To get the vertex of the parabola we proceed as follows;
y=-7(x-4)^2-5
The above can be written as:
y=-7x^2+56x-117
The values of a,b and c are:
a=-7, b=56 and c=-117
x=-b/(2a)
x=-56/(-7*2)=4
but;
y=-7x^2+56x-117
y=-7(4)^2+56(4)-117
y=-5
Thus;
x=4 and y=-5
The vertex will be at point (4,-5)
Answer:
, option B
Step-by-step explanation:
Complex numbers:
The most important relation that involves complex numbers is given by:

Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:



In this question:
The solutions are:

We have to find the polynomial. All option have
. So

The correct answer is given by option b.
Answer:
D
Step-by-step explanation:
Using the Cosine rule to find AC
AC² = BC² + AB² - (2 × BC × AB × cosB )
= 18² + 12² - ( 2 × 18 × 12 × cos75° )
= 324 + 144 - 432cos75°
= 468 - 111.8
= 356.2 ( take the square root of both sides )
AC =
≈ 18.9
-----------------------------------------
Using the Sine rule to find ∠ A
=
( cross- multiply )
18.9 sinA = 18 sin75° ( divide both sides by 18.9 )
sinA =
, then
∠ A =
(
) ≈ 66.9°
16 - 14 = 2
Think of it as in objects. You have 16 candies, and you eat 14. How many do you have left? You can count it and see. You have 2 left. So 16 - 14 = 2
Hope that helps :)
Answer:
- 75 and - 28
Step-by-step explanation:
To evaluate f(6) substitute x = 6 into f(x)
f(6) = - 2(6)² - 3 = - 2(36) - 3 = - 72 - 3 = - 75
Similarly
g(5) = - 5(5) - 3 = - 25 - 3 = - 28