Answer:
domain: x>3/5
Step-by-step explanation:
First we need to derive our function g(x) to get a new function g'(x)
To do this we will have to apply chain rule because we have an inner and outer functions.
Our G(x) = square root(3-5x)
Chain rule formula states that: d/dx(g(f(x)) = g'(f(x))f'(x)
where d/dx(g(f(x)) = g'(x)
g(x) is the outer function which is x^1/2
f(x) is our inner function which is 3-5x
therefore f'(x)= 1/2x^(-1/2) and f'(x) = -5
g'(f(x)) = -1/2(3-5x)^(-1/2)
Applying chain rule then g'(x) = 1/2 (3-5x)^(-/1/2)*(-5)
But the domain is the values of x where the function g'(x) is not defined
In this case it will be 3-5x > 0, because 3-5x is a denominator and anything divide by zero is infinity/undefined
which gives us x >3/5
Perimeter = (length+width) x 2
Let w units be the width of the rectangle.
Length of the rectangle = 2w
Perimeter:
(2w+w) x 2 = 60
(3w)2 = 60
6w = 60
w = 10
Area:
2(10) x 10
= 20 x 10
= 200 units
Answer:
35 degrees
42 degrees
x = 8 degrees
x = 7 degrees
Step-by-step explanation:
1)
m <1 = 70/2 = 35 degrees
2)
m <1 = 84/2 = 42 degrees
3)
6 + 4 x = (9 x + 4) / 2
12 + 8 x = 9 x + 4
12 - 4 = x
x = 8 degrees
4)
3 x - 1 = x + 13
2 x = 14
x = 7 degrees
Answer: #20, x = 3
#21, x = 1/2
Step-by-step explanation:
#20) x + 4 + x + 2+ x + 5 = x + 3 +x+3+x+1+x+1
3x + 11 = 4x + 8
<u>-3x -3x</u>
11= x + 8
<u> - 8 - 8</u>
3 = x
#21) 12x(5) = 6x + 9 + x + 10 + x + 7
60x =8x + 26
<u> -8x -8x</u>
52x = 26
divide both sides by 52
x = 1/2
