Answer:
15 cm
Step-by-step explanation:
The length of the shorter pole can be found by forming and subsequently solving 2 equations.
Start by defining the variables that are going to be used in the working.
Let the original length of the shorter pole be a cm and that of the longer pole be b cm.
'Product' refers to the multiplication operation.
ab= 285 -----(1)
On the other hand, 'sum' refers to the addition operation.
Length of shorter pole after cutting= a -2
Length of longer pole after cutting= b -2
(a -2) +(b-2)= 30
a +b -4= 30
Adding 4 to both sides:
a +b= 30 +4
a +b= 34 -----(2)
From (2):
a= 34 -b -----(3)
Let's solve by substitution:
Substitute (3) into (1):
b(34 -b)= 285
Expand:
34b -b²= 285
b² -34b +285= 0
Factorise:
(b -15)(b -19)= 0
b -15= 0 or b -19= 0
b= 15 or b= 19
Substitute into (1):
a(15)= 285 or a(19)= 285
a= 285 ÷15 or a= 285 ÷19
a= 19 or a= 15
Since a <b, a= 15 and b= 19.
Thus, the length of the shorter pole is 15 cm.
Answer:
1/6
1/6
1/36
Events A and B are independent
Step-by-step explanation:
Suppose:
A = event that first die lands on 2
B = event that second die lands on 2
Sample space:
Die 1 = 1,2,3,4,5,6
Die 2 = 1,2,3,4,5,6
Sample space of both die combined is attached below
Probability = (total number of required outcomes / total number of possible outcomes)
Probability that first die lands on 2:
P(A) = 1/6
Probability that second die lands on 2:
P(B) = 1/6
Probability of A and B:
P(A and B) = 1/6 × 1/6 = 1/36
Evebts A and B are independent because, the outcome of one event does not affect the occurrence of the other event.
Each room has width a, length b and heigth c. Let's use following formulas for area:
Floor and ceiling:
A1=a*b
Left and right wall:
A2=b*c
Front and back wall:
A3=a*c
a=30ft
b=20ft
c=9ft
We do not need to paint floor and ceiling, so total area that needs to be painted is:
A(unit)=2*A2+2*A3
A(unit)=2*b*c+2*a*c
A(unit)=2*20*9+2*30*9
A(unit)=360+540
A(unit)=900ft^2
We have 4 units so total area that needs to be painted is:
A(total)=4*A(unit)
A(total)=4*900
A(total)=3600ft^2
Answer:
C) $171.52
Step-by-step explanation:
First she returned something which gave her more money than she started with. (165+46.5=211.5). Then she spent 11.98 (for socks) and 28.00 (for lunch and movie) both of which decreased her money. So (211.5 - (11.98+28)) = $171.52
<span>4k – 6 = -2k – 16 – 2
</span>4k+2k = – 16 – 2+6
6k=-12
k=-2
Hope this helps