Simplify as
y = 4x^2 + 22x + 13
x coordinate of the vertex = -22 / (2*4) = -22/8 = -11/4
y coordinate = 4(-11/4)^2 + 22 (-11/4) + 13 = -69/4
x^2 - 5x + y^2 = 214 complete the square on x
x^2 - 5x + 25/4 + y^2 = 214 + 25/4
(x - 5/2)^2 + y^2 = 881/4
The area = (881/4) pi ≈ 691/94
ab^4 = 48
ab^2 = 4 divide the frist equation by the second
b^2 = 12
b = sqrt 12 = 2sqrt 3
2x + 1y = 3.15 → x = 3.15 - y
1y + 1z = 3.50 → z = 3.50 - y
1x + 2y + 3z = 8.15
1(3.15 -y) + 2y + 3(3.50 - y) = 8.15
3.15 - y + 2y + 10.50 - 3y = 8.15
-2y = 8.15 - 3.15 - 10.50
-2y = - 5.50
y = 5.50 / 2 = 2.75 = 275 cents
https://web2.0calc.com/questions/rectangle_45
Let P be the number of pages
(1/5)P = 1st day
20 = second day
(1/6)( P - (1/5)P -20) = (1/6) ((4/5)P - 20) = (2/15)P - 10/3 = third day
(1/2)P = fourth day
(1/5)P + 20 + (2/15)P -10/3 = (1/2)P multiply through by 60
12P + 1200 + 8P - 200 = 30P
1200 - 200 = 30P -20P
1000 = 10P
P = 1000 / 10 = 100 pages
A45
12/sqrt 2 D 12
B 90 12/sqrt 2 C 45
By AAS, triangle ABD congruent to triangle CBD
[ ABC] = (1/2)(12/sqrt 2)^2 = (1/2)(144/2) = 144/4 = 36
[ABD] = (1/2)[ABC] = 18
xy = x + y → xy - x = y → x ( y - 1) = y → x = y / (y - 1)
xz = x + z
yz = y + z → yz - z = y → z (y - 1) = y → z = y/(y - 1)
x = z
So
z*z = z + z
z^2 = 2z
z^2 - 2z = 0
z ( z - 2) = 0
z = 0 reject
z = 2
\(f(x) = \sqrt{x - \sqrt{x}}. \)
No such three-digit integer exists
https://web2.0calc.com/questions/right-triangles_33
