For the first inequality, the solution is derived as follows:
4p > -8...... by subtracting 1
p > -2....... when divided by 4
This solution is represented on a graph as an open dot at -2, with the shading extending rightwards.
Since no inequality symbols incorporate "or equal to", all depicted dots remain open. The correct option is the first one:
a number line marked with open circles at -2 and 5, shaded in between.
Answer:
The best mortgage option for them is (3).
Step-by-step explanation:
Mortgage offers (1) and (2) are similar since Damarco and Tanya's down payment of $34,000 (20% of the purchase price) requires them to pay interest over 30 years for both scenarios. Although option (1) entails approximately $750 monthly payments and option (2) requires about $9,000 annually, the total payments are quite comparable as option (2)'s interest rate, starting at 3.5%, could potentially rise but is unlikely to exceed 5%, while option (1) maintains a fixed annual interest rate of 4.25%.
Option (3), however, demands interest payments for only 8 years at a relatively lower annual rate of 4%. If they commit to $18,000 annually with a $34,000 down payment and repay the remaining balance (under $35,000) at the end of 8 years, it leads to the lowest total payment and quickest mortgage clearance among the three options. Therefore, this choice aligns best with their financial objectives.
The largest common divisor (GCD) here is 24, indicating how many identical sets can be created. To find this using Euclid's algorithm, you start by dividing the larger number (72) by the smaller one (48) and check the remainder, which is 24. Since 24 evenly divides all the numbers (48, 72, 120), it serves as the GCD. Each of the 24 sets will include 2 blue crayons, 2 green crayons, 2 yellow crayons, 3 red crayons, and 5 colored pictures.
