Answer:
Step-by-step explanation:
y=x^2-x+1
We want to solve for x.
I'm going to use completing the square.
Subtract 1 on both sides:
y-1=x^2-x
Add (-1/2)^2 on both sides:
y-1+(-1/2)^2=x^2-x+(-1/2)^2
This allows me to write the right hand side as a square.
y-1+1/4=(x-1/2)^2
y-3/4=(x-1/2)^2
Now remember we are solving for x so now we square root both sides:
The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.
This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.
That is we want:
Add 1/2 on both sides:
The last step is to switch x and y:
Answer:
Slope Intercept form of the equation is 
Step-by-step explanation:
Here, the two point line are given as is A(-6,-3) and B(6,-7)
The slope of the line AB = 
⇒ the slope of AB is m = (4/3)
By SLOPE INTERCEPT FORMULA:
The equation of a line with slope m and a point (x0, y0) is given as
(y-y0)= m (x-x0)
⇒ The equation of line with point (6,-7) is:
Now, the given equation is -x + 3y = -27
Convert it in the SLOPE INTERCEPT FORM y = mx + c
We get, 3y = x - 27
or, 
Hence, the Slope Intercept form of the equation is
x - y = - 11 .............( 1 )
y + 7 = - 2x ...............( 2 )
from equation ( 1 )
x - y = - 11
x = -11 + y ...........( 3)
putting x in equation ( 2 )
y + 7 = - 2 x
y + 7 = -2 ( -11 + y ) y + 7 = 22 - 2 y y + 2 y =22 - 7
3 y = 15 y = 15 / 3
putting value of y in equation 3
x = -11+ ( 13 /5 ) x = -33 /3 + 15 / 3 ( l.c.m)
x = -17 / 5
check
x = -11 + y
- 17 / 5 = -11 + 13 / 5
-17 /5 = -17 / 5
[tex] 3(x + 5) - 2(x + 2) = 20 \\
3x + 15 - 2x - 4 = 20\\
5x + 11 = 20\\
5x = 9\\
x = 1\frac{4}{5} [tex]
Let volume of 4% solution = x and of 14% be y
them x + y = 65........(1) also using the actual weights of salt:-
0.04x + 0.14y = 65*0.06 = 3.9
multiplying the above equation by -25 we have
-x - 3.5y = -97.5 adding this to equation (1)
--2.5y = -32.5
y= 13
and x = 65 - 13 = 52
so we need 13 mls of the 14%, and 52 mls of the 4% solution.
