Answer:
x = 9
Step-by-step explanation:
Rule: the two interior angles F and E when added, equal <FGH.
so
6x + 16 + 60 = 13x + 13 Combine the terms on the left.
6x + 76 = 13x + 13 Subtract 13 from both sides.
6x + 76-13 = 13x Combine
6x + 63 = 13x Subtract 6x from both sides.
63 = 7x Divide by 7
63/7 = x
x = 9
The sample space is:
(1, 1); (1, 2) - sum of 3; (1, 3); (1, 4); (1, 5) - sum of 6; (1, 6);
(2, 1) - sum of 3; (2, 2); (2, 3); (2, 4) - sum of 6; (2, 5); (2, 6);
(3, 1); (3, 2); (3, 3) - sum of 6; (3, 4); (3, 5); (3, 6) - sum of 9;
(4, 1); (4, 2) - sum of 6; (4, 3); (4, 4); (4, 5) - sum of 9; (4, 6);
(5, 1) - sum of 6; (5, 2); (5, 3); (5, 4) - sum of 9; (5, 5); (5, 6);
(6, 1): (6, 2); (6, 3) - sum of 9; (6, 4); (6, 5); (6, 6)
![\bf \cfrac{(x-2)(x+3)}{2x+2}\implies \cfrac{x^2+x-6}{2x+2}~~ \begin{array}{llll} \leftarrow \textit{2nd degree polynomial}\\ \leftarrow \textit{1st degree polynomial} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{vertical asymptote}}{2x+2=0}\implies 2x=-2\implies x=-\cfrac{2}{2}\implies x=-1](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%28x-2%29%28x%2B3%29%7D%7B2x%2B2%7D%5Cimplies%20%5Ccfrac%7Bx%5E2%2Bx-6%7D%7B2x%2B2%7D~~%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Cleftarrow%20%5Ctextit%7B2nd%20degree%20polynomial%7D%5C%5C%20%5Cleftarrow%20%5Ctextit%7B1st%20degree%20polynomial%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bvertical%20asymptote%7D%7D%7B2x%2B2%3D0%7D%5Cimplies%202x%3D-2%5Cimplies%20x%3D-%5Ccfrac%7B2%7D%7B2%7D%5Cimplies%20x%3D-1)
when the degree of the numerator is greater than the denominator's, then it has no horizontal asymptotes.
quick note:
when the degree of the numerator is 1 higher than the degree of the denominator, then it has an slant-asymptote, so this one has a slant-asymptote.
A) the slope of the line: -5/11
b) the perpendicular slope of the line: 11/5
Answer:
Part A : <u>|x-2.5| ≤ 0.75 , x ∈ [1.75,3.5]</u>
Part B : yes, the lifeguard should add more chlorine.
Step-by-step explanation:
Part A:
Let C is the variation of the level of chlorine in a hot tub.
Level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
To find absolute value inequality, need to find the standard level of chlorine 1.75 + C or 3.25 - C
1.75 + C = 3.25 - C
2C = 5
C = 2.5
So, the standard level would be 2.5 ppm,
If x represents the present level of chlorine,
Then it would be lie within 1.75 ppm of 3.25 ppm.
1.75 ≤ x ≤ 3.25
Subtract 2.5 from all sides
1.75 - 2.5 ≤ x -2.5 ≤ 3.25 - 2.5
-0.75 ≤ (x-2.5) ≤ 0.75
which is equivalent to the following absolute value inequality.
<u>|x-2.5| ≤ 0.75</u>
<u>And the solve of the inequality : x ∈ [1.75,3.5]</u>
Part B: If x = 1.0 ppm,
∴ |1.0-2.5| = 1.5 which is not less than equal to 0.75.
Another explanation:
the minimum safe level of chlorine in a hot tub is 1.75 ppm
Since 1 < 1.75
Therefore, lifeguard should add more chlorine.
