Answer:
C = F - 32 /(9/5)
Step-by-step explanation:
F = (9/5)C + 32
Subtract 32 from both sides
F - 32 = (9/5)C + 32 - 32
F - 32 = (9/5)C
Divide both sides by (9/5)
F - 32/(9/5) = (9/5)C/(9/5)
F - 32/(9/5) = C
C = F - 32 /(9/5)
Answer:
a) f(16) = 42
b) f(16) = 54
c) f(16) = 162
d) f(16) = 30
Step-by-step explanation:
a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3
b = y - mx = 6 - 3(4) = 6 - 12 = - 6
f(16) = 3(16) - 6 = 42
b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ
n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3
f(16) = 2/3 × 16ⁿ = 54
c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ
b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2
f(16) = 2eᵇ¹⁶ = 162
d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)
⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)
f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4
f(16) = a㏑(b16) = 30
X --- <span>first number
y --- </span><span>second number
x + y = 2x - 15
x - y = 2y - 5
x - 2x + y = -15
x - y - 2y = - 5
-x + y = -15
x - 3y = - 5
-----------------
-2y = -20 /:(-2)
y = 10
</span>x - 3y = - 5 ⇒ x = - 5 + 3y = - 5 + 3 · 10 = - 5 + 30 = 25
Ans.:
x = 25
y = 10
y - 14 = 12( x + 1)
the equation of a line in ' point - slope form ' is
y - b = m(x - a) → (m is slope and (a, b) a point on the line)
here m = 12 and (a , b) = ( - 1, 14)
y - 14 = 12(x - (-1)) ⇒ y - 14 = 12( x + 1)
Given:
The system of equation is
To find:
Whether (3,4) is a solution of the given system or not.
Solution:
We have,
...(i)
...(ii)
Putting the value of y in (ii) from (i), we get
Divide both sides by -7.
Putting in (i), we get
So, the only solution of the given system is 
.
Hence, (3,4) cannot be a solution of given system, Hence the correct option is B.
