15x + 11x + 8x+5 = 180
34x + 5 = 180
34x = 180-5
34x = 175
x = 5.147
by substitution each value by of x by 5
75 + 55 + 45 = 175
Answer:
Option 4 -
Step-by-step explanation:
Given : In a circle with a radius of 6 ft, an arc is intercepted by a central angle of 3π/2 radians.
To find : What is the length of the arc?
Solution :
Length of an arc is given by:
where r is the radius of the circle, r= 6 ft.
and
is the angle in radian, ![\theta=\frac{3\pi }{2}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cfrac%7B3%5Cpi%20%7D%7B2%7D)
Substitute the value given in the formula,
Therefore, Option 4 is correct.
The arc of length is
270 dollars because 1440 divided by 12 equals 120. 120 times 2.25
is $270.000
Answer:
See explanation
Step-by-step explanation:
y=g(x) represents the number of bread loaves Sonia bakes per hour, where x is the number of hours she works;
z=f(y) represents the amount of money Sonia earns per loaf, where y is the number of loaves she makes,
so
z=f(g(x)) represents the amount of money Sonia earns per loaf, where x is the number of hours she works.
Now
![y=g(x)=\sqrt{2x^3}\\ \\z=f(y)=9y^2+1,](https://tex.z-dn.net/?f=y%3Dg%28x%29%3D%5Csqrt%7B2x%5E3%7D%5C%5C%20%5C%5Cz%3Df%28y%29%3D9y%5E2%2B1%2C)
so
![z=f(g(x))=9(g(x))^2+1=9(\sqrt{2x^3})^2+1=9\cdot (2x^3)+1=18x^3+1](https://tex.z-dn.net/?f=z%3Df%28g%28x%29%29%3D9%28g%28x%29%29%5E2%2B1%3D9%28%5Csqrt%7B2x%5E3%7D%29%5E2%2B1%3D9%5Ccdot%20%282x%5E3%29%2B1%3D18x%5E3%2B1)
- 57 - 12i
distribute the parenthesis
= 81i² - 36i + 24 + 24i
[ note that i² = (√- 1 )² = - 1 ]
= - 81 - 36i + 24 + 24i ( collect like terms )
= - 57 - 12i