Answer:
See below
Step-by-step explanation:
Here we need to prove that ,
Imagine a right angled triangle with one of its acute angle as 
.
- The side opposite to this angle will be perpendicular .
- Also we know that ,
And by Pythagoras theorem ,
Where the symbols have their usual meaning.
Now , taking LHS ,
- Substituting the respective values,
Since LHS = RHS ,
Hence Proved !
I hope this helps.
For this problem, the confidence interval is the one we are looking
for. Since the confidence level is not given, we assume that it is 95%.
The formula for the confidence interval is: mean ± t (α/2)(n-1) * s √1 + 1/n
Where:
<span>
</span>
α= 5%
α/2
= 2.5%
t
0.025, 19 = 2.093 (check t table)
n
= 20
df
= n – 1 = 20 – 1 = 19
So plugging in our values:
8.41 ± 2.093 * 0.77 √ 1 + 1/20
= 8.41 ± 2.093 * 0.77 (1.0247)
= 8.41 ± 2.093 * 0.789019
= 8.41 ± 1.65141676
<span>= 6.7586 < x < 10.0614</span>
Answer:
Simple interest is calculated using initial principle while compound interest is calculated considering the interest also .
Step-by-step explanation:
Interest is the cost of borrowing money, where the borrower pays a fee to the lender for using his money. The interest, typically expressed as a percentage, can either be compounded or simple .
Simple interest is based on the principal amount , while compound interest is based on the principal amount and the interest that adds onto it in every period and the final principle is used for calculating the interest.
Simple interest is calculated on the principal amount of a loan and it's easier to find out than compound interest.
The hypotenuse is the longest side of a right angle triangle. Also,
hypotenuse² = base² + height²
Checking if the equation, Pythagoras theorem, is satisfied:
27² = 10² + 24²
729 ≠ 676
Thus, this is not a right triangle.
1)
45x^3+5x
the GCF is 5x because that is a factor of both.
The answer would be 5x(9x^2+1)
2)
u^2-5u+6
factoring is finding what multiplies to the last number to add to the middle number. Those numbers are -3 and -2.
the answer would be (u-3)(u+2)
3)
m^2-49
difference of perfect squares
answer is (m+7)(m-7)
4)
x^5+4x^4+3x^3
GCF is x^3 so it's x^3(x^2+4x+3)
Factor that and it's x^3(x+3)(x+1)
