a) 62.855m
We will need to use the Pythagorean Theorem here, as we know a and c, but not b. I have attached an image of a triangle sketch to set up the problem, which should hopefully help us to visualize this problem a bit better.
Pythagorean Theorem: a^2 + b^2 = c^2
(19.8)^2 + b^2 = (65.9)^2
392.04 + b^2 = 4342.81
b^2 = 3950.77
b = 62.855 (rounded to 3 places)
b) m = 0.315
The gradient is also known as the slope. I've shown what the points would be in the image attached. Now that we know the value of b (x in the points in image), we can use points E and C to find the slope.
Point 1: (0,0)
Point 2: (62.855, 19.8)
m = (19.8 - 0) / (62.855 - 0)
m = 19.8 / 62.855
m = 0.315 (rounded to three places)
c) 17.485 degrees
The angle of inclination would be angle C. To find angle C, we will need to use an inverse trigonometry function. Any can be used since we know all of the side lengths, but I will show Sine here, opposite / hypotenuse.
sin(x) = 19.8 / 65.9
x = sin^-1 (19.8/65.9)
x = 17.485 degrees (rounded to 3 places)
Hope this helps!! :)
Answer:
The vertex is the point (-1,2)
Step-by-step explanation:
we have
Convert into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
----> equation in vertex form
The vertex is the point (-1,2)
Answer:
FALSE
Step-by-step explanation:
6+8 = 14
The Triangle Inequality Theorem says:
the sum of any 2 sides of a triangle must be greater than the measure of the third side.
It's $6.99. You add the 4.3 + 1.7. Then take the 41.94 and divide the 6 you got from adding the other numbers.