Question

Task 2:
Use the table to complete each part.

a. Copy the table. Extend the table by writing expressions for y when x = 5, 6, and 7.

b. Simplify each expression for y in the table from part (a). What pattern do you notice in the simplified expressions?

c. Write an equation that relates x and y. Us your equation to find the value of y when x = 15.

The Table:

x | y
1 | 1
2 | 1 + 2
3 | 1 + 2 +4
4 | 1 + 2 + 4 + 8

Answer 1

plz help!

Answer 2

let's get the actual answers for the y values

x | y
1 | 1 = 1
2 | 1 + 2 = 3
3 | 1 + 2 +4 = 7
4 | 1 + 2 + 4 + 8 = 15

5 | 1+2+4+8+16 = 32
6 | 1+2+4+8+16+32 = 63

Did you notice that all the sums are one less than a power of 2

e.g for x = 3, the sum = 7 = 2^3 - 1
for x = 6 , the sum = 63 = 2^6 - 1

so when x = 15, the sum should be 2^15 - 1 = 32767

Answer 3

Okay thanks can you help with this one?

Task 3:
Solve. Show all your work and explain your steps.

You are buying gifts for 10 people. You decide to buy each person either a CD or a DVD. A CD costs $12 and a DVD cost $20.

a. Let c = the number of CDs you decide to buy. What is an expression in terms of c for the number of DVDs you buy?

b. What is an expression in terms of c for the cost of the CDs? For the cost of the DVDs?

c. Write and simplify an expression in terms of c for the total cost of all the gifts you buy.

Answer 4

Let c = the number of CDs you decide to buy
Then the number of DVDs is 10 - c

cost of CD = 12c
cost of DVD = 20(10-c)

total cost = 12c + 20(10-c)
= 12c + 200 - 20c
= 200 - 8c

Answer 5

thank you ssssoooooo much !

Answer 6

The property used is Distributive correct? Would we say it has commutative property of addition as well or just Distributive?
thanks