Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
Answer:
51 students.
Step-by-step explanation:
First you need to establish a rate 6/100+3/50
8*100=800 6*8=48
3/50
850-800=50 3/50
48+3=51
Answer:
8 $10 notes
Step-by-step explanation:
I started by working it backwards. $93-$3 equals $90. So we have three of our 13 notes. We need ten more. Well the most $10 notes we can have is 8. if we had 8 $10 notes that would give us $80. $90-$80=10. We can take ten and divide it by five so we have 2 $5 notes.
So in total he would have 8 $10 notes, 2 $5 notes, and $3 one dollar notes which adds up to 13 notes
Answer:
y = 11.5
Step-by-step explanation:
Given 2 secants from an external point to the circle.
Then the product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
6(6 + y) = 5(5 + 16)
36 + 6y = 5 × 21 = 105 ( subtract 36 from both sides )
6y = 69 ( divide both parts by 6 )
y = 11.5
23.
store price = 14 + 0.5(14)
store price = 21
customer price = 21 + 0.08(21)
customer price = 21 + 1.68
customer price = $22.68
24.
formula: A = P(1 + rt)
A = 140(1 + (0.03)(2))
A = 140(1.06)
A = 148.40
interest = 148.40 = 140
interest = $8.40
Hope this helps!! :)
