Answer:
3x+4=19
Step-by-step explanation:
let x be how much longer she can run the race and still beat her previous time
55(min) + x(min) < 1(hr) + 10(min)
55(min) + x(min) < 60(min) + 10(min)
55 + x < 60 + 10
x < 60 + 10 - 55
x < 15(min)
since isosceles has 2 sides that are equal then,
270 - 108 = 162
divide 162 by 2
162 ÷ 2 = 81
so, C
The right answer is C)
Consistent and independent system of two linear equations is a system such that there is only one solution for the system, that is, the two straight lines cross at a point. So we can analyze each case and I have attached some graphs to provided you with examples. Those graphs aren't about the equations but it's about general cases:
A) Consistent and dependent. If we divide this given equation by 2 we get the same line. (See Figure 1)
B) Inconsistent. No solutions. (See Figure 2)
C) Consistent and Independent. (See Figure 3)
D) Consistent and dependent.
Answer:
(a) 0.4242
(b) 0.0707
Step-by-step explanation:
The total number of ways of selecting 8 herbs from 12 is

(a) If 2 herbs are selected, then there are 8 - 2 = 6 herbs to be selected from 12 - 8 = 10. The number of ways of the selection is then

Note that this is the number of ways that both are included. We would have multiplied by 2! if any of them were to be included.
The probability = 
(b) If 5 herbs are selected, then there are 8 - 5 = 3 herbs to be selected from 12 - 5 = 7. The number of ways of the selection is then

This is the number of ways that both are included. We would have multiplied by 5! if any of them were to be included. In that case, our probability will exceed 1; this implies that certainly, at least, one of them is included.
The probability = 