Answer:
1179
Step-by-step explanation:
Answer:
A. y=
x-3
B.y=
x-3
Step-by-step explanation:
Okay so essentially, the first thing you need to do is find the slope and y intercept for each equation. To find the slope, I like to look at the two points and divide the rise (How much it goes up or down) by the run (How much it moves left or right). For A the rise is 6 and the run is 4, so the slope is 6/4 or 3/2. To find the equation for A, you also need the y-intercept which is just the y value (how high up or down) it is when it crosses the y axis. In graph a, this is at -3. Because the equation of a line is y=mx+b (m being slope and b being y intercept), we know the equation for a is y=
x-3. We can do the same thing for B. The rise is -3 and the run is 4, so the slope is -3/4. The y value when x is equal to zero is 2, so that is the y intercept. The equation is y=
x-3
Hello there!
Given the sequence:
![\displaystyle \large{ 1, - 3,9, - 27,...}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%201%2C%20-%203%2C9%2C%20-%2027%2C...%7D)
The question reveals it to be geometric sequence since it has common ratio.
<u>G</u><u>e</u><u>o</u><u>m</u><u>e</u><u>t</u><u>r</u><u>i</u><u>c</u><u> </u><u>S</u><u>e</u><u>q</u><u>u</u><u>e</u><u>n</u><u>c</u><u>e</u> / <u>R</u><u>a</u><u>t</u><u>i</u><u>o</u><u> </u><u>F</u><u>o</u><u>r</u><u>m</u><u>u</u><u>l</u><u>a</u>
<u>
</u>
Define 'r' as common ratio.
First, let's check the common ratio by using the formula above.
<u>R</u><u>a</u><u>t</u><u>i</u><u>o</u><u> </u><u>C</u><u>h</u><u>e</u><u>c</u><u>k</u>
![\displaystyle \large{r = \frac{ - 3}{1} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ 9}{ - 3} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ - 27}{9} \longrightarrow - 3 }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7Br%20%3D%20%20%5Cfrac%7B%20-%203%7D%7B1%7D%20%5Clongrightarrow%20%20-%203%20%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7Br%20%3D%20%20%5Cfrac%7B%209%7D%7B%20-%203%7D%20%5Clongrightarrow%20%20-%203%20%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7Br%20%3D%20%20%5Cfrac%7B%20-%2027%7D%7B9%7D%20%5Clongrightarrow%20%20-%203%20%7D)
Therefore, the common ratio or r-value is -3.
To find the 7th term of sequence, you can by using the General Geometric Terms.
<u>G</u><u>e</u><u>n</u><u>e</u><u>r</u><u>a</u><u>l</u><u> </u><u>T</u><u>e</u><u>r</u><u>m</u><u> </u><u>o</u><u>f</u><u> </u><u>G</u><u>e</u><u>o</u><u>m</u><u>e</u><u>t</u><u>r</u><u>i</u><u>c</u>
![\displaystyle \large{a_n = a_1 {r}^{n - 1} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7Ba_n%20%3D%20a_1%20%7Br%7D%5E%7Bn%20-%201%7D%20%7D)
a1 is defined as the first term of sequence.
r is common ratio.
n is the term.
Since we want to find 7th term:
![\displaystyle \large{a_7 =1{( - 3)}^{7 - 1} } \\ \displaystyle \large{a_7 =1{( - 3)}^{6} } \\ \displaystyle \large{a_7 =729 }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7Ba_7%20%3D1%7B%28%20-%203%29%7D%5E%7B7%20-%201%7D%20%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7Ba_7%20%3D1%7B%28%20-%203%29%7D%5E%7B6%7D%20%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7Ba_7%20%3D729%20%7D)
Therefore, the 7th term of this sequence is 729.
Let me know if you have any questions!
Topic: Sequence and Series / Geometric Sequence
Area= 1/2 b xh
Sooo= 1/2 x 12 x 7= 42
Answer: 42 inches squared