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
Given parameters:
Equation:
(x-4)²=9
Problem: Solve the equation by both factoring and extracting the square root.
Solution:
Starting equation:
(x-4)²=9
Subtracting 9 from both sides brings us to zero;
(x-4)² - 9 = 0
(x -4)² - 3² = 0
This fits the concept of the difference of squares;
x² - y² = (x + y)(x-y)
Let x = x-4 and y = -3
Then input and solve;
(x - 4 -3)(x - 4 -(-3)) = 0
(x - 7)(x - 1) = 0
S thus,
x - 7 = 0 or x-1 = 0
x = 7 or 1
<pBy extracting the square roots;
(x-4)² = 9
√(x-4)² = √9
x - 4 = 3
x = 4 + 3 = 7; however, this is not the sole solution
Thus, direct extraction of the square root is not the method for complete solutions.
(1 3/4) divided by (1/5) =
(7/4) ÷ (1/5) =
7/4 multiplied by 5/1 =
35/4 or 8 3/4 <===
QR is 12, as you establish a proportion: 21/14 = x/8, then cross-multiply to obtain 14x = 168, which you solve by dividing to find x = 12.
