$\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=1\\
r=3\\
n=7
\end{cases}
\\\\\\
a_7=1\cdot 3^{7-1}\implies a_7=1\cdot 3^6\implies a_7=1\cdot 729\implies a_7=729$

7 0

3 years ago

(−3 + 8i)(−3 − 8i) =

Mice21 [21]

Answer: 73

Step-by-step explanation:

Multiply using the FOIL method, then combine the real and imaginary parts of the expression.

8 0

3 years ago

Jose takes a job that offers a monthly starting salary of $2200 and guarantees him a monthly raise of $105 during his first year

vodka [1.7K]

Answer:

$3355

Step-by-step explanation:

Since the job offers starting salary of $2200 and monthly raise of $105 during his first year of training.

∴ a = 2200 and d = 105

Since the general form of A.P is,

a, a + d, a + 2d, a + 3d, ............. $a_{n}$

Where, $a_{n}$ is the last term of A.P or his monthly salary at the end of his training and n is the number of terms in a series.

So, the A.P is:

2200, 2200 + 105, 2200 + 2(105) ......... $a_{n}$

2200, 2305, 2410 ............ $a_{n}$

Since there is 12 month in a year therefore, n = 12.

$a_{n} = a + (n - 1) d\\$

. $a_{n}$ = 2200 + ( 12 - 1) × 105

= 2200 + 11 × 105

= 2200 + 1155

= 3355

∴ . $a_{n}$ = 3355

So the monthly salary of Jose at the end of his training is 3355$.

8 0

3 years ago

What is the area of the triangle in the diagram?

Vladimir [108]

1/2sqrt((x_1^2+y_1^2)(x_2^2+y_2^2))

The area of a triangle is equal to 1/2bh (one half base times height). Since this is a right triangle, the base and height are the two legs connected to the 90* angle. To find the values of these sides, we will use Pythagorean Theorem, root a squared plus b squared.

Short leg: <x(1),y(1)>

This leg can be seen as the hypotenuse of an invisible right triangle. The x value, x(1), is how far over the x value has gone from the origon at x=0. Imagine a leg alone the x-axis, going from (0,0) to (x(1),0). The y value of the point, y(1), works the same way. This leg will go from our previous mark at (x(1),0) to the point (x(1),y(1)). This shows that the short leg of the main triangle is the hypotenuse, with a height of y(1) and base of x(1). Pythagoreum Theorem shows that the length of this leg is equal to sqrt(x_1^2+y_1^2).

Long leg: <x(2), y(2)>

The same process works here, giving us sqrt(x_2^2+y_2^2).

Now for the area, we have the b and h values. Our equation reads 1/2sqrt(x_1^2+y_1^2)sqrt(x_2^2+y_2^2).

But we can simplify this (yay). The two square roots can be written together as sqrt((x_1^2+y_1^2)(x_2^2+y_2^2))

So the correct answer is 1/2sqrt((x_1^2+y_1^2)(x_2^2+y_2^2))

5 0

3 years ago

Read 2 more answers