GRADE 9 MATH EASY PLEASE HELP

Question

Some questions I really don't understand. Please help on as many as you can. Thank you.

 

1) Write an expression using exponents, and find the total area of a pair of squares given their side lengths

a) 6cm,7cm

b)4cm,9cm

 

2)The population of deer on Mount Washington is 2500. If the growth of the deer population is 1.5% each year. Determine the expression that can be used to calculate the deer population after n years.

a)P= 2500(1.5)ⁿ

b)P= 250091.015)ⁿ

c)P= 2500(1.15)ⁿ

d)P= 2500(0.015)ⁿ

 

3)Express each number as a product of two powers

a) 100

b) 108

c) 72

d) 2500

 

That's all! Thank you so much! :)

 

Answer 1

Answer (1): since the area has the units of (length)²....the total area of the pair of squares whose side lengths are:

(a) (6cm)² + (7cm)² = 36cm² + 49cm²

(b) (4cm)² + (9cm)² = 16cm² + 81cm²

 

Answer (2):

At n=1 year: P = 2500(1 + 0.015)

 

n=2 years: P = 2500(1 + 0.015) + [2500(1+0.015)](0.015) = 2500[1+2(0.015)+ (0.015)²]

This looks like 2500(x²+2x+1) or 2500(x+1)² where x=0.015

 

Expand the equation at n=3 and you'll find that P will have the form 2500(x+1)(x²+2x+1) = 2500(x+1)³ where x=0.015

 

So P(n) = 2500(1+0.015)ⁿ = 2500(1.015)ⁿ where n=#of years

 

 

Answer (3):

(a) 100 = 25 x 4 = (5²)(2²)

(b) 108 = 27 x 4 = (3³)(2²)

(c) 72 = 9 x 8 = (3²)(2³⁾

(d) 2500 = 100 x 25 = (10²)(5²)

Answer 2

The answer to #2 should actually be b) P=2500(1.015)ⁿ

 

The population is growing by 1.5% per year, and b) includes the original population and 1.5% "interest" each year

 

d) would represent the population decreasing to 1.5% of its previous value each year.

Answer 3

1. a): A=Area = (6 cm)² + (7 cm)² = (36 cm²) + (49 cm²) = 85 cm²

 

1. b) A = Area =  (4 cm)² + (9 cm)² = (16 cm²) + (81 cm²) = 97 cm²

 

2. The answer is d) ρ = 2500(0.015)ⁿ

 

3. a) 100 = (2)(50) = (2)(2)(25) = (2)(2)(5)(5) = (2²)(5²)

 

3. b) 108 = (2)(54) = (2)(2)(27) = (2)(2)(3)(9) = (2)(2)(3)(3)(3) = (2²)(3³)

 

3. c) 72 = (2)(36) = (2)(2)(18) = (2)(2)(2)(9) = (2)(2)(2)(3)(3) =(2³)(3²)

 

3. d) 2500 = 2(1250) = (2)(2)(625) = (2)(2)(5)(125) =(2)(2)(5)(5)(25) = (2)(2)(5)(5)(5)(5)

 

∴2500 = (2²)(5⁴)