Answer:
19 letters
Step-by-step explanation:
Suppose Number of Amy's full name letters = X
Number of Stephanie's full name letters = Y
Now, according to given condition that ''number of letters in Stephanie's full name is sixteen less than twice the number of letters in Amy's full name'',
Equation 1 becomes
Y = 2X-16
Now, according to second condition, product of their names' letter is 418. So,
Equation 2 becomes
XY = 418
Deducing value of X from equation 1,
X = (Y+16)/2
Putting this value in equation 2 we get,
{(Y+16)/2}*Y = 418,
By simplifying this equation we get a quadritic equation
(Y^2)+16Y-836=0
By breaking middle term (You can use quadratic formula here as well)
(Y^2)+38Y-22Y-836=0
Y(Y+38)-22(Y+38)=0
(Y-22)(Y+38)=0
At this stage we have two values for Y,
Y=22, or Y=-38
Now considering only positive value since the number of letters in a name can not be in negative number,
Y=22,
So X=(Y+16)/2
X=19
The total area is 448 in^2. Each triangle is 56 in^2 and each parallelogram is 140 in^2
Answer:
The angle measure for angle c is 138 degrees
Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
