Answer:
4<C
<10
Step-by-step explanation:
Theorem: Given a triangle with sides A, B and C the sum of the lengths of any two sides of a triangle must be greater than the third side:
1. A+B>C
2. B
+C
>A
3. A+C>B
Thus given two sides of A=3 and B=7 C can be:
7
−3<C
<
7+3
C range
4<C
<10
Answer:
x = y - 13
Step-by-step explanation:
y = 1/2 of mike's debt
x = Ted's debt
x = y - 13
Answer:
1.) 8.09g ; 2) 206.7 years
Step-by-step explanation:
Given the following :
Half-life(t1/2) of Uranium-232 = 68.9 years
a) If you have a 100 gram sample, how much would be left after 250 years?
Initial quantity (No) = 100g
Time elapsed (t) = 250 years
Find the quantity of substance remaining (N(t))
Recall :
N(t) = No(0.5)^(t/t1/2)
N(250) = 100(0.5)^(250/68.9)
N(250) = 100(0.5)^3.6284470
N(250) = 100 × 0.0808590
= 8.0859045
= 8.09g
2) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?
Using the relation :
N / No = (1/2)^n
Where N = Amount of remaining or left
No = Original quantity
n = number of half-lifes
N = 12.5g ; No = 100g
12.5 / 100 = (1/2)^n
0.125 = (1/2)^n
Converting 0.125 to fraction
(1/8) = 1/2^n
8 = 2^n
2^3 = 2^n
n = 3
Recall ;
Number of half life's (n) = t / t1/2
t = time elapsed ; t1/2 = half life
3 = t / 68.9
t = 3 × 68.9
t = 206.7 years
The slope of the rise over run.
Answer:
y + 9 = - 2(x - 9)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (9, - 9) and (x₂, y₂ ) = (- 2, 13)
m = 
= 
= - 2
Using (a, b ) = (9, - 9 ) , then
y - (- 9) = - 2(x - 9) , that is
y + 9 = - 2(x - 9)
