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Vikki [24]
3 years ago
11

T is the midpoint of AE. AT=4x-3 and TE= 2x+7, find the length of AE

Mathematics
1 answer:
iris [78.8K]3 years ago
7 0

If T is the midpoint, then that means its exactly 1/2 of the way between 2 points

this means we can set the 2 given values equal

4x - 3 = 2x + 7

first move like terms to the same side

2x = 10

x = 5

now that we know the length of x, we plug it back in to get the length

4x - 3 + 2x + 7 = 6x + 4

6(5) + 4 = 34

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Convert mixed number to improper fraction

5 and 3 over 45

3

4

= ( 5 × 4 ) over 4

5 × 4

4

+ 3 over 4

3

4

= ( 20 + 3 ) over 4

20 + 3

4

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4

Step 1 of 2: Add, sub-step b: Convert mixed number to improper fraction.

Convert mixed number to improper fraction

2 and 11 over 122

11

12

= ( 2 × 12 ) over 12

2 × 12

12

+ 11 over 12

11

12

= ( 24 + 11 ) over 12

24 + 11

12

= 35 over 12

35

12

Step 1 of 2: Add, sub-step c: Find common denominator.

Find common denominator

23 over 4

23

4

+ 35 over 12

35

12

= ( 23 × 3 ) over ( 4 × 3 )

23 × 3

4 × 3

+ ( 35 × 1 ) over ( 12 × 1 )

35 × 1

12 × 1

= 69 over 12

69

12

+ 35 over 12

35

12

12 is the least common multiple of denominators 4 and 12. Use it to convert to equivalent fractions with this common denominator.

Step 1 of 2: Add, sub-step d: Add.

Add

69 over 12

69

12

+ 35 over 12

35

12

= ( 69 + 35 ) over 12

69 + 35

12

= 104 over 12

104

12

                 

5 0
2 years ago
Read 2 more answers
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