Will give 50 points or as many as you need but asap with a few questions: 51. what is ∑4n equal to? (will show the actual one in images) n=12.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=4.46. enter the explicit rule for the geometric sequence. 3/2, 3/4, 3/8, 3/16, 3/32, … an=

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)

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)