Answer:
Step-by-step explanation:
Given a general quadratic formula given as ax²bx+c = 0
To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;
Step 1:
Bringing c to the other side
ax²+bx = -c
Dividing through by coefficient of x² which is 'a' will give:
x²+(b/a)x = -c/a
- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:
x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a + b²/4a²
- Taking the square root of both sides
√(x+b/2a)² = ±√-c/a + b²/√4a²
x+b/2a = ±√(-4ac+b²)/√4a²
x+b/2a =±√b²-4ac/2a
- Taking b/2a to the other side
x = -b/2a±√√b²-4ac/2a
Taking the LCM:
x = {-b±√b²-4ac}/2a
This gives the vertex form with how it is used to Solve a quadratic equation.
Answer:
Step-by-step explanation:
Term Definition
Linear regression line The line that goes through a set of points either exactly or approximately.
Difference The result of a subtraction operation is called a difference.
Answer:
y = 5/9x - 37/3
Step-by-step explanation:
5x - 9y = 8
-9y = -5x + 8
y = 5/9x - 8/9
- When a line is parallel, the slope remains the same.
y = 5/9x + b
-9 = 5/9(6) + b
-9 = 10/3 + b
-37/3 = b
Answer:
<em>Total cost=$73.60
</em>
Step-by-step explanation:
<u>Arithmetics To Solve Simple Problems
</u>
Sometimes the use of the most basic operations can be handy to solve problems of a variety of complexities without the use of equations or algebra. We'll approach to the solution of this question by pure logic and basic operations.
If the gift was originally meant to be paid for all 5 brothers, each one would have paid one-fifth of the cost. But since the younger brother won't be paying anything, the cost will be divided among the other four brothers, each one of which will pay now one-fourth of the cost. But this new division is $3.68 more than the previous one. If we take the difference between both fractions, we get

That fraction is the portion of the money they are paying in excess, so the total cost should be twenty times that excess, i.e.
Total cost= 20*3.68=$73.60
Let's check. Each brother should have paid $73.60/5=$14,72. But the four brothers really paid $73.6/4=$18.40. The difference is cost is $18.40-$14,72=$3.68 as required