Answer:
x = -4
x = -6
Step-by-step explanation:
X^2+10x+24=0
(b/2)^2 = (10/2)^2 = 25
X^2+10x+25=-24+25
(x+5)^2 = 1
(x+5) = ± 1
x = +1 -5 = -4
x = -1 -5 = -6
(5 + 2) + 1 = 5 + (2 + 1)
Total angles on a straight line
(9x + 8) + 37 = 180
9x + 45 = 180
9x = 180 - 45
9x = 135
Divide through by 9
x = 15
The series' value is maximized if the sum only consists of positive terms. Notice that each term in the sum takes the form 4<em>n</em> + 1 for integer <em>n</em>. This means the smallest positive integer that the sum can involve is 1, so the maximum value is
<em>S</em> = 29 + 25 + 21 + … + 9 + 5 + 1
Reversing the order of terms gives the same sum,
<em>S</em> = 1 + 5 + 9 + … + 21 + 25 + 29
Adding terms in the same positions gives us twice this sum,
2<em>S</em> = (29 + 1) + (25 + 5) + (21 + 9) + … + (1 + 29)
Notice how each grouped sum adds to 30. There are 8 terms in the sum, since 4<em>n</em> + 1 = 29 when <em>n</em> = 8. So
2<em>S</em> = 8 × 30 = 240 ===> <em>S</em> = 120
3.5 because 42 divided by 12 is 3.5
