<h2>I hope it's helpful for you</h2>
The completely factored form of f(x) = 6x³ - 13x² - 4x + 15 is f(x) = (x + 1)(2x - 3)(3x - 5)
<h3>How to factor the expression?</h3>
The expression is given as:
f(x) = 6x³ - 13x² - 4x + 15
Expand the expression
f(x) = 6x³ - 19x² + 6x² + 15x - 19x + 15
Rewrite as:
f(x) = 6x³ + 6x² + 15x- 19x² - 19x + 15
Factorize the equation
f(x) = (x + 1)(6x²- 19x + 15)
Expand (6x² - 19x + 15)
f(x) = (x + 1)(6x² - 10x - 9x + 15)
Factorize the expression
f(x) = (x + 1)(2x - 3)(3x - 5)
Hence, the completely factored form of f(x) = 6x³ - 13x² - 4x + 15 is f(x) = (x + 1)(2x - 3)(3x - 5)
Read more about factorized expression at:
brainly.com/question/7438300
Answer:
1. ∠1 = 60
2. ∠2 = 40
3. ∠3 = 80
4. ∠4 = 80
5. ∠5 = 60
6. ∠6 = 120
7. ∠7 = 100
8. ∠8 = 60
9. ∠9 = 120
10. ∠10 = 100
Step-by-step explanation:
Answer:
Step-by-step explanation:
Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year. This means that for each year, her income is 104% of the previous year. So the rate of increase is 104/100 = 1.04. This rate is in geometric progression. The formula for the sum of n terms of a geometric sequence is expressed as
Sn = a(r^n - 1)/r-1
Where
Sn is the nth term
a is the first term
n is the number of terms.
r is the rate or common ratio
From the information given,
a = 33000
r = 1.04
The formula for Alexis total earning over n years will be
Sn = 33000(1.04^n - 1)/(1.04 - 1)
Her earnings for the next 15 years would be
S15 = 33000(1.04^15 - 1)/(1.04 - 1)
S15 = 33000(0.8009) / 0.04
S15 = $668167.50
Answer:
Volume of the frustum = ⅓πh(4R² - r²)
Step-by-step explanation:
We are to determine the volume of the frustum.
Find attached the diagram obtained from the given information.
Let height of small cone = h
height of the large cone = H
The height of a small cone is a quarter of the height of the large cone:
h = ¼×H
H = 4h
Volume of the frustum = volume of the large cone - volume of small cone
volume of the large cone = ⅓πR²H
= ⅓πR²(4h) = 4/3 ×π×R²h
volume of small cone = ⅓πr²h
Volume of the frustum = 4/3 ×π×R²h - ⅓πr²h
Volume of the frustum = ⅓(4π×R²h - πr²h)
Volume of the frustum = ⅓πh(4R² - r²)
