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3 years ago

If B is the midpoint of AC, AB = 6x + 1 and BC = 3x + 10, then what is the length of AC?

Mathematics

1 answer:

sweet [91]3 years ago

6 0

Answer:

AC = 38

Step-by-step explanation:

A mid point divides a line in 2 equal parts. That means that one segment is equal to the other.

6x + 1 = 3x + 10 Subtract 3x from both sides

6x-3x + 1 = 3x -3x + 10 Combine

3x + 1 = 10 Subtract 1 from both sides

3x + 1 -1 = 10 - 1

3x = 9 Divide by 3

3x/3 = 9/3

x = 3

6x + 1 = 6*3 + 1 = 19

3x +10= 3*3 + 10 = 19

Both segments are 19 units long

AC = 19 + 19 = 38

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3 years ago

It takes Lucas 3 hours to cycle from his home to his friends village but if travels 5 mph slower, it will take him 1.5 hours lon

Alika [10]

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Step-by-step explanation:

Lets assume the distance from Lucas home to friend's village is x miles

The time taken to cycle from Lucas home to friend's village is 3 hrs....t₁

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Time taken in the second instance when travelling at a slower speed

= $\frac{x}{\frac{x}{3}-5 }=4.5\\ \\\frac{3x}{x-15} =4.5\\\\\\3x=4.5(x-15)\\\\3x=4.5x-67.5\\\\\\67.5=4.5x-3x\\\\\\67.5=1.5x\\\\\\67.5/1.5=x\\\\\\45=x$

The distance from friend's village to Lucas's house is 45 miles

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Formula for speed:brainly.com/question/13664094

Keywords: cycle,home, village, travels,slower,longer

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3 years ago