Answer:
x = 10
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Geometry</u>
- All angles in a triangle add up to 180°
Step-by-step explanation:
<u>Step 1: Set up equation</u>
(x + 1)° + (10x - 7)° + (8x - 4)° = 180°
<u>Step 2: Solve for </u><em><u>x</u></em>
- Combine like terms: 19x - 10 = 180
- Isolate <em>x</em> term: 19x = 190
- Isolate <em>x</em>: x = 10
To find the number of schedules knowing that she can only take one of each subject, you will multiply ALL the possible numbers of options for each.
2 x 3 x 3 x 4 =72
There are 72 different possible class schedules.
To integrate, let's first clean out the inside, and simplify:
We can now safely substitute the value of u:
Now, we can write that:
This is much easier to integrate:
![16\int{u^4} \ du = 16[\frac{1}{5}u^5] + C](https://tex.z-dn.net/?f=16%5Cint%7Bu%5E4%7D%20%5C%20du%20%3D%2016%5B%5Cfrac%7B1%7D%7B5%7Du%5E5%5D%20%2B%20C)
Simplify:
Replace u (final answer):
Hope I could help with your integration.
Step-by-step explanation:
2).
Given that 1/(7+5√2)
We know that
The Rationalising factor of a+√b is a-√b
The denominator = 7+5√2
The Rationalising factor of 7+5√2 is 7-5√2
On Rationalising the denominator then
=> [1/(7+5√2)]×[ (7-5√2)/(7-5√2)]
=> [1×(7-5√2)]/(7+5√2)(7-5√2)]
=> (7-5√2)/[(7+5√2)(7-5√2)]
=> (7-5√2)/[7²-(5√2)²]
Since , (a+b)(a-b) = a²-b²
Where , a = 7 and b = 5√2
=> (7-5√2)/(49-50)
=> (7-5√2)/(-1)
=> -7+5√2
=> 5√2-7
3).
Given that (x-2)³
This is in the form of (a-b)³
Where, a = x and b = 2
We know that
(a-b)³ = a³-3a²b+3ab²-b³
=> (x-2)³ = x³-3(x²)(2)+3(x)(2)²-2³
=> (x-2)³ = x³-6x²+12x-8
The coefficient of x² is -6
Answer:
1/4: 1s/4
7/8: 7x/s
Step-by-step explanation:
