A.) 7^4x = 10
log base 10 (7^4X) = log base 10 (10)
4x log base 10 (7) = 1
4x (0.8451) = 1
3.3804x = 1
x = 0.2958
b.) ln(2) + ln(4x-1) = 5
ln (2 * 4x-1) = 5
ln (8x-2) = 5
log base (3) (8x-2) = 5
e^5 = 8x-2
e^5+2 = 8x
x = 18.8016
The volume of the prism given its dimensions is equal to 160 cubic units.
<h3>What is the volume of the
prism?</h3>
The given prism is made up of two prisms. The volume of the prism is the volume of the two shapes.
- One of the prisms have the dimensions: 4 x 4 x 5.
Volume = 80
- The other prism has the dimensions: 8 x 2 x 5.
Volume = 80
Volume of the prism = 80 x 2 = 160 cubic units.
To learn more about rectangular prisms, please check: brainly.com/question/8890358
Answer:
(x, y, z) = (4, -1, 3)
Step-by-step explanation:
To solve the system of equations:
2x − 3y + 4z = 23 .........................(1)
x + 2y − 4z = −10 ..........................(2)
3x − y + 2z = 19..............................(3)
Simultaneously, we do that by first eliminating one variable from any two equations to have an equation in two variables. The process is repeated with one of the used equations and the third unused equation to have a second equation in two variables. The two equations in two variables obtained can then be easily solved simultaneously.
Let us eliminate z from (1) and (2)
Add (1) and (2)
(1) + (2):
3x - y = 13 ........................................(4)
Multiply (3) by 2
(3) × 2
6x - 2y + 4z = 38 ............................(5)
Add (5) and (2)
(5) + (2):
7x + 0 + 0 = 28
x = 28/7 = 4
Putting this in (4)
3(4) - y = 13
y = 12 - 13 = -1
Putting this in (3)
3(4) - 4(-1) + z = 19
z = 19 - 16 = 3
Therefore,
(x, y, z) = (4. -1, 3)
1/2, 8/18 = 4/9, which is close to 4/8 wich is equal to 1/2
