Answer:
This is a geometric sequence because any term divided by the previous term is a constant called the common ratio. r=36/18=18/9=2 A geometric sequence is expressed as
\begin{gathered}a_n=ar^{n-1},\text{ where a=initial term, r=common ratio, n=term number}\\ \\ a_n=9(2^{n-1})\\ \\ a_6=9(2^5)\\ \\ a_6=288\end{gathered}an=arn−1, where a=initial term, r=common ratio, n=term numberan=9(2n−1)a6=9(25)a6=288
Answer: The sailboat is at a distance of 15 km from the port.
Step-by-step explanation: Given that a sail boat leaves port and sails 12 kilometers west and then 9 kilometers north.
We are to find the distance between the sailboat from the port in kilometers.
Since the directions west and north are at right-angles, we can visualize the movement of the sailboat in the form of a right-angled triangle as shown in the attached figure.
The sailboat moves leaves the port at P and reach O after sailing 12 km west. From point O, again it moves towards north 9 km and reach the point S.
PS = ?
Using the Pythagoras theorem, we have from right-angled triangle SOP,
Thus, the sailboat is at a distance of 15 km from the port.
Answer:
(7,2)
Step-by-step explanation:
x + y = 9 + 2x - 3y = 8 is really two equations, and you should show this by separating x + y = 9 from 2x - 3y = 8 through the use of a comma, or the word "and," or through writing only one equation per line.
Here you have the system of linear equations
x + y = 9
2x - 3y = 8.
Let's solve this system by elimination. Mult. the 1st eqn by 3, obtaining the system
3x + 3y = 27
2x - 3y = 8
-------------------
5x = 35, so that x = 7. Subbing 7 for x in x + y = 9, we get 7 + y = 9, indicating that y = 2.
Thus, the solution to this system of equations is (7,2).
Answer: Z.
Step-by-step explanation:
They want you to figure formula then find right graph, but do it fastest way. If it doubles each year, graph can't be straight line, eliminate Y.
A(0) has to be $5, eliminate W. A(1) has to be double A(0), eliminate X. Check: Z shows A(1) is 10, A(2) is 20.
Answer:the orginal price of the tennis racket is $47
Step-by-step explanation:
Let x represent the original price of the tennis racket at the sports store.
Leah has a 20% off coupon for the sports store. The tennis racket is available at a discount of 10%.
The store applies the coupon after the 10% is taken. The value of the discount on the original price of the tennis racket would be
10/100 × x = 0.1 × x = $0.1x
The discounted price of the racket would be
x - 0.1x = 0.9x
The value of the coupon would be
20/100 × 0.9x = 0.2 × 0.9x = 0.18x
The selling price after the coupon was applied would be
0.9x - 0.18x = 0.72x
She buys the racket for $34. This means that
0.72x = 34
x = 34/0.72 = $47
