Answer:
(cos a cos b - sin a sin b)
Step-by-step explanation:
It's easy
Answer:
Discriminant is positive.
Step-by-step explanation:
From the given graph,
Vertex of the parabola = (-3, -2)
y - intercept of the parabola = (0, 1)
Vertex form of a parabola opening upwards is,
y = a(x- h)² + k
Here (h, k) is the vertex.
By substituting the values of the vertex in this equation.
y = a(x + 2)² - 3
Since this parabola passes through (0, 1)
1 = a(0 + 2)² - 3
a = 
a = 1
So the equation of the parabola will be
y = (x + 2)² - 3
y = x² + 4x + 4 - 3
y = x² + 4x + 1
Here a = 1, b = 4 and c = 1 (comparing with standard quadratic equation y = ax² + bx + c)
Discriminant of a quadratic equation is represented by,
(b² - 4ac)
Therefore, the value of discriminant = (4)² - 4(1)(1)
= 16 - 4
= 12
Therefore, discriminant of the given graph is positive.
Your answer is x=84. hope this helps.
Answer:
The Answer is: The first number is 10 and the second number is 8.
Step-by-step explanation:
Let f = first number and s = second number.
The first number is 2 larger than the second:
f = n + 2
The numbers times each other is 80:
f * n = 80
Substitute the value of f, which is (n + 2):
n(n + 2) = 80
n^2 + 2n = 80
n^2 + 2n - 80 = 0
(n + 10)(n - 8) = 0
n^2 + 10n - 8n - 80 = 0, so the first number is 10 and the second one is 8.
Another method, just from thinking about it:
factor 80:
8 * 10, is the first factoring I thought of. I then noted that the difference between the two is 2 and if you multiply them they equal 80.
Hope this helps! Have an Awesome Day!! :-)