Answer:
(x+5)^2+(y-12)^2=256
Step-by-step explanation:
Comparing the given (x+5)^2+(y-12)^2=256
to (x - h)^2 + (y - k)^2 = r^2,
we see that h must be -5, k must be 12 and r must be 16. This is the desired equation of the circle with center at (-5, 12) and radius 16.
Answer:
30 degrees.
Step-by-step explanation:
Rotational symmetry is defined as a figure having the same appearance when rotated by a certain angle.
The wheel has 12 "handles." We can use these as reference points when rotating the image.
We also know that we can rotate by a total of 360 degrees. We can say that:
360/12 = 30 degrees.
Each time you rotate the wheel by 30 degrees, the image will end up on another handle (looks the same). This shows rotational symmetry.
I hope this helps!
10P8 = 10!/(10 - 8)! = 10!/2! = 1,814,400
The length of the envelope is 6.3 inches
Step-by-step explanation:
Width of the envelope = 3 inches
Diagonal of the envelope = 7 inches
To find:
The length of the envelope.
Let the length of the envelope be 'l'
We can use pythogoras theorem to calculate the length.
l = √(49-9)
l = √(40)
l = 6.3 inches
The length of the envelope is 6.3 inches
I am setting the week hourly rate to x, and the weekend to y. Here is how the equation is set up:
13x + 14y = $250.90
15x + 8y = $204.70
This is a system of equations, and we can solve it by multiplying the top equation by 4, and the bottom equation by -7. Now it equals:
52x + 56y = $1003.60
-105x - 56y = -$1432.90
Now we add these two equations together to get:
-53x = -$429.30 --> 53x = $429.30 --> (divide both sides by 53) x = 8.10. This is how much she makes per hour on a week day.
Now we can plug in our answer for x to find y. I am going to use the first equation, but you could use either.
$105.30 + 14y = $250.90. Subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40
Now we know that she makes $8.10 per hour on the week days, and $10.40 per hour on the weekends. Subtracting 8.1 from 10.4, we figure out that she makes $2.30 more per hour on the weekends than week days.
