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: 34.64 m
Step-by-step explanation:
Given: A boat is 60 m from the base of a lighthouse.
The angle of depression between the lighthouse and the boat is 37°.
By using trigonometric ratios :
here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m
Hence, the lighthouse is 34.64 m tall.
Answer:
she had 16
16
She got c
16 + c
She now has 32
16 + c = 32
I don't know if that's the exact answer, but basically, 16 needs to be added to c, and it needs to equal 32.
Hope this helps! :)
Answer:
22
Step-by-step explanation:
because i swiched the x's to the 7 and multipled
Answer/Step-by-step explanation:
a. Using two points on the line (0, 2) and (4, 12), find the gradient:
Gradient = ∆y/∆x = (12 - 2) / (4 - 0) = 10/4 = 2.5
Gradient = 2.5
b. The gradient, 2.5, represents the unit rate. That is, the volume of the oil in the tank per second.
i.e. 2.5 litres per second
c. The value, L = 2 represents the y-intercept, which is the starting value or initial volume of oil in the tank at 0 secs.
