What is the simplest form of the expression (5x + 3xy + 4y) + (4x – 2xy – 2y)? a. x + xy + 2y b. x2 + xy + 2y c. 9x + 5xy + 2y d. 9x + 5xy + 6y e. 9x + xy + 2y
2. 5y + 2z + 3x2 – (2y – 2z + 4x) is equivalent to: f. 7y + 4z + 3x2 – 4x g. 3y + 3x2 – 4x h. 3y + 4z + 3x2 – 4x j. 3y + 4z + 7x k. 3y + 4z + 7x2
3. which of the following polynomials is equivalent to (x – 1)(x + 1)(x – 1)? a. x2 – x + 1 b. x2 – x – 1 c. x3 – x2 – x + 1 d. x3 – x2 – x – 1 e. x3 – 2x2 – 2x + 1
4. what is the product (2a + 6)2? f. 2a2 + 12a + 36 g. 4a2 + 12a + 36 h. 4a2 + 36 j. 4a2 + 24a + 36 k. 4a2 – 36
5. among the following arithmetic operations, which could the symbol ♣ represent given that the equation (6 ♣ 1)3 – (4 ♣ 1)2 = 200 is true? i. subtraction ii. multiplication iii. division a. ii only b. iii only c. ii and iii only d. i and iii only e. i, ii, and iii

1). Option E

2). Option H

3). Option C

4). Option J

5). Option C

Step-by-step explanation:

1). (5x + 3xy + 4y) + (4x - 2xy - 2y)

= (5x + 4x) + (3xy - 2xy) + (4y - 2y)

= 9x + xy + 2y

Option E. is the answer.

2). 5y + 2z + 3x²- (2y - 2z + 4x)

= 5y - 2y - 4x + 2z + 2z + 3x²

= 3y - 4x + 4z + 3x²

Option H is the answer.

3). (x - 1)(x + 1)(x - 1)

= (x² - 1)(x - 1)    [Since (a - b)(a + b) = a² - b²]

= x²(x - 1) - 1(x - 1)

= x³ - x² - x + 1

Option C is the answer.

4). (2a + 6)²

= 4a² + 24a + 36

[Since (a + b)² = a² - 2ab + b²]

Option J. is the answer.

5). For subtraction,

(6 - 1)³ - (4 - 1)²

= 5³ - 3²

= 125 - 9

= 116

But the result is 200 so operation subtraction is not the answer.

For Multiplication,

(6 × 1)³ - (4 × 1)²

= 6³ - 4²

= 216 - 16

= 200

For division,

(6 ÷ 1)³ - (4 ÷ 1)²

= 6³ - 4²

= 216 - 16

= 200

Therefore, Option C. is the answer.

46.2+112.3

step-by-step explanation:

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;