With amounts measured in gallons, let
x = amount of 65% antifreeze
y = amount of 90% antifreeze
1 gal of the 65% brand contains 0.65 gal of pure antifreeze; x gal would contain 0.65x gal. Similarly, y gal of the 90% brand contains 0.90y gal of pure antifreeze.
To obtain 120 gal of 80% antifreeze solution (which contains 0.80•120 = 96 gal of pure antifreeze), we must have
x + y = 120 … … … … … [total volume of antifreeze solution]
0.65x + 0.90y = 96 … [total volume of pure antifreeze]
Solve the first equation for y :
y = 120 - x
Substitute this into the second equation and solve for x :
0.65x + 0.90 (120 - x) = 96
0.65x + 108 - 0.90x = 96
0.25x = 12
x = 48
Solve for y :
y = 120 - 48
y = 72
Answer:
m<PTR = 140°
Step-by-step explanation:
First, find the value of x. To find the value of x, derive an equation which you'd use in solving for x.
m<PTQ = (x + 28)°
m<RTS = (2x + 16)°
m<PTQ = m<RTS (vertical opposite angles are congruent)
Therefore:
x + 28 = 2x + 16
Solve for x. Combine like terms
28 - 16 = 2x - x
12 = x
x = 12
Find m<PTQ
m<PTQ = (x + 28)
plug in the value of x
m<PTQ = 12 + 28 = 40°
m<PTR + m<PTQ = 180° (supplementary angles)
m<PTR + 40° = 180° (substitution)
m<PTR = 180 - 40 (subtracting 40 from each side)
m<PTR = 140°
Hehsjrjsownsirieus disowned me because
we are given with the data of a parabola with vertex at (2, 2) and directrix at y = 2.5. the formua should be ax^2 + b x + c = y because of the directrix.
(x-h)^2 = 4a (y-k)
(x-2)^2 =4a (y-2)
a is the equidistant distance from focus to vertex and from vertex to directrix that is equal to -0.5
then the answer is
(x-2)^2 =-0.5*4 (y-2)
x2 - 4x + 4 = -2y +4
x2-4x+2y = 0
answer is C
Answer:
square root 45 lies between 6 and 7
Step-by-step explanation:
I hope it's helpful!
