5/6 x 12
60 / 6 = 10
It takes 10 feet of string to make 12 bracelets.
Answer:
Last option.
Step-by-step explanation:
The consecutive exterior angle theorem states that the exterior angles are supplementary if two lines are cut by a transversal.
m∠1 + m∠7 = 180
m∠2 + m∠8 = 180
Answer:
D.5
Step-by-step explanation:
You can write the following equations from the information given:
y=x+3 (1)
11x+5y=47 (2)
x is the number of hardback books
y is the number of paperback books
You can replace (1) in (2):
11x+5(x+3)=47
11x+5x+15=47
16x=47-15
16x=32
x=32/16
x=2
Then, you can replace the value of x in (1) to find the value of y:
y=2+3
y=5
According to this, the answer is that Jamal bought 5 paperback books.
Answer:
∫
= 
Step-by-step explanation:
To find:
∫
Solution:
Method of substitution:
Let 
Differentiate both sides with respect to 

[use
]
So,
∫
= ∫
=
where
is a variable.
(Use ∫
)
Put 
∫
= 
Use 
So,
∫
= 
where 
Without using substitution:
∫
= ∫
= 
So, same answer is obtained in both the cases.
Answer:
a₁ = - 24
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₇ = 2a₅ , then
a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )
- a₁ - 2d = 0 → (1)
The sum to n terms of an AP is
=
[ 2a₁ + (n - 1)d ]
Given
= 84 , then
(2a₁ + 6d) = 84
3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )
2a₁ + 6d = 24 → (2)
Thus we have 2 equations
- a₁ - 2d = 0 → (1)
2a₁ + 6d = 24 → (2)
Multiplying (1) by 3 and adding to (2) will eliminate d
- 3a₁ - 6d = 0 → (3)
Add (2) and (3) term by term to eliminate d
- a₁ = 24 ( multiply both sides by - 1 )
a₁ = - 24