Answer:
m<C = 42°
Step-by-step explanation:
Given:
m<A = (2x - 2)°
m<C = (4x - 6)°
m<DBC = (5x + 4)°
Thus:
m<DBC = m<A + m<C (exterior angle theorem of a triangle)
(5x + 4)° = (2x - 2)° + (4x - 6)°
Solve for x
5x + 4 = 2x - 2 + 4x - 6
Collect like terms
5x + 4 = 6x - 8
5x - 6x = -4 - 8
-x = -12
Divide both sides by -1
x = 12
✔️m<C = (4x - 6)°
Plug in the value of x
m<C = 4(12) - 6 = 48 - 6
m<C = 42°
Answer:
height of cylinder = 4/3 h
Step-by-step explanation:
The solid has a cylinder surmounted with a cone .Therefore, the volume of the solid is the sum of the cone and the cylinder.
volume of the solid = volume of cylinder + volume of cone
volume of the solid = πr²h + 1/3πr²h
let
height of the cylinder = H
recall
the height of the cone = 2h
volume of the solid = πr²h + 1/3πr²h
3(1/3πr²2h) = πr²H + 1/3πr²2h
2πr²h = πr²H + 2/3 πr²h
πr²(2h) = πr²(H + 2/3 h)
divide both sides by πr²
2h = H + 2/3 h
2h - 2/3h = H
H = 6h - 2h/3
H = 4/3 h
height of cylinder = 4/3 h
Answer:
y = 2
Step-by-step explanation:
y ∝ kx
y = 
× 9 = 
First, write the expression.
180=(x+96)+5x
Second, add all coefficients.
180=6x+96
Subtract 96 from each side.
180-96=6x+96-96
84=6x
Divide both sides by 6.
14=x
Now that you have found the value of x, substitute x to solve the angles.
The first angle:
x+96
14+96=110 degrees
The second angle:
5*x
5*14=70 degrees
The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.
<h3>
Exponential function</h3>
An exponential function is in the form:
y = abˣ
where y,x are variables, a is the initial value and b is the multiplicative factor.
Let y represent the amount of substance remaining after x hours. Hence:
a = 9375, at x = 4, y = 15:
15 = 9375(b)⁴
b = 0.2
y = 9375(0.2)ˣ
For the 7th hour, x = 7:
y = 9375(0.2)⁷ = 0.12
The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.
Find out more on Exponential function at: brainly.com/question/12940982
