Find the radius of the circle. 6(x – 3)2 + 6(y + 7)2 = 216​

Find the radius of the circle. 6(x – 3)2 + 6(y + 7)2 = 216