In triangle ABC shown below, side AB is 8 and side AC is 6:

Mathematics

2 answers:

lbvjy [14]3 years ago

8 0

Segment AD is 4, and segment AE is 3. This is because AB is 8, and half of 8 is 4, and then AC is 6, and half of 6 is 3.

Gekata [30.6K]3 years ago

4 0

Answer:

Segment AD is 4, and segment AE is 3.

Step-by-step explanation:

Given,

In triangle ABC,

AB = 8 unit,

AC = 6 unit,

We have to prove :

[tex]DE=\frac{BC}{2}{/tex]

By the Midpoint Theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Thus, for proving the required statement we need to prove D and E are midpoints of AB and AC respectively,

That is, AD = DB and AE = EC

∵ AB = 8 ⇒ AD + DB = 8 ⇒ AD + AD = 8 ⇒ 2AD = 8 ⇒ AD = 4

Similarly,

2AE = 6 ⇒ AE = 3

Hence, LAST option is correct.

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Express 1400 as a product of its prime factors in index form

exis [7]

Answer:

$2^3 X5^2 X7$

Step-by-step explanation:

Given the number: 1400

A number is said to be prime when it can only be divided by 1 and itself.

We can express 1400 as a product of its prime numbers by gradually decomposing it into smaller units.

$1400=14X100\\14=2X7\\100=10X10=2X5X2X5\\$Therefore:\\1400=2 X 7 X 2 X 5 X 5 X 5\\Reorganising\\1400=2 X 2 X 2 X 5 X 5 X 7\\Therefore, 1400 expressed as a product of its prime factors is:\\1400=2^3 X5^2 X7$