Need help with algebra 2!
1 answer:
Answer:
Step-by-step explanation:
First, we'll solve for the missing angle.
The interior angles of a triangle add up to 180, so let's make an equation.
Now we can use the law of sines.
Where the lowercases are the side lengths and the uppercases are the angle measures.
Plug in the values we know.
Solve using a calculator.
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Answer:
Length is 20 m and width is 4 m.
Step-by-step explanation:
Given:
Perimeter of the rectangular alley,
Length is 5 times the width.
Let width be .
So, as per question,
Length,
Now, perimeter of rectangle is given as:
Plug in 48 for ,
for
and
for b.
Therefore, width is 4 m.
Length is m.
Answer:
Summation notation is:
If you prefer it a little more simplified:
Step-by-step explanation:
First my favorite part, finding a pattern between the consecutive terms.
This is an arithmetic series because the terms are going up by 5 each time.
So arithmetic sequence, think linear equations:
x | y
1 -9
2 -4
3 1
4 6
..................
n 66
We are going to have to find that n but will will eventually...
The equation for a line in point slope form is where
is a point on the line and m is the slope.
We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).
I'm going to use the first point (1,-9).
So the equation in point slope form is
Subtract 9 on both sides:
Now we need to know how many terms we are adding so what is x if y=66.
Add 9 on both sides:
Divide both sides by 5:
Add 1 on both sides:
We have 16 terms in this sequence where the 16th term is 66.
Summation notation is:
You could simplify the 5(x-1)-9.
Distribute: 5x-5-9
Add like terms: 5x-14