What is the sum of the interior angles of the polygon shown below?
2 answers:
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Answer:
- Q9 - B) 8
- Q10 - D) 4.5
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<h2>Question 9</h2>We have a diagram and need to find the number of routes without repeat paths:
or
We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.
This gives us the number of routes:
Total number is:
The matching answer choice is B
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<h2>Question 10</h2>From the given we can observe that:
ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.
From similarity we get same ratio of corresponding sides:
We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:
As per ratio of corresponding sides:
As per segment addition:
From the two equations above we get:
Now, the required area is:
This is matching the answer choice D
Answer:
Step-by-step explanation:
Instead of using the standard form, we can use the vertex form of a quadratic equation:
Where a is the leading coefficient, and (h, k) is our vertex.
Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:
Now, we need to determine a.
We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:
Solve for a. Subtract within the parentheses:
Add 4 to both sides:
Square:
Solve:
Thererfore, the value of a is 4.
So, our function is:
Now, let’s find our roots. Set the equation to 0 and solve for x:
So, our roots are 1 and 3.
The greater root is 3 and the lesser root is 1.
Therefore, m-n, where m>n, is 3-1 or 2.
Our final answer is 2.