Q 1.) Expand using identities:
i. (a+2b)²
ii. (5x-3y)²
iii. (3a+4)(3a-4)(9a²+16)

Step-by-step explanation:

#1.

(a + 2b)²

Using identity (x + y)² = x² + 2xy + y², we get:

= (a)² + (2b)² + 2 × (a) × (2b)

= a² + 4b² + 4ab

= a² + 4ab + 4b² Ans.

#2.

(5x - 3y)²

Using identity (a - b)² = a² - 2ab + b², we get:

= (5x)² + (3y)² - 2 × (5x) × (3y)

= 25x² + 9y² - 30xy

= 25x² - 30xy + 9y² Ans.

#3.

(3a + 4)(3a - 4)(9a² + 16)

Using identity (x + y)(x - y) = x² - y², we get:

= [(3a)² - (4)²][9a² + 16]

= (9a² - 16)(9a² + 16)

= (9a²)² - (16)²

= 81a⁴ - 256 Ans.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;