a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.

John is 9, Brian is 6.

Step-by-step explanation:

I)

Let represent John's age and represent Brian's age.

John is three years older than Brian. In other words:

The product of their ages is 54. Or:

II)

Write this as a quadratic by substituting:

III)

Solve the quadratic:

Since age cannot be negative, Brian must be 6 years old right now.

John is three year older, so John is 9.

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week

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step-by-step explanation: