<u>Given</u>:
The quadratic equation is
We need to determine the solutions of the quadratic equation.
<u>Solution</u>:
Let us solve the equation to determine the value of x.
Adding both sides of the equation by 5x and 3, we get;
The solution of the equation can be determined using quadratic formula.
Thus, we get;
Thus, the two roots of the equation are and
Hence, the solutions of the equation are and
Answer:
she saves $40
Step-by-step explanation:
first of all, you find 20% of $50, that is,
(20/100) * $50
then you get: $10
next step is to subtract this answer from the $50, that is: $50 - $10 = $40
have a great day!!
6.5% tax because the difference is $1.43
22 x 0.65 = $1.43
Answer:
Third answer shown
Step-by-step explanation:
Since each equation has a right side equal to the same thing, y, those right sides must be equal to each other.
x + 3 = -2x + 6
Add 2x to both sides. 2x 2x
3x + 3 = 0 + 6
3x + 3 = 6
Subtract 3 on both sides. -3 -3
3x = 3
Divide both sides by 3. x = 1
Now, let's see what y must be if x equals 1.
Line M: y = x + 3 --> y = 1 + 3 --> y = 4
Line N: y = -2x +6 --> y = -2(1) +6 --> y = -2 + 6 --> y = 4, confirmed
So the ordered pair (x, y) that satisfies <u><em>both </em></u>equations is (1, 4)
*** This means that if you graphed both lines on an xy-coordinate plane, the point (1,4) would be the point where the two lines intersect.
That is the third answer shown.
A little bit of trained eyeballing can help here. Let me tell you how I saw the answer without any computation.
Remember that the expansion of a squared binomial is
So, the square of a binomial has the following properties, which you can easily spot:
- It has three terms
- Two of them are perfect squares
- The third is twice the product of the two roots.
Well, in this case we do have three terms, and indeed is the square of 11x, and 1 is the square of itself. The only thing we have to check is that 22x is twice the product of 11x and 1, which is true.
So, the answer is
If you want to see some explicit calculations, just use the quadratic formula
to see that there is a double solution , and then use the formula
to come to the same conclusion.