Answer:
The proof is explained below.
Step-by-step explanation:
Given m∠ADB = m∠CDB and AD ≅ DC
we have to prove that m∠BAC = m∠BCA and BD⊥ AC
In ΔADO and ΔCDO
∠OAD=∠OCD (∵ADC is an isosceles triangle)
AD=DC (∵Given)
∠ADO=∠CDO (∵Given)
By ASA rule, ΔADO≅ΔCDO
In ΔBAD and ΔBCD
AD=DC (∵ABC is an isosceles triangle)
∠ADB=∠CDB (∵Given)
DB=DB (∵common)
By ASA rule, ΔADB≅ΔCDB
Now, ΔADB≅ΔCDB and ΔADO≅ΔCDO
⇒ ΔADB-ΔADO≅ΔCDB-ΔCDO
⇒ ΔABO≅ΔCBO
Hence, by CPCT, m∠BAC = m∠BCA
Now, we have to prove that BD⊥ AC i.e we have to prove m∠BOA=90°
Now, ΔABO≅ΔCBO therefore by CPCT, m∠BOA = m∠BOC
But, m∠BOA + m∠BOC=180° (linear pair)
⇒ m∠BOA + m∠BOA=180°
⇒ 2m∠BOA=180° ⇒ m∠BOA=90°
Hence, BD⊥ AC
(5x-3)(4x+5) the last step you have to look at the two terms that you are adding together the 4x(5x-3) and the 5(5x-3) and see what is similar. well the whole bracket is the same the 5x-3 so factor that out and collect the other leftover terms so the 4x and the +5 and thats what goes in the second bracket
Answer:
64 pretzels in a 16 oz bag
1 oz will contain 64/16 pretzels = 4
5 oz will therefore contain 4 x 5 = 20 pretzels
Step-by-step explanation:
See here for a deeper explanation! ^^
Hopefully it helps :)
brainly.com/question/200543
Answer:
-6x^2+21x+18
Step-by-step explanation:
Answer:
(x^4-8)^45 /180 +c
Step-by-step explanation:
If u=x^4-8, then du=(4x^3-0)dx or du=4x^3 dx by power and constant rule.
If du=4x^3 dx, then du/4=x^3 dx. I just divided both sides by 4.
Now we are ready to make substitutions into our integral.
Int(x^3 (x^4-8)^44 dx)
Int(((x^4-8)^44 x^3 dx)
Int(u^44 du/4)
1/4 Int(u^44 dul
1/4 × (u^45 / 45 )+c
Put back in terms of x:
1/4 × (x^4-8)^45/45 +c
We could multiply those fractions
(x^4-8)^45 /180 +c
