Answer: 
Step-by-step explanation:
<u>Given information</u>
∡ 1 = 90°
∡ 2 = 50°
∡ 3 = x°
Total Angle = 180° <em>(Triangle angle sum theorem)</em>
<u>Given formula</u>
∡ 1 + ∡ 2 + ∡ 3 = Total Angle
<u>Substitute values into the formula</u>
(90) + (50) + (x) = (180)
<u>Combine like terms</u>
140 + x = 180
<u>Subtract 140 on both sides</u>
140 + x - 140 = 180 - 140
Hope this helps!! :)
Please let me know if you have any questions
1) Taking in account that the function is f(x)= -(2/3) |x+4|-6, I enclose a file with the graph.
That helps you to conclude:
a) The graph of f(x) has a vertex on (-4, -6)
b) When you multiply a function times 2/3 it is vertically compressed which is equivalent to horizontally streched.
c) The graph of f(x) opens downward
d) The domain of f(x) is all the real values (the absolute function accepts any value of x either positive or negative)
Answer: the graph of f(x) is horizontally stretched.
Answer:
19. x = 65
20. x = 12
21. x = 35, y = 85
Step-by-step explanation:
19. 2x -10 = 120
2x (-10 + 10) = (120 +10)
2x/2 = 130/2
x = 65
20. 2x + 4x + 108 = 180
6x + (108 - 108) = (180 - 108)
6x/6 = 72/6
x = 12
21. 2x + 25 = 3x - 10
2x + (25 - 25) = 3x (- 10 - 25)
(2x - 3x) = (3x - 3x) - 35
-x/-1 = -35/-1
x = 35
3x - 10 + y = 180
3(35) - 10 + y = 180
105 - 10 + y = 180
(95 - 95) + y = (180 - 95)
y = 85
F(x)=-9/x which is equal to:
f(x)=-9x^(-1) So the power rule for differentiation is used...
Power rule: f(x)=x^e, df/dx=ex^(e-1) so:
df/dx=-9(-1)x^(-1-1)
df/dx=9x^(-2) or if you prefer...
df/dx=9/x^2
df/dx(6)=9/36=1/4
Answer: x=4
Step-by-step explanation:
The perimeter´s formula for this kind of polygons is
The triangle perimeter would be:
(x+2)+(x+3)+(x+3)
And the rectangle:
(x+2)+(x+2)+x+x
For them to have the same value, we should equal them:
(x+2)+(x+3)+(x+3)=(x+2)+(x+2)+x+x
Working with this:
3x+8=4x+4
x=4
