Answer:
a₄₂ = 107
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂₇ = 66 , then
a₁ + 26d = 66 , that is
- 12 + 26d = 66 ( add 12 to both sides )
26d = 78 ( divide both sides by 26 )
d = 3
Then
a₄₂ = - 16 + (41 × 3) = - 12 + 123 = 111
Answer:
92 cm
Step by step explanation:
first: you divide the rectangle into two right angled triangles using the diagonal
secondly:
you use pythagoras theorem to find the width of the rectangle
110²= 60²+ w²
w²= 110²- 60²
w²= 12100- 3600
w²= 8500
w= 92.195
w= 92 cm
Answer:
The shortest height is 36 inches
Step-by-step explanation:
Here in this question, we want to know the shortest height with which boxes of 12 inches tall staked will be the same height with which boxes of 18 inches staked beside it
This is a question that has to do with multiples; In other words, we are simply looking for the lowest common multiple of 12 and 18;
The multiples of both are as follows;
12 - 12, 24,36,48,60•••••
18-18,36,54,72••••••
We can see that at the point 36, both have their first multiple match
So we can say that the lowest common multiple of 18 and 12 is 36
Answer:
sin O = 
Step-by-step explanation:
given tan O = 
= 
Then this is a right triangle with legs 3 and 4
Using Pythagoras' identity then the hypotenuse (h ) is
h = 
= 
= 5, hence
sin O = 
=
Answer:
Step-by-step explanation:
To find (fg)(x), we have to look at f(x) and g(x) and multiply the two quantities together. We are already given the two quantities individually so all that is left is the multiplication:
If we reorder the terms to go from highest degree to lowest, we get our final answer to be the following:
