By using the rules that the value inside square root can’t be negative and the denominator value can’t be zero, the domain for the given function is a) x<-1 and x>1 b) p≤1/2 c) s>-1.
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Write the restrictions that should be imposed on the variable for each of the following function. Then find, explicitly, the domain for each function and write it in the interval notation a) f(x)=(x-2)/(x-1) b) g(p)=√(1-2p) c) m(s)= (s^2+4s+4)/√(s+1)
Ans. We know that a number is not divisible by zero and number inside a square root can not be negative. In both the cases the outcome will be imaginary.
a) For this case the denominator x-1 can not be zero. So, x ≠1 and the domain is x<-1 and x>1.
b) For this case the value inside square root can’t be negative. So, p can’t be greater than 1/2 the domain is p≤1/2.
c) For this case also the value inside square root can’t be negative and the denominator value can’t be zero. So, s can’t equal or less than -1 and domain is s>-1.
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Answer: The length of AC is 18 ft.
Step-by-step explanation:
By the given diagram,
AM = MB and CN = NB
M and N are the mid points of the sides AB and CB respectively,
Thus, by the mid point theorem,
MN ║ AC,
By the alternative interior angle theorem,
∠BMN ≅ ∠BAC
∠BNM ≅ ∠BCA
Thus, by AA similarity postulate,
ΔBMN ≅ ΔBAC
By the property of similar triangles,





Thus, The length of AC is 18 ft.
Answer:
8 and 12
Step-by-step explanation:
The perimeter of the given rectangle is ...
P = 2(L +W)
P = 2(14 +21) = 2(35) = 70
The scale factor to the similar triangle is ...
similar perimeter/original perimeter = 40/70 = 4/7
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The dimensions of the similar triangle are the original triangle dimensions multiplied by this scale factor:
(14)(4/7) = 8
(21)(4/7) = 12
The sides of the similar triangle are 8 and 12.
Answer:
3x^2-7
-7 is the constant
3 is the coefficient
x is the variable
Step-by-step explanation:
(3x^2)+(-7)
Answer: 20 students
Step-by-step explanation: 20 students who take the bus to school. Therefore thirty students do not take the bus to school.