Answer:
X = 3
Step-by-step explanation:
STEP 1: Isolate a square root on the left hand side
Original equation
√4x-3+√2x+3 = 6
Isolate
√4x-3 = -√2x+3+6
STEP 2: Eliminate the radical on the left hand side
Raise both sides to the second power
(√4x-3)2 = (-√2x+3+6)2
After squaring
4x-3 = 2x+3+36-12√2x+3
STEP 3: Get remaining radical by itself
Current equation
4x-3 = 2x+3+36-12√2x+3
Isolate radical on the left hand side
12√2x+3 = -4x+3+2x+3+36
Tidy up
12√2x+3 = -2x+42
STEP 4: Eliminate the radical on the left hand side
Raise both sides to the second power
(12√2x+3)2 = (-2x+42)2
After squaring
288x+432 = 4x2-168x+1764
STEP 5: Solve the quadratic equation
Rearranged equation
4x2 - 456x + 1332 = 0
This equation has two rational roots:
{x1, x2}={111, 3}
STEP 6: Check that the first solution is correct
Original equation, root isolated, after tidy up
√4x-3 = -√2x+3+6
Plug in 111 for x
√4•(111)-3 = -√2•(111)+3+6
Simplify
√441 = -9
Solution does not check
21 ≠ -9
STEP 7: Check that the second solution is correct
Original equation, root isolated, after tidy up
√4x-3 = -√2x+3+6
Plug in 3 for x
√4•(3)-3 = -√2•(3)+3+6
Simplify
√9 = 3
Solution checks !!
Solution is:
x = 3
Answer:
7 orange and black fish
Step-by-step explanation:
a fifth of the remaining fish is 7 because you are doing 35*1/5. 35 is the remaining number of fish because already half of the other fish is 35 and they are orange
Answer: 1578
Step-by-step explanation:
The answer is 1578
Answer:
Length of wire for circle is 0.44 ft
Length of wire for square is 0.56 ft
Step-by-step explanation:
Let x is circumference of the circle
then
(1-x) = perimeter of the square
Find the radius of the circle
r = (x/2.π)
Find the area of the circle
a = π(x/2π)^2
a = π(x^2/4π^2)
Cancel π
a = x^2/4π
Find the area of the square:
a = (1-x/4)^2
a = (1-2x+x^2)/16
Total area
A = (x^2/4π)+(1-2x+x^2/16)
A = 4x^2+3.142-6.284x+3.142x^2
A = 7.142x^2-6.284x+3.142
Find the axis of symmetry [x = -b/(2a)]
x = -(-6.284)/{2.(7.142)}
x = 6.284/14.284
x = 0.44 ft, the piece of wire creating a circle
and
1 - 0.44 = 0.56 ft, the piece of wire creating the square
These lengths should give minimum area of the circle and square together
Answer:
x = -1 /2= -0.5 y = 15 /10= 1.5