Given:
The equation is,
Explanation:
Simplify the equation by using logarthimic property.
Simplify further.
Solve the quadratic equation for x.
From the above equation (x - 6) = 0 or (x - 3) = 0.
For (x - 6) = 0,
For (x - 3) = 0,
The values of x from solving the equations are x = 3 and x = 6.
Substitute the values of x in the equation to check answers are valid or not.
For x = 3,
Equation satisfy for x = 3. So x = 3 is valid value of x.
For x = 6,
Equation satifies for x = 6.
Thus values of x for equation are x = 3 and x = 6.
<span>Given the quadratic equation: f(x) = -2x^2 - 2x - 1, the axis of symmetry can be obtained by finding the line that divides the function into two congruent or identical halves. Thus, it should pass through the vertex and is equal
to the x-coordinate of the vertex. </span>
<span>Note that a quadratic
equation in standard form: y = ax^2 + bx + c, has the vertex located at (h,k) where, h = -b/2a and k is determined by evaluating y at
h. In this case, a = -2, b = -2, thus, h = -0.5, k = 0.5. Thus, the vertex is located at (-0.5, 0.5) and the axis of symmetry is at x = -0.5. </span>
To solve with Elimination:
Write the equations under one another, like this:
2x - y = -1
+ 3x + 4y = 26
Ideally, we would like for one of the variables to be eliminated when we add vertically (straight down). But if we add them as they are this does not happen. We must manipulate one of the equations so that it will happen. Again, you can try to eliminate either x or y. I always look for a term that has a coefficient of 1 (or negative 1). So, let's use that y from the first equation again.
If the coefficient of the y in the other equation is POSITIVE 4, then I need the coefficient from the first equation to be its opposite, NEGATIVE 4. To do this, simply multiply the first equation by 4, this will create MAGIC!
4( 2x - y = -1)
+ 3x + 4y = 26
Be certain to Distribute across the entire first equation, so multiply all three terms by 4.
8x - 4y = -4
+ 3x + 4y = 26
Now add straight down (vertically). The y term will be eliminated.
11x = 22
Divide both sides of the equation by 11.
x = 2
Almost there! Now, substitute the 2 in for x in either of the original equations. Either one will work. I'm gonna use the second equation.
3x + 4y = 26
3(2) + 4y = 26
6 + 4y = 26
Subtract 6 from both sides of the equation.
4y = 20
Divide both sides of the equation by 4.
y = 5
That's it! There it is again. Put it all together. If x = 2 and y = 5, then the solution is the ordered pair, (2,5).
its (a) because (a) is C(x)=3x4+30x and 9+21 is 30 so its 3x2+30
