I'll mark as brainliest if you get the correct answer WITH step by step explaination.​

ANSWER:

value of "a" is: a= -b√3+7+4√3

value of "b" is:  

STEP-BY-STEP EXPLANATION:

1. (rationalize the denominator)

(2 + √3) × (2 + √3) =a + b√3

2. (write the repeated multiplication in exponential form)

(2 + √3)² =a + b√3

3. (use (a + b)² = a² + 2ab + b²  to expand the expression)

4 + 4√3 + 3 = a + b√3

4. ( add the numbers)

7 + 4√3 = a + b√3

5. (move the variable to the left-hand side and change its sign. then, move the constants to the right-hand side and change their signs)

6. (change the signs on both sides of the equation)

a = -b√3 + 7 + 4√3

1. (rationalize the denominator. then, use the commutative property to reorder the terms)

(2 + ) × (2 + ) = a + b   →  (2 + ) × (2 + ) = a + b

2. (write the repeated multiplication in exponential form)

(2 + √3)² =a + b

3. (use (a + b)² = a² + 2ab + b²  to expand the expression)

4 + 4 + 3 = a + b

4. (add the numbers)

7 + 4 = a + b

5. (move the expression to the left-hand side and change its sign. then, move the constants to the right-hand side and change their signs)

- b + 7  + 4 = a  → -b = a - 7 - 4

6. (divide both sides of the equation by )  

b =

7. (rationalize the denominator)

b =

8. (write all numerators above the common denominator)

b =  

there you go! I hope this helped. goodluck! :)

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;