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The formula for a circle is (x – h)^2 + (y – k)^2 = r^2.

Now we just make the formula into our problem: (x-7)^2+(y-8)^2=10^2

Then we substitute (13,16) into the formula. If the solution is right, then (13,16) is on circle O. If not, then it's not.

(13-7)^2+(16-8)^2=100

6^2+8^2=100

36+64=100

100=100

This equation is true, so the answer is yes.

Mathisfornerds, please, instead of making so many topics, put all of your questions in a numbered list for one topic.

Your question is similar to your other questions, just change the equation into slope-intercept form and do the samething and do the samething I did for your other question.

4y + 1x  + 40  =  0     rearrange as

4y  =  -1x - 40          divide both sides by 4

y  = (-1/4)x - 10

The slope of this line is  -1/4   ....a perpendicular line will have a negative reciprocal slope = 4

So...using the point-slope form, we have

y  = 4 ( x - 1/2)  + 0       simplify

y = 4x  -  2

Here's the graph of both lines :  https://www.desmos.com/calculator/xzeqsobhzr

The line parallel to another line has the same slope.

Therefore, our line would be \(y=\frac{1}{4}+b\), b being the y-intercept.

We also know that the line passes through point (-8,-7). We can substitute the points into the line equation to solve b.

We get \(-7=\frac{1}{4}\times-8+b\Rightarrow-7=-2+b\Rightarrow b=-5\)

The line is \(y=\frac{1}{4}x-5\)

Check it by using desmos.com

y =  2x + 3y  =  24   ???

Is there a typo here  ??

Agree with Hectictar !     Diameter is given in this question ....radius was in the last question !        Good catch Hec !

Wait a minute!! The diameter is  29  inches, not the radius.

250 * 29π  inches / 1 minute

=   7250π  inches / 1 minute

=   7250π inches / (1/60 hours)

=   (7250π / 63360 miles) / (1/60 hours)

=   7250π / 1056 miles per hour

≈   21.569  miles per hour

[ 6n^2 + 5 ]  / [3n^2]

We have  a   Same Degree / Same Degree situation

The limit  as n approaches infinity in  Same / Same   is simply the ratio of the coefficients on the highest powers of n in the numerator / denominator...so...the limit  is  6 / 3  =  2

Correct  !!!

f(0)  = f(1) = f(2) = f(3)   = 1

And f(4)  = 0

In the form

ax^4 + bx^3 + cx^2 + dx + e        

If f(0)  = 1, then  e  = 1

And we have this system

a + b + c + d  =  0

16a + 8b + 4c + 2d  = 0

81a + 27b  + 9c + 3d  =  0

256a + 64b + 16c + 4d  = -1 

The solution to this system is

a = -1/24     b  =  1/4      c  =  -11/24   d = 1/4

So...the polynomial  is

(-1/24)x^4  + (1/4)x^3 - (11/24)x^2 +  (1/4)x  + 1

And   f(5)  =  - 4

You are asked to do the same thing in this question, but the Table you are given is for interest only.

The way they have calculated it, per $100, is as follows: $100 x 11% x 18 months/12 months=$100 x 0.11 x 1.5 years =$16.50 as you can see from the Table under 11% and across 18 months.

Then, they want you to calculate it for $3,400. So, what you are supposed to do is the following:

$3,400/$100 x $16.50/18 =$31.17 - This is the monthly interest on $3,400, which is calculated INCORRECTLY!!!.

Then, they want you to take $3,400 / 18 months =$188.89 of principal per month. Then you add this to the monthly interest of $31.17. So, $188.89+$31.17 =$220.06 - which is one of the "answers" given to you, which is INCORRECT. If you accept this payment, then the interest rate would have to be 19.92% compounded monthly.

The correct monthly payment can be calculated using the following formula:

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}

PMT=$3,400 x 0.11/12{[1 + 0.11/12]^18 / [1 + 0.11/12]^18 - 1}

PMT=$31.16667 x {[1.0091667]^18 / [1.0091667]^18 - 1}

PMT=$31.16667 x {[1.1785069491] / [0.1785069491]}

PMT=$31.16667 x           6.60202280493......

PMT=$205.76 - This is the accurate monthly payment for the $3,400 Loan @ 11% compounded monthly over a period of 18 months.

Got the same answer again. Thanks!

Great!  If we BOTH got the same answer, it is likely I got the right answer too!     Thanx    !

250 rot/min x pi x 2r = distance / min

250 x pi x 2 x 29 = 45553.093  in/min

in/min x  60 min/hr  x  1 ft/ 12 in x 1mi/5280ft = 43.137 m/hr

Okay. I got the right answer. Thanks!

60 m/hr  x  5280 feet/m  x  12 in/ft  x  1 hr/60min =  63360 in/min

Circumference = pi x 2r = pi x 30 = 94.2477 inches/circumf

63360 in /min  x  1 circumf/94.2477 inches = 672.27 circumf/min = rpm

Hi 👋 RedGlasses

Why is the math is like this? And it is so so so hard  

What you are asked to do is to take the payment from the Table, which in this case is $2.199 per month over a period of 5 years, or 5 years x 12 months =60 months.

Then the monthly payment for $4,300 would be: $4,300/100 x $2.199 =$94.56 - which is accurate in this case.

Each dish will hold

[ 2. 5 lbs ] /  3  =   25/30 lbs.   =   (5/6)lb

And one bowl will serve 10 people....so....each person will have a serving size  of

( 5 /6)  / 10   lbs    =   5/60 lbs   =  1/12  lbs  

6. The period is  pi / 2

7.  The graph is vertically stretched by a factor of 2  and shifted up 3 units

5.   

We can solve for the period, p,  as follows

(1/4) p  = 2pi      multiply both sides by 4

p   =  8 pi

The frequency  =  1 / period  =    1  / [ 8 pi ]  

4.      f(x)  =  (1/2)cos ( x)  +  5

The "1/2 "  does not affect the midline..it only halves the normal amplitude

The "5" shifts  the normal cosine graph up 5 uints

So....the midline  is   y = 5

Here's the graph : https://www.desmos.com/calculator/lkmkkpvrzq

3.

Reflected over the x axis gives us  y  = -cos (x)

Shifted down 2 units gives  y  =  -cos(x) - 2 = g(x)

1.  Minimum value  is   2.5

2.  Period  =  6pi      Amplitude = 5      Midline :  y  = -2 

Since we have a y intercept of  (0, -2)  the sine function seems he best choice...here's the function :

y  =  5sin (x /3 )  - 2

Here's the graph : https://www.desmos.com/calculator/shtgla34yy