Algebra Answers

We do a proof by induction to show the following inequality is true for all n∈N: 4ⁿ ≥ 4n

Let P(n) represent the statement: 4ⁿ ≥ 4n

For n=1: LHS = 4¹ = 4 and RHS = 4(1) = 4

Since 4≥4, P(1) is true.

Assume true for n=k: P(k)true means 4^k ≥ 4k

Show true for n=k+1 assuming P(k):

Provide the correct proof.

Create a table for the equation:

y= 2^x

In Desmos, type in the coordinates:

(1,3) (9,2)

(3,1)

(0,1) (, 1,0)

(-1, 0.333) (0.333, -1)

What is their relationship between x and y coordinates?

In desmos, type in the coordinates:

(0.04, -2)

(0.2, -1)

(1,0)

(5,1)

(25,2)

(125, 3)

What relationship do you see between the x and y coordinates?

Evaluate the following polynomial expression using Horner’s rule. Assume the value of x

is 3.

𝑃(𝑥) = 10x⁵ + 6x⁴+ 3x³ − 6x² + 8𝑥 + 15

Show all the intermediate steps.

Evaluate the following polynomial expression using Horner’s rule. Assume the value of x is 3.

𝑃(𝑥)=10𝑥􏰀 +6𝑥􏰁 +3𝑥􏰂 −6𝑥􏰃 +8𝑥+15

Show all the intermediate steps.

Guide to Calculating Speed:

Drag the circle labels over the correct wheels

1. back tire: n= 0.2
2. front tire: n= 0.3
3. front tire; n= 0.3
4. back tire: n= 0.2

then add up the n values of each tire for total n value

At the arcade, Sammy won two blue tickets, 1 yellow ticket and 3 red tickets for a total of 1,500 points. Jamal won 1 blue, 2 yellow and 2 red for 1225 points. Yvonne won 2 blue, 3 yellow and 1 red for 1200 points. How much is each ticket worth?

There are 100 pappadam at a kalyaana beef.. for a man .. u should give 10 pappadams.. for a woman .. u should give 5 pappadams .. and for a kid .. you should give 1/2 ( half ) pappadam.. and 100 people who went to the kalyanam got pappadam too .. how many men, women and children were there in this 100 people ?

B. Evaluate the following algebraic expressions for the given value of x

1.2x—7 where x=4

Solution:

2.4x—8/3x+4 where x=—1

Solution:

3.x²—6x+5 where x=—3

Solution: