Answer:
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
----> by angle addition postulate
substitute the given values
Answer:
no I don't know I am sorry for this question
Answer:
<h3>
44</h3>
Step-by-step explanation:
z - some integer
2z - first given even integer (the smaller one)
2z+2 - even integer consecutive to 2z (the larger one)
2(2z) - twice the smaller number
2(2z) - 40 - the number 40 less than twice the smaller number
2(2z) - 40 = 2z + 2
4z - 40 = 2z + 2
2z = 42
2z+2 = 42+2 = 44
check:
2(2z)-40 = 2(42)-40 = 84-40 = 44
The sum of two numbers
x + y = 21
x = smaller number
y = larger number
Larger Number = y = (2x -6)
Substitute (2x - 6) for y
x + y = 21
x + (2x - 6) = 21
3x - 6 = 21
3x = 21 + 6
3x = 27
3x / 3 = 27 / 3
x = 9
Smaller number = x = 9
Find the larger number by inserting 9 into (2x - 6)
(2x - 6)
(2(9) - 6)
18 - 6
12
So
x = 9
y =12
Check our answer by inserting x = 9 and y = 12 into x + y = 21
x + y =21
9 + 12 = 21
21 = 21
So since we have 21 = 21 we know our answer is correct.
Answer:
It is not a right triangles because 15^2 + 13^2 is NOT EQUAL to 19^2
let x, y, and z be the angles inside the triangle.
Law of cosines says:
19^2 = 13^2 + 15^2 - 2(13)(15)cos x
361 = 169 + 225 - 390 cos x
-33 = -390 cos x
-33/-390 = cos x
11/130 = cos x
x = inverse cosine (11/130)
= 85.14609471338569.....
Per law of sines:
sin x/19 = sin y / 13
(13/19)sinx = sin y
inverse_sine ( (13/19) sin x) = y
y = 42.9810733896016548....
Per law of sines
sin x/19 = sin z / 15
z = inverse_sine( (15/19) sin x)
= 51.8728352950227805....
So it is an acute triangle and yes, these angles add up to 180
