Find the length of EF
1 answer:
Answer:
9
Step-by-step explanation:
1. First, we need to set up an equation to find the value of x and then the length of EF.
2. We know that DG is equal to 33, so we can add all the three sections it's cut into altogether to get 33. Therefore, we get an equation of:
3. (Solving for x)
Step 1: Simplify both sides of the equation.
Step 2: Add 58 to both sides.
Step 3: Divide both sides by 7.
4. Now that we know x is equal to 13, we can plug that value in for the expression 3x - 30.
Therefore, the length of EF is 9.
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Answer:
1. 13, 18, 23, 28, 33, 38, 43, 48, 53
<em>Conjecture:</em> Each term is 5 more than the previous term.
2. 512, 256, 128, 64, 32, 16, 8, 4, 2
<em>Conjecture:</em> Each term is half of the previous term.
3. 1, 8, 27, 64, 125, 216, 343, 512, 729
<em>Conjecture:</em> Each term is a cube. To find the nth term, cube n.
4. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
<em>Conjecture:</em> Each term is the next consecutive prime number.
5. <u><em>Correct as is</em></u>
6. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
<em>Conjecture:</em> Each term is the sum of the 2 previous numbers.
Step-by-step explanation:
1.
Given: 13, 18, 23, 28
<em>We add 5 to each number</em>
13 + 5 = 18
18 + 5 = 23
23 + 5 = 28
28 + 5 = 33
33 + 5 = 38
38 + 5 = 43
43 + 5 = 48
48 + 5 = 53
2.
Given : 512, 256, 128, 64
<em>Divide each number by 2</em>
512 ÷ 2 =256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
3.
Given: 1, 8, 27, 64
<em>We have to cube n:</em>
<u><em>n³ = consecutive number cubed</em></u>
<u><em></em></u>
1³ = 1 or 1 × 1 × 1
2³ = 8 or 2 × 2 × 2
3³ = 27 or 3 × 3 × 3
4³ = 64 or 4 × 4 × 4
5³ = 125 or 5 × 5 × 5
6³ = 216 or 6 × 6 × 6
7³ = 343 or 7 × 7 × 7
8³ = 512 or 8 × 8 × 8
9³ = 729 or 9 × 9 × 9
4.
Consecutive prime number: <u><em>Consecutive prime numbers are those that have no gaps or prime numbers between them.</em></u>
Look at the picture in the link:
6.
Given: 1, 1, 2, 3, 5, 8
<em>We must add the two previous numbers to get the next term:</em>
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 = 34 = 55
34 + 55 = 89
