Questions: 2. Show that 4=3,7,9 4. Copy and complete the × 3 magic square below. 8 4 6 5. A box contains 24 books of mass 750 g each. Another box contains 10 books of mass 5.8 kg. Find the total mass of the two boxes.

2. Show that 4=3,7,9 4. Copy and complete the × 3 magic square below. 8 4 6 5. A box contains 24 books of mass 750 g each. Another box contains 10 books of mass 5.8 kg. Find the total mass of the two boxes.
Transcript text: 2. Show that $4=\{3,7,9\}$ 4. Copy and complete the $\times 3$ magic square below. \begin{tabular}{|c|c|c|} \hline 8 & & 4 \\ \hline & 6 & \\ \hline & & \\ \hline \end{tabular} 5. A box contains 24 books of mass 750 g each. Another box contains 10 books of mass 5.8 kg. Find the total mass of the two boxes.
failed

Solution

failed
failed

Solution Steps

Step 1: Finding the missing values in the magic square

A magic square is a square grid filled with distinct numbers such that the sum of the numbers in each row, column, and diagonal is the same. In this 3x3 magic square, the numbers given are 8, 6, and 4. The magic sum can be determined by adding 8+6+4 = 18. Since a 3x3 magic square's numbers sum to 15 traditionally, and we are given a magic sum of 18, we can infer these values are multiplied by a factor of 1.2 (since 18/15 = 1.2). Therefore, a traditional magic square's values, which are 2, 7, 6; 9, 5, 1; 4, 3, 8, need to be multiplied by 1.2. This gives us 2.4, 8.4, 7.2; 10.8, 6, 1.2; 4.8, 3.6, 9.6.

The given magic square can now be completed.

| 2.4 | 8.4 | 7.2 | |---|---|---| | 10.8 | 6 | 1.2 | | 4.8 | 3.6 | 9.6 |

Step 2: Listing the elements and subsets of M

Given M = {3, 7, 9}.

i. n(M), the number of elements in set M, is 3.

ii. Set M has 2³ = 8 subsets.

iii. The subsets of M are: {}, {3}, {7}, {9}, {3,7}, {3,9}, {7,9}, {3,7,9}.

Step 3: Finding the scale factor and BC

Triangle A'B'C' is an enlargement of triangle ABC. The sides A'B' corresponds to AB, B'C' corresponds to BC, and A'C' corresponds to AC.

i. The scale factor (k) can be found by taking the ratio of corresponding sides: k = A'B' / AB = 9m / 3m = 3

ii. The scale factor is the same for all corresponding sides: B'C'/BC = k BC = B'C' / k = 6m / 3 = 2m

Final Answer:

  1. | 2.4 | 8.4 | 7.2 | |---|---|---| | 10.8 | 6 | 1.2 | | 4.8 | 3.6 | 9.6 |

  2. i. n(M) = 3 ii. 8 subsets iii. {}, {3}, {7}, {9}, {3,7}, {3,9}, {7,9}, {3,7,9}

  3. i. Scale factor (k) = 3 ii. BC = 2m

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Consider the following two ordered bases of (R^3) : - (langle-1,1,-1rangle,langle-1,2,-1rangle,langle-2,2,-1rangle) - (langle-1,-1,1rangle,langle 1,2,-1rangle,langle 1,1,0rangle) a. Find the change of basis matrix from the basis to the basis. ([id]square^square=) [ beginarrayccc square square square square square square square square endarray ] b. Find the change of basis matrix from the basis to the basis. ([id]口^circ=) [ beginarrayccc square square square square square square square square endarray ]
failedAnswered
Should there be a comma before the highlighted word? Mufasa tried to build a model ship out of ice; it started to melt in the warm bathtub however.
failedAnswered
Graph the function. F(x) = 3-x, if x ≤ 2 1+2x, if x > 2
failedAnswered
Question 4 1 pts As grapes ripen: The acidity level and the sugar level both drop The acidity level and the sugar level both increase The acidity level increases and the sugar level drops The acidity level drops and the sugar level increases
failedAnswered
Find all points having an x-coordinate of 1 whose distance from the point (-3,-2) is 5. The point(s) is(are) . (Type an ordered pair. Use a comma to separate answers as needed.)