Answer:
(2, -3) and r = 3.
Step-by-step explanation:
you can also plug this equation in desmos but I guess it's good to know how to do it also:
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2
Now in order to make a perfect square on both sides, we need to do this:
First add 9 to both sides:
x^2 + 6x + 9 + y^2 -4y +4 = 9.
I purposely shifted it to show the perfect square created when you add 9 to both sides. Factor:
(x+3)^2 + y^2 - 4y + 4 = 9.
now the second bolded part is allso a perfect square. Factor:
(x+3)^2 + (y-2)^2 = 9
Based on the equation of a circle, the center must be at (2, -3) and the radius is the square root of 9 which is 3.
:)
Answer:
w=-7/3 and w=-9/5
Step-by-step explanation:
Given: 15w^2+62w+63=0
Factor: (3w+7)(5w+9)=0
Zero Product Property: 3w+7=0 and 5w+9=0
Solve each equation: w=-7/3 and w=-9/5
Let me know if you would like me to explain more.
Answer:
Step-by-step explanation:
Your exponential formula is in the form y = ab^x. In this form, the coefficient 'a' is the initial value, the y-intercept, the value when x=0. The value 'b' is the growth factor, which is 1 more than the growth rate per increment of x. This problem is asking for the growth rate to be expressed as a percentage.
__
Given p(x) = 78500(1.02^x), we can compare to the exponential function form to see that ...
- a = 78,500
- b = 1.02 = 1 +0.02 = 1 +2%
The value of x is zero in the year 2000, so the population that year is ...
p(0) = a = 78,500
The increase per year is the value of 'b' with 1 subtracted:
growth rate = 2% per year
Answer:
Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°
Step-by-step explanation:
To find the measure of Angle a, we add 55 and 45, then subtract the sum from 180.
180 - 100 = 80
Angle a is 80°.
Then, we solve for Angle b. Line segment CD is congruent to Line AB, so Angle b is congruent to 55°.
After that, we find Angle c. Line segment AC is congruent to Line segment BD, so Angle c is congruent to 45°.
Lastly, we solve for Angle d using the same method we used for Angle b and Angle c. Angle d is congruent to Angle a, so it measures 80°.
So, Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°.
