Answer:
vertex = (2, - 9 )
Step-by-step explanation:
Given a quadratic in standard form : ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= - 
x² - 4x - 5 ← is in standard form
with a = 1, b = - 4, thus
= - 
= 2
Substitute this value into the quadratic for corresponding value of y
(2)² - 4(2) - 5 = 4 - 8 - 5 = - 9
vertex = (2, - 9 )
Answer:
25
Step-by-step explanation:
The increments are 0.4, and the width of the interval is 10, so the number of increments (the number of times you need to use Euler's method) is:
10 / 0.4 = 25
This does not appear to be a right triangle. However, we know 2 sides and the included angle, so can find the unknown side length. Let x represent this length. Then:
x^2 = (9 m)^2 + (12 m)^2 - 2(9m)(12 m)*cos 30 degrees, or
x^2 = 81 + 144 - 216(sqrt(3) / 2). Please solve for x^2 and then solve the result for x, making sure to choose the positive value. The result will be the length of the side opposite the 30 degree angle.
With 1 of 3 angles known, and 3 of 3 sides known, you can use the Law of Sines to find the other two angles. As a reminder, the Law of Sines looks like this:
a b c
-------- = --------- = ----------
sin A sin B sin C.
You can give the 30-deg angle any name you want; then a, the length of the side opposite the 30-deg angle, which you have just found. And so on.
Answer:
m =-1.25
Step-by-step explanation:
5.2m + 5 = 2.9m – 3 – 4.1m
Combine like terms
5.2m + 5 = -1.2m – 3
Add 1.2m to each side
5.2m +1.2m +5 = -1.2m +1.2m -3
6.4m +5 = -3
Subtract 5 from each side
6.4m +5-5 = -3-5
6.4m = -8
Divide each side
6.4m/6.4 = -8/6.4
m =-1.25
