Write the standard equation for the circle center left parenthesis negative 6 comma 7 right parenthesis, r = 9.A. left parenthesis x minus 6 right parenthesis squared plus left parenthesis y plus 7 right parenthesis squared equals 9
B. left parenthesis x minus 7 right parenthesis squared plus left parenthesis y plus 6 right parenthesis squared equals 81
C. left parenthesis x plus 6 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 81
D. left parenthesis x plus 6 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 9

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

The standard form equation for a circle is

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

where h and k are the coordinates of the center. Our center is given as (-6,7) and the radius is given as 9, so that information fits into our standard form like this:

$(x-(-6))^2+(y-7)^2=9^2$ and simplified, it looks like this:

$(x+6)^2+(y-7)^2=81$

That's choice C

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It will take five builders 62 days to complete a particular project. At this rate, how long would the project take if there were only two builders?(SHOW WORK)

Answers

Answer:

2 builder complete work = 155 days

Step-by-step explanation:

Given:

5 builder complete work = 62 days

So,

1 builder complete work = 62 days × 5

if,

2 builder complete work = [62 days × 5] / 2

2 builder complete work = 155 days

A sphere has a radius of 5cm what is the volume of the sphere

Answers

Answer:

$(500)/(3)\pi$

Step-by-step explanation:

The equation for Volume of a Sphere is:

$V=(4)/(3)\pi r^3$

We can plug in the given radius into the equation:

$V=(4)/(3)\pi5^3=(4)/(3)\pi125=(500)/(3)\pi$

George worked for 6.2 hrs each day for 5 days. He earned 18.50$ per hour. How much did he earn in all?

Answers

573.5

18.50 times 6.2 is how much he will make a day then multiply by 5 to see what he made

How many strings of eight uppercase English letters are there if no letter can be repeated?

Answers

............................3................................

Evaluate the summation of 20 times 0.5 to the n minus 1 power, from n equals 3 to 12.

Answers

Answer:

The sum of the series is 9.99

Step-by-step explanation:

We are given the series $\sum_(n=3)^(12)20(0.5)^(n-1)$ .

So, $a_(n)=20(0.5)^(n-1)$ , where n=3 to 12

Then, we have,

$1.\ a_(3)=20(0.5)^(3-1)\na_(3)=20(0.5)^(2)\na_(3)=5$

$2.\ a_(4)=20(0.5)^(4-1)\na_(4)=20(0.5)^(3)\na_(4)=2.5$

Thus, the common ratio is $r=(2.5)/(5)=0.5$

Since, the sum of first n terms of a series is $S=(a_(1)(1-r^(n)))/(1-r)$ .

As n = 3 to 12, then the number of terms = 10, first term=a₃= 5 and r= 0.5

So, the sum of 10 terms is $S=(5(1-(0.5)^(10)))/(1-0.5)$

i.e. $S=(5(1-0.00098))/(0.5)$

i.e. $S=(5* 0.99902)/(0.5)$

i.e. $S=(4.9951)/(0.5)$

i.e. S = 9.99

Hence, the sum of the series is 9.99

Answer: 9.99

Step-by-step explanation:

I just took the quiz!

Given the general identity tan X =sin X/cos X , which equation relating the acute angles, A and C, of a right ∆ABC is true?A. tan A = sin A/sin C
B. cos A = tan (90-A)/sin (90-C)
C. sin C = cos A/tan C
D. cos A = tan C
E. sin C = cos (90-C)/tan A

Answers

First, note that $m\angle A+m\angle C=90^(\circ).$ Then

$m\angle A=90^(\circ)-m\angle C \text{ and } m\angle C=90^(\circ)-m\angle A.$

Consider all options:

$\tan A=(\sin A)/(\sin C)$

By the definition,

$\tan A=(BC)/(AB),\n \n\sin A=(BC)/(AC),\n \n\sin C=(AB)/(AC).$

Now

$(\sin A)/(\sin C)=((BC)/(AC))/((AB)/(AC))=(BC)/(AB)=\tan A.$

Option A is true.

$\cos A=(\tan (90^(\circ)-A))/(\sin (90^(\circ)-C)).$

By the definition,

$\cos A=(AB)/(AC),\n \n\tan (90^(\circ)-A)=(\sin(90^(\circ)-A))/(\cos(90^(\circ)-A))=(\sin C)/(\cos C)=((AB)/(AC))/((BC)/(AC))=(AB)/(BC),\n \n\sin (90^(\circ)-C)=\sin A=(BC)/(AC).$