In this number tree, the integers greater than or equal to 0 are written out in increasing order, with the top row containing on
1 answer:
Answer:
The fifth integer in row 10 using the number tree pattern is 515.
Step-by-step explanation:
The attached picture is instrumental to understanding the solution to this. There are different methods to approach this problem. But we will use observations to solve the problem.
Looking at the tree diagram, we see that the first row has 1 integer, the second has 2, the third has 4 and the fourth has 8. From here, we can see that a row has 2^n numbers where n = 0, 1, 2, 3, 4, . . .
Row 1 = 2^0 = 1 number
Row 2 = 2^1 = 2 numbers
Row 3 = 2^2 = 4 numbers
Row 4 = 2^3 = 8 numbers. And so on.
Also we notice that the last number in row 4 is 14. This can be gotten by adding the total number of numbers from row 1 to row 4 which is
1 + 2 + 4 + 8 = 15 but the first number on the chart is 0 which means we have to take out the first integer to get the last integer on row 4. Doing this, we have 14.
Since our aim is to know the fifth number in row 10, then we need to know the last number in row 9 then count from the first number in row 10 to the fifth. Using 2^n to get the number of numbers in each row like we've done above we can add the number of numbers to know the total numbers we have from row 1 to row 9 as follows:
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 = 511
As we've said previously, 0 is the first integer in the tree and should be removed to know the last number in row 9. This would be 510.
If 510 is the last number in row 9 is 510, then the first number in row 10 would be 511. Counting to the fifth number we get to 515. Thus the fifth number in row 10 using the number tree pattern is 515.
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Answer:
B is the triangle
A and E can be thought of as triangles as well with angles 0°, 0° and 180°, but it will be just a line with 3 points. So it depends whether this is a question with multiple answers or not.
Step-by-step explanation:
- Thinking Process:
We need to find a formula for a triangle that uses all the sides
Cosine rule uses all sides:
we can rearrage this formula and make the angle the subject:
- now you can just put the values from each option in the question into this formula and see if it gives an answer or not.
<u>Try A. (1,2,3)</u>
put a = 1, b = 2, c = 3 (keep in mind that you can take 'a' 'b' and 'c' as 3,2 and 1 or any other arrangement within the option A(1,2,3). All we are doing here is checking whether the answer exists or not)
, now graphically it seems that this is just a line with 3 points, or technically you can think of as the sides of the triangle are overlapping each other, and the angle between the sides is 0 0 and 180. It depends on whether the question is asking you to be technical or not. Since the question already stated there are 3 line segments, so we can think of it as a triangle.
<u>Try B.(3,4,5)</u>
, this is a triangle (specifically, this is a right angled triangle)
<u>Try C.(1,10,100)</u>
from the calculator you'll see a 'math error', this shows that there is no answer, because can only accept values within -1 and 1 inclusive. Hence no such triangle exists with lengths (1,10,100).
Similarly you can try the formula with all other options, and find whose answers exists or not.
Finally, to complete the answer, let's
Try E.(1,3,4)
, hence this is also one of those "3 points on a straight line triangles" similar to A(1,2,3)
so the answer is either A,B and E OR just B
Hope this helps :)