This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems from the image. 5. Look at the number line and write down the decimal numbers represented by the letters A to D. Step 1: Determine the value of each small segment on the number line. The distance between 0 and 0,05 is divided into 5 equal segments. The value of each segment is (0,05)/(5) = 0,01. Step 2: Calculate the value for each letter. A is 3 segments from 0. So, A = 3 × 0,01 = 0,03. B is 2 segments from 0,05. So, B = 0,05 + (2 × 0,01) = 0,05 + 0,02 = 0,07. C is 1 segment from 0,1. So, C = 0,1 + (1 × 0,01) = 0,1 + 0,01 = 0,11. D is 4 segments from 0,1. So, D = 0,1 + (4 × 0,01) = 0,1 + 0,04 = 0,14. The decimal numbers are: A: 0,03 B: 0,07 C: 0,11 D: 0,14 Challenge: Determine the next four terms in the pattern below: 3,001; 3; 3,002; 2,999; 3,003; 2,998; 3,004; 2,997; 3,005; 0.7cm; 0.7cm; 0.7cm; 0.7cm. Step 1: Identify the pattern. This pattern consists of two interleaved sequences. Step 2: Analyze the first interleaved sequence (terms at odd positions). The terms are 3,001; 3,002; 3,003; 3,004; 3,005. This sequence increases by 0,001 each time. The next terms in this sequence would be 3,005 + 0,001 = 3,006 and 3,006 + 0,001 = 3,007. Step 3: Analyze the second interleaved sequence (terms at even positions). The terms are 3; 2,999; 2,998; 2,997. (Note: 3 can be written as 3,000) This sequence decreases by 0,001 each time. The next terms in this sequence would be 2,997 - 0,001 = 2,996 and 2,996 - 0,001 = 2,995. Step 4: Combine the next terms from both sequences. The original sequence alternates between the two patterns. The last term given is 3,005 (from the first sequence). So, the next term will be from the second sequence: 2,996. The term after that will be from the first sequence: 3,006. The term after that will be from the second sequence: 2,995. The term after that will be from the first sequence: 3,007. The next four terms are: 2,996; 3,006; 2,995; 3,007 The next four terms in the pattern are 2,996; 3,006; 2,995; 3,007. Last free one today — make it count tomorrow, or type /upgrade for unlimited.