Which matrix represents the system of equations shown below

Answer:

a. 80 students

b. 92 students

Step-by-step explanation:

Designate arts students as A and dance students as D.

Thus, we have,[['[TAG_14]]

n(A) = 35

n(D) = 57

Required

To determine n(A or D)

For (a):

We find that:

n(A and D) = 12

The calculation for n(A or D) is as follows:

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 12

n(A or D) = 80

b. Given the details

n(A and D) = 0 since no students are enrolled in both classes as indicated in (a)

Using the same formula as in (a).

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 0

n(A or D) = 92

Answer:

The three errors are:

1) Incorrectly swapping the variables x and y.

2) Failure to use the ± symbol.

3) The domain is wrong; it should be x ≤ 0.

Step-by-step explanation:

Review the following steps.

Step 1:

The initial step is incorrect because the variables x and y were switched improperly; it should be:

Step 2:

Step 3:

Step 4: , for x ≥ 0

Step 4 contains an error as the ± sign is required. Additionally, the function's domain is inaccurately stated.

The radicand must be nonnegative, implying that x must satisfy x ≤ 0.

Answer:

The total weight of 15 bags is 258.21 kilograms.

The combined volume of 15 bags is 2.222 cubic yards.

Step-by-step explanation:

In terms of dimensions, a pound is equivalent to 0.453 kilograms, and a cubic yard is equal to 27 cubic feet. We'll calculate the weight and volume for 15 bags by utilizing these conversions:

Weight

The total weight of 15 bags equals 258.21 kilograms.

Volume

The total volume of 15 bags sums up to 2.222 cubic yards.

Answer:

x=9,-1 and

Explanation:

We are given the quadratic equation

, which we then compare with the standard form of a quadratic. The general quadratic is identified as

. From our given equation, it follows that a=1,b=-8,c=-9

. To calculate the discriminant, we insert these values into the formula

. Now, to find the value of x

The formula is

. The resulting equation will be obtained by rewriting the original equation through rearranging 9 to the right side and applying negative signs within brackets to convert the expression into the form of

Answer:

The result to your inquiry is 2 7/24.

Step-by-step explanation:

Data:

Hank's cows yield = 4 3/4 and 4 1/8

Debra's cows yield = 5 1/2 and 5 2/3

Process:

1.- Convert the mixed numbers into improper fractions:

For Hank: (16 + 3)/4 = 19/4 and (32 + 1)/8 = 33/8.

For Debra: (10 + 1)/2 = 11/2 and (15 + 2)/3 = 17/3.

2.- Add Hank's and Debra's milk quantities:

Hank: 19/4 + 33/8 = 38/8 + 33/8 = 71/8.

Debra: 11/2 + 17/3 = 33/6 + 34/6 = 67/6.

3.- Subtract Hank's total from Debra's total:

67/6 - 71/8 = (268 - 213)/24.

Thus, it simplifies to 55/24.

- Convert back to a mixed number:

2

24 55

7

Where 55/24 equals 2 7/24.

4.- Conclusion:

Debra produced 2 7/24 more milk than Hank.