The 1 is in the ten thousands place
If the triangles are similar, the base should be 24 inches. The legs on the first triangle are 12 inches. To get 36 inches (the other triangle), we multiply 12 by 3. 12 x 3 = 36. Because you did that to the legs, you must also do it to the base. 8 x 3 = 24. Therefore, the base of the second triangle is 24 inches.
Answer: b
Step-by-step explanation:
Answer:
Radius: 

Step-by-step explanation:
Given

Solving (a): The radius of the circle
First, we express the equation as:

Where


So, we have:

Divide through by 9

Rewrite as:

Group the expression into 2
![[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B12%7D%7B9%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
![[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
Next, we complete the square on each group.
For ![[x^2 + 3x]](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D)
1: Divide the 
2: Take the 
3: Add this 
So, we have:
![[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
![[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%20%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2)
Factorize
![[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2)
Apply the same to y
![[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2%20%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%5Cfrac%7B9%7D%7B4%7D%20%2B%5Cfrac%7B16%7D%7B36%7D)
Add the fractions
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B-19%20%2A%204%20%2B%209%20%2A%209%20%2B%2016%20%2A%201%7D%7B36%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B21%7D%7B36%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B2%7D%7B3%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
Recall that:

By comparison:

Take square roots of both sides

Split

Rationalize





Solving (b): The center
Recall that:

Where


From:
![[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B2%7D%7B3%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
and 
Solve for h and k
and 
Hence, the center is:

Hello!
We are trying to describe the behavior of the graph given in the question.
To help us understand how to solve this question, we would need to understand <u>concavity.</u>
There are two types of concavity:
- Concave <em>up</em>
- Concave <em>down</em>
When a graph is concave up, the slope of the line would look like a "U".
When a graph is concave down, the slope of the line would look like a "U" that is flipped upside down.
In this case, we can see that the graph is concave down.
We can tell that the <em>slope</em> is negative due to the fact that the slope is going <u>down,</u> which results in the graph having a negative slope.
We can also tell that the graph is decreasing due to the fact that the line is doing downward.
Answer:
C). negative and decreasing