Answer:
The perpendicular line would be y = -3x - 7
Step-by-step explanation:
To find the equation of the line, we first need to solve the original line for y.
-x + 3y = 9
3y = x + 9
y = 1/3x + 3
Now we know the slope of the original line to be 1/3. Since perpendicular lines have opposite and reciprocal slope, we know the new line to have a slope of -3. We can then use that along with the given point in point-slope form to find the equation.
y - y1 = m(x - x1)
y - 2 = -3(x + 3)
y - 2 = -3x - 9
y = -3x - 7
Answer:
The hexagon has an area of 220.6 square units.
Step-by-step explanation:
You can solve this by realising that the hexagon can be divided into 6 equilateral triangles of the same area.
The area of the triangle is the same as a rectangle of the same width and height, but divided by two, and we're told that the width of the side is 9.2, and the height is eight. So the total area of the hexagon is:
6 × (9.2 × 8) / 2
= 9.2 × 24
= 220.6
So the hexagon has an area of 220.6 square units.
hello :<span>
<span>an equation of the circle Center at the
O(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =0 and b = 0 (Center at the origin)
r = AO
r² = (AO)²
r² = (4-0)² +(5-0)² = 16+25=41
an equation of the circle that satisfies the stated conditions.
Center at the origin, passing through B(4, 5) is : x² +y² = 41</span></span>
x² +y² - 41=0
Answer: 10 inches
Step-by-step explanation:
200/10 = 20
20 x 0.5 = 10
To solve this, we are going to use the recursive formula for a geometric sequence:
where
is the nth term of the geometric sequence.
is the first term of the geometric sequence.
is the common ratio
is the position of the term in the sequence.
We know that the starting salary is $42,000, so
. Now, to find the common ratio
, we need to find the next term in the sequence first:
We know from our problem that t<span>he company automatically gives a raise of 3% per year, so the next term in the sequence will be 42000 + 3%(42000) = 42000 + 1260 = 43260. Remember that the common ratio is the current term of the geometric sequence divided by the previous term of the sequence; we know that our current term is 43260 and the previous term is 42000, so:
</span>
<span>Now we can plug the values in our recursive formula:
</span>
We can conclude that the recursive definition for the geometric sequence formed by the salary increase is: