Simplify the expression.
2 answers:
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Answer:
Option C. No solution is the right answer.
Step-by-step explanation:
Here the given equations are y = x²+2x+3 -----(1)
and y = 4x-2 -------(2)
Now we substitute the value of y from equation 2 into 1.
x²+2x+3 = 4x-2
x²+2x+3-2x = 4x-2-2x
x²+3 = 2x-2
x²+3-2x = 2x-2x-2
x²-2x+3 = -2
x²-2x+5 = 0
Then value of
Since in this solution √(-20) is not defined. Therefore there is no solution.
Answer:
The equation of the line is
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
In which m is the slope and b is the y-intercept.
Slope of - 1/3
This means that
So
Through the point (-6, -6)
This means that when . So
The equation of the line is
Short Answer
There are two numbers
x1 = -0.25 + 0.9682i <<<< answer 1
x2 = - 0.25 - 0.9582i <<<< answer 2
I take it there are two such numbers.
Let one number = x
Let one number = y
x + y = -0.5
y = - 0.5 - x (1)
xy = 1 (2)
Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1 Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0 Order these by powers
-x^2 - 0.5x -1 = 0 Multiply though by - 1
x^2 + 0.5x + 1 = 0 Use the quadratic formula to solve this.
a = 1
b = 0.5
c = 1
x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i
x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i
These two are conjugates. They will add as x1 + x2 = -0.25 - 0.25 = - 0.50.
The complex parts cancel out. Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.
Check
(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375
Notice
The two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.
The final result is 0.9375 and 0.0625 add up to 1
There are two numbers
x1 = -0.25 + 0.9682i <<<< answer 1
x2 = - 0.25 - 0.9582i <<<< answer 2
I take it there are two such numbers.
Let one number = x
Let one number = y
x + y = -0.5
y = - 0.5 - x (1)
xy = 1 (2)
Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1 Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0 Order these by powers
-x^2 - 0.5x -1 = 0 Multiply though by - 1
x^2 + 0.5x + 1 = 0 Use the quadratic formula to solve this.
a = 1
b = 0.5
c = 1
x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i
x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i
These two are conjugates. They will add as x1 + x2 = -0.25 - 0.25 = - 0.50.
The complex parts cancel out. Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.
Check
(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375
Notice
The two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.
The final result is 0.9375 and 0.0625 add up to 1