Answer:
Tn = -n^2 - n + 21 is the formula for the nth term.
Step-by-step explanation:
The second differences are all equal in this quadratic sequence.
Now, the quadratic sequence has a formula of Tn = an^2 + bn + c
Find the value of a in an^2 by dividing the difference by 2:
-2/2 = -1
a = -1
Since T1 is 19 and T2 is 15 we can put that into the equation and simplify:
b + c = 20
2b + c = 19
Thus, b = -1 , c = 19 and the general formula for the nth term is Tn = -n^2 - n + 21
Answer:
15/20 simplified is 3/4
Step-by-step explanation:
So a 3/4 chance or a 75% chance of not drawing a blue marble.
Answer:
a = 1.5
VW = 9 ft
Step-by-step explanation:
Since the tangent lines connect both circles, we know that the line VU and VX are congruent (equal). Thus, we can set them equal to each other and solve for a:
a + 4 = a² + 0.25 Set equal
a² - a = 3.75 Isolate a values
a² - a + 0.25 = 3.75 + 0.25 Complete the square
(a + 0.5)² = 4 Factor
a + 0.5 = 2 Simplify
a = 1.5
Now we need to calculate VW, but thats easy because its equal to TV, and since we know a, we can just plug it in:
((1.5) + 7.5) ft
9 ft
Answer:
47
Step-by-step explanation:
Simplify the following:
-26 + 6 - -67
Hint: | Multiply -1 and -67 together.
-(-67) = 67:
-26 + 6 + 67
Hint: | Evaluate 6 + 67 using long addition.
| 1 |
| 6 | 7
+ | | 6
| 7 | 3:
73 - 26
Hint: | Subtract 26 from 73.
| 6 | 13
| 7 | 3
- | 2 | 6
| 4 | 7:
Answer: 47
