Answer:
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form: x=-45
x
=
−
5
4
Decimal Form:x=-1.25
x
=
−
1.25
Mixed Number Form:x=-14
x
=
−
1
1
4
Answer:
B.a vertical shift of 9 units up
Step-by-step explanation:
Given 

It means shifting
unit vertically.
Now, we will find the value of
for the given function


Hence, vertical shift of 9 units.
Answer:
2^3 * 5^2
Step-by-step explanation:
We need to break 200 down into prime numbers
200 = 20*10 These are not prime
= 4*5 * 2*5 The 4 is not prime
= 2*2*5 * 2*5 This is prime
Rearranging
= 2*2*2*5*5
= 2^3 * 5^2
Answer:
18
Step-by-step explanation:
You can see from the table that 2 bracelets are made every 30 minutes.
There are 9 intervals of 30 minutes each in 4.5 hours.
So, the number of bracelets that are made in 4.5 hours is
9x2=18
Another way to see this is to note from the table that 4 bracelets are made in 60 minute, which is 1 hour. So, in 4 hours, 16 bracelets will be made. Also, from the table, 2 bracelets are made in 30 minutes, which is 1/2 hour. So, adding up, 18 bracelets are made in 4.5 hours.
Answer:
see explanation
Step-by-step explanation:
The n th term ( explicit formula ) of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₁₂ = - 95 and a₃₇ = - 270 , then
a₁ + 11d = - 95 → (1)
a₁ + 36d = - 270 → (2)
Subtract (1) from (2) term by term to eliminate a₁
25d = - 175 ( divide both sides by 25 )
d = - 7
Substitute d = - 7 into (1) and solve for a₁
a₁ + 11(- 7) = - 95
a₁ - 77 = - 95 ( add 77 to both sides )
a₁ = - 18 , thus
= - 18 - 7(n - 1) = - 18 - 7n + 7 = - 7n - 11
= - 7n - 11 ← explicit formula
--------------------------------------------------------------
The recursive formula allows a term in the sequence to be found by adding the common difference d to the previous term, thus
=
- 7 with a₁ = - 18 ← recursive formula