Answer:
The solution of the exponential equation
is
x = 2.996
Step-by-step explanation:
To solve the exponential equation ![4e^{x} = 80](https://tex.z-dn.net/?f=4e%5E%7Bx%7D%20%3D%2080)
First, we will isolate
by dividing both sides of the equation by 4, so that we get
![\frac{4e^{x}}{4} = \frac{80}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4e%5E%7Bx%7D%7D%7B4%7D%20%20%3D%20%5Cfrac%7B80%7D%7B4%7D)
![e^{x} = 20](https://tex.z-dn.net/?f=e%5E%7Bx%7D%20%3D%2020)
Now, we will take the ln of both sides of the equation to get
![ln(e^{x}) =ln(20)](https://tex.z-dn.net/?f=ln%28e%5E%7Bx%7D%29%20%3Dln%2820%29)
(NOTE:
)
Then,
![x =ln(20)](https://tex.z-dn.net/?f=x%20%3Dln%2820%29)
![x = 2.9957](https://tex.z-dn.net/?f=x%20%3D%202.9957)
∴ x = 2.996 (to three decimal places)
Hence, the solution of the exponential equation
is
x = 2.996
Answer:
x = 15 degrees
3 angles in triangle are 44, 44 and 92 degrees.
Step-by-step explanation:
When the lines are parallel the internal angles add up to 180 degrees. So:-
8x + 7 + 2x + 23 = 180
10x + 30 = 180
10x = 150
x = 15
In the triangle:-
The angle adjacent to 136 = 180 - 136
= 44 degrees. As 2 sides of the triangle are congruent the other base angle = 44 degrees also.
The third angle = 180 - 2(44) = 92 degrees
Answer:
76
Step-by-step explanation:
Applying the formula to calculate the discriminant Δ=b2−4(a)(c)
Δ=b2-4(a)(c) with : a=3, b=−10, c=2
Δ=(−10)2−4⋅(3)⋅(2) = 100−24 = 76
The discriminant of the polynomial is equal to 76.
Same thing as 7 times 5 which is 35.
Answer:
The legs
Step-by-step explanation: