Answer:
Step-by-step explanation:
Factor the Polynomial.
3
x
4
(
x
+
5
)
2
Answer: "12" .__________________________________ " x = 12 " .__________________________________
Explanation:
__________________________________
The TWO (2) angles:
Angle 1) "(10x − 20)° " ; AND:
Angle 2) " (6x + 8)° " ;
______________________________
form a "straight line" ; so by definition; ∡1 and ∡2 are supplementary angles; and as such, m∡1 and m∡2 add up to 180°.
We are asked to solve for "x" .
___________________________________
10x − 20 + 6x + 8 = 180 ;
Combine the "like terms" on the "left-hand side" of the equation:
_________________________________________
10x + 6x = 16x ;
- 20 + 8 = -12 ;
__________________________________________
Rewrite the equation:
16x − 12 = 180 ;
__________________________________________
Add "12" to both sides of the equation;
__________________________________________
16x − 12 + 12 = 180 + 12 ;
to get:
16x = 192 ;
_________________________________________
Divide EACH SIDE of the equation by "16" ; to isolate "x" on one side of the equation; and to solve for "x" ;
_________________________________________
16x / 16 = 192 ;
x = 12 .
<span>__________________________________________
</span>Let us check our answer, by plugging in "12" for "x" in the original equation:
__________________________________________
→ 10x − 20 + 6x + 8 =? 180 ? ;
→ 10(12) − 20 + 6(12) + 8 =? 180 ? ;
→ 120 − 20 + 72 + 8 = ? 180 ?
→ 120 − 20 = 100 ; 100 + 72 = 172; 172 + 80 =? 180 ? Yes!
__________________________________________________________
A is the weight
B is the frequency
C is weight times frequency
D is mean minus weight
E is D raised to the 2nd power ; variance
F is E times frequency ; total variance
A B C D E F
65 1 65 7.97 63.47 63.47
68 2 136 4.97 24.70 49.40
69 5 345 3.97 15.76 78.80
70 8 560 2.97 8.82 70.57
71 7 497 1.97 3.88 27.17
72 3 216 0.97 0.94 2.82
90 2 180 17.03 290.02 580.04
95 <u> 2 </u> <u> 190 </u> 22.03 485.32 <u> 970.64</u>
30 2,189 1,842.91
2,189 / 30 = 72.97 mean
1,842.91 / 30 = 61.43 variance
√61.43 = 7.8377 or 7.84 standard deviation.