(1) The value of x is 25
(2) The measure of ∠CBD is 60°
Explanation:
(1) The given two angles are vertical angles. Since, vertical angles are equal, we can add the two angles to determine the value of x.
Thus, we have,
Subtracting 5x from both sides, we have
Adding 10 to both sides , we have,
Thus, the value of x is 25.
(2) It is given that the measure of ∠ABC = (x+7)° and ∠CBD = (2x+14)°
Since, these two angles are supplementary angles and supplementary angles add upto 90°
Thus, we have,
Simplifying, we get,
Thus, substituting the value of x in ∠CBD = (2x+14)° to determine its value.
Thus, the measure of ∠CBD is 60°
A + b = 147....a = 147 - b
5.85a + 4.40b = 786
5.85(147 - b) + 4.40b = 786
859.95 - 5.85b + 4.40b = 786
-5.85b + 4.40b = 786 - 859.95
- 1.45b = -73.95
b = -73.95 / -1.45
b = 51 <== she used 51 lbs of type B coffee
Step-by-step explanation:
An exponentially decaying signal is of the form x(t) = Ce^(-αt) in terms of an initial value C and a decay rate α > 0. The signal equals a fraction 1/e of its initial value after the characteristic time scale t = 1/α.
Given
x(t) = 2e^(-t/3) + e^(-t) + 3e^(-t/2)
The decay rates are: 1/3, 1, and 1/2.
The slowest decay rate α is the minimum of {1/3, 1, 1/2} = 1/3.
The corresponding time scale
is only 2/3 times larger than the next faster decay rate 1/2, so the decay rates are NOT well separated. The slowest component is larger than 0.5 as long as t < (ln3)/0.5 ≈ 2.2.
The other two components add
up to more than the value of the slowest component. We conclude that the component with slowest decay rate dominates measurements on any interval even in the presence of noise.
In order to solve this we need to get x by itself on one side.
We need o start by adding across the 4 so that we get:
x/3 = -7 + 4 = -3
We then need to multiply both sides by 3 to get a singular x:
x = -3 * 3 = -9
Answer:
26
Step-by-step explanation:
2(9)-(-3)+5
2(9)+3+5
18+8
26
