Answer:
Step-by-step explanation:
Each year, he gets a 3 percent raise. This means that his salary between consecutive years increasing by a common ratio. The formula for determining the sum of the first n terms, Sn of a geometric sequence is expressed as
Sn = (ar^n - 1)/(r - 1)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
From the information given,
a = 35000
r = 1 + 3/100 = 1 + 0.03 = 1.03
Therefore, the expression that gives the total amount Alex has earned in his first n years of his career is
Sn = [35000(1.03)^n - 1]/(1.03 - 1)
Sn = [35000(1.03)^n - 1]/0.03
Answer:
x=-5
Step-by-step explanation:
Vertical lines have the same x value all the time. They are of the form x=
Since it passes through the point (-5,-2) the x value must be -5
x=-5
Answer:
Movie: $4.25
Video Game: $5.25
Step-by-step explanation:
For this problem, we can use system of equations to solve for the rental costs of the movies and video games. Let's use x for movies and y for video games.
Equation 1
5x+3y=37
Equation 2
2x+6y=40
To start, we can use elimination to solve for x and y. Let's cancel out y. To do so, we have to multiply the first equation by 2 to get the y equal.
10x+6y=74
Now that the y are equal, we can subtract both equations.
8x=34
x=4.25
The movie rental cost is $4.25.
Now that we know x, we can plug in to find y.
2(4.25)+6y=40
8.5+6y=40
6y=31.5
y=5.25
The rental cost for video games is $5.25.
Answer:
<h2>After two seconds, the ball reached 9 units up.</h2>
Step-by-step explanation:
The given function is
The given function models the path of the ball.
The maxium height the ball reached is given by the vertex of this function, which has coordinates 
, where 
and 
.
From the equation, we know that 
, 
and 
. Replacing these values, we have
Where 
determines the height and 
the time when the maximum height was reached by the ball.
The maximum height is 9 units.
Therefore, after two seconds, the ball reached 9 units up.
The area for 27 is 64cm^2.
For the mean, you add up all the numbers then divide by how many numbers there are. So you would do 45+96+100+39+50 and divide it by 5. So your mean is 66.
Now for 29.
For when n=5 is 8
For when n=8 is 14
For when n=14 is 26
Hope this helps!
