Answer:
b) 6/7
c) 14
Step-by-step explanation:
b) Scale Factor = Red/(Red+Blue) = 8/(8+6) = 8/14 = 6/7.
c) x = 8+6 = 14.
EXTRA TIP: If you aren't sure, think about wheter these triangles are isosceles(from the diagram). Hope this helps!
Step-by-step explanation:
1. The first step has 1 block. The second step has 2 blocks. The third step has 3 blocks. So the nth step needs n blocks.
2. A staircase with n steps has 1 + 2 + 3 + ... + n steps. This is an arithmetic sequence where the first term is 1 and the last term is n. The sum of the first n terms is:
y = n/2 (1 + n)
3. Solve for n.
2y = n (1 + n)
2y = n² + n
0 = n² + n − 2y
Using quadratic formula:
n = [ -1 ± √(1 − 4(1)(-2y)) ] / 2
n = [ -1 + √(1 + 8y) ] / 2
N is a placeholder for a number. In this case, it is 4
We will replace every copy of 'n' with '4' and then simplify
So n+8 turns into 4+8 which simplifies to 12
Is 12 less than or equal to 13? Yes it is. Specifically it is less than 13. So n = 4 is part of the solution set.
Here is how you'd write it all out using algebra
The last inequality is true so the first inequality is true when n = 4. This is another way to see that n = 4 is a solution.
Step-by-step explanation:
the intersection of the interval: (-∞, 7) and [-5, +∞)
is [-5, 7)
and the union of the interval: (-∞, 7) and [-5, +∞)
is (-oo, +oo)