You can acquire 42 cookies through 12 different combinations. The first method involves purchasing 2 packs of 21 (21x2 = 42). The second consists of acquiring 1 pack of 21 alongside 3 packs of 7 (21 + 3x7 = 42). The third way is to buy 1 pack of 21 and 21 individual cookies (21 + 21 = 42). The fourth option combines 1 pack of 21, 1 pack of 7, and 14 single cookies (21 + 7 + 14 = 42). The fifth strategy includes 1 pack of 21, 2 packs of 7, and 7 individual cookies (21 + 14 + 7 = 42). The sixth way is to opt for 6 packs of 7 (7x6 = 42). The seventh option is to purchase 5 packs of 7 along with 7 individual cookies (7x5 + 7 = 42). For the eighth method, you can buy 4 packs of 7 and 14 single cookies (7x4 + 14 = 42). The ninth way is to get 3 packs of 7 with 21 single cookies (7x3 + 21 = 42). The tenth consists of acquiring 2 packs of 7 plus 28 individual cookies (7x2 + 28 = 42). The eleventh strategy involves 1 pack of 7 and 35 single cookies (7 + 35 = 42). Lastly, the twelfth method is simply buying 42 individual cookies (42 = 42).
Answer:
Detailed solution:
Given:
The problem to solve is:
Convert the equation into the standard quadratic form 
, where 
represent constants.
So, by adding 
to both sides, we get:
Note that 
.
The roots of this quadratic are found by applying the quadratic formula given as:
Substitute into the formula and calculate for 
.
Hence, the roots are:
A)
4(q - 10) = 76..... Tim earned 4 points for each correct answer, totaling 76 points. He got 10 answers right less than the total number of questions on the test.
b)
q = 10 + 76/4
q = 29
Thus, the overall number of questions on Tim's math test amounted to 29.
Answer:
With the addition of a child, both the family's income and expenses increase. Although the initial expenses might be higher, the financial benefits will manifest over time.
