Question

WILL GIVE 50 POINTS OR AS MANY AS YOU NEED BUT HELP ASAP WITH A FEW QUESTIONS:

5
1. What is ∑4n equal to? (will show the actual one in images)
n=1

2.What is (f−g)(x)?



f(x)=x4−3x2+5x−7

g(x)=x3−3x2+3x−1



Enter your answer, in standard form, in the box.

(f−g)(x)=

3. What is (f⋅g)(x)?



f(x)=x2−5x+4

g(x)=x3−1



Enter your answer, in standard form, in the box.

(f⋅g)(x)=

4. Let f(x)=x2−9 ​ and g(x)=x2−7x+12 .

What is (fg)(x) ?




x−4x+3 where ​ x≠−3,4 ​

x−4x+3 where x≠−3,3

x+4x−3 where ​ x≠−3,3 ​

x+3x−4 where x≠3,4


5. What is the recursive rule for the sequence?

4.4, 5.8, 7.2, 8.6, 10, …


an=an−1−1.4 , where ​ a1=4.4 ​ ​ ​

an=an+1+1.4 , where ​ a1=4.4 ​ ​ ​

an=an+1−1.4 , where ​ a1=4.4 ​ ​ ​

an=an−1+1.4 , where a1=4.4

6. Enter the explicit rule for the geometric sequence.



3/2, 3/4, 3/8, 3/16, 3/32, …

an=

Answer 1

Answers

1. 1,364

2. x⁴ + 2x - 6

3. x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4. x⁴ - 7x³ - 21x² + 63x -108

5. a(n-1) + 1.4

6. 3/(2× 2ⁿ⁻¹)

Step-by-step explanation

Q1

Σ4ⁿ = 4¹ + 4² + 4³ + 4⁴ + 4⁵

= 4 + 16 + 64 + 256 + 1024

= 1,364

Q2. What is (f−g)(x)?

f(x)=x4−3x2+5x−7

g(x)=x3−3x2+3x−1

(f−g)(x) = (x⁴−3x²+5x−7

) - (x³−3x²+3x−1)

=x⁴ + 2x - 6

3. What is (f⋅g)(x)?

f(x)=x2−5x+4

g(x)=x3−1

(f⋅g)(x) = (x³−1)(x²−5x+4

)

= x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4. Let f(x)=x2−9 ​ and g(x)=x2−7x+12 .

What is (fg)(x)?

(fg)(x) = (x²−9)(x²−7x+12)

= x⁴ - 7x³ - 12x² - 9x² + 63x -108

= x⁴ - 7x³ - 21x² + 63x -108

5. What is the recursive rule for the sequence?

4.4, 5.8, 7.2, 8.6, 10, …

5.8 = 4.4 = 1.4, 10 - 8.6 = 1.4 The sequence is an AP where the common difference is 1.4 and the first term a is 4.4.

We and 1.4 to the previous term in order to get the next term.

an = a(n-1) + d

= a(n-1) + 1.4

6. Enter the explicit rule for the geometric sequence.

3/2, 3/4, 3/8, 3/16, 3/32, …

common ratio r, = 4/3 ÷3/2 = 1/2

First term a, = 3/2

an = arⁿ⁻¹

= (3/2)(1/2)ⁿ⁻¹

= 3/(2× 2ⁿ⁻¹)