If chords are ll then alternate interior angels equal each other
ABC equal BCD.
angle BAC =90 degree
angle BDC =90 degree because both lie on diameter.
triangle BAC congruent to BDC because the same side BC and two angles.
so AC=BD from congruence of triangles

AO=BO=CO definition of circumcircle which is enter of the circle that passes through all three vertices of the triangle.
triangle ABO congruent to triangle AOC
because of side and two angles ASA
angle ABO=BAO=CAO=OCA
so AB=AC from congruence of triangles

35-8=27
44-12=32
27x32 =864 cm^2

Let x to be the speed of the plane in still air.
x+30 will be speed with wind
x-30 - speed against the wind.
since the time will be the same in both directions we can make the equation.
the basic formula for rate and time is t=distance/speed
200/x-30 = 300/x+30
solve...

x+y=48
x-y =2
solve the system by adding two equations
2x=50
x =25
y=23

Can be some animal who made the hole in the bag or eat flour.

X^2-4=(x+2)(x-2), so x+2 is the factor.

3y=2x-21 divide the both parts by 3
y= 2/3x -7 where 2/3 is the slope

(k^4-9k^2)+(2k^3-18k)-(15k-135)=
k^2(k^2-9)+2k(k^2-9)-15(k^2-9)=
(k^2-9)(k^2+2k-15)=
(k+3)(k-3)(k+5)(k-3)

Let time = x
identify velocity for both ants.
first ant has the velocity 139.61/23 =6.07 cm/min
the second ant has velocity 88/1.6 =55cm/min
they both traveled the same time
the equation will look: 6.07x +55x =150.41
solve for x

Patrick has 10
Lee has 10*9 =90
Andrew has .09*90 =81
200-(10+90+81)=19 seeds need to be collected

Let x to be his hiking rate and x+10 is his riding rate
12/10+x + 8/x = 5
solve for x
12x+8(10+x)/x(10+x)=5
12x+80+8x=5x(10+x)
5x^2+30x-80=0
x^2+6x-16=0
x=2 miles per hour hiking rate, 12m/hr is his riding rate

Let x be one piece of pipe, 2x is second piece
x+2x = 156
3x=156
x=52 , second 104in

It is parabola looking down and has the maximum, find the vertex of equation.(p,R)
vertex = -b/2a just substitute fro your equation
-1900/2(-1/2) = 1900 it is your x for vertex
put it in your equation and calculate:
R= -1/2(1900)^2 +1900x1900 = -1805000 + 3610000= 1805000
price...

No slope for the vertical line. The equation of the line is X=2

X is the amount of soybean meal
Y is the amount of corn bean meal
X+Y = 280
0.14X + 0.07Y = 0.13x280
solve the system by multiplying the first equation by 0.14
0.14X+.14Y =39.2
substruct the second from the first
.07Y =2.8
Y =40 lb
X =...

Let x to be the first number
y is the second
x+2y=1
2x+y =14
solve the system by multiplying the first by 2
2x +4y=2
2x+y =14
substract second fro the first
3y = -12
y = -4
x =9

Let x be the speed of the boat in still water.
x+4 is down stream speed
x-4 is upstream speed
36/x+4 = 12/x-4
36(x-4) =12(x+4)
solve for x
24x = 192
x =8miles per hour

X is the amount to be mixed
0.1x + 100% (16-x) = 16x 0.14
0.1x + (16-x) = 6.4

11 feet because square has the equal sides, you need to square root from 121.