Answer:
The function of g(x) = 5x + 2
Step-by-step explanation:
Let us use the composite function to solve the question
∵ f(x) = 2x - 1
∵ f(g(x)) = 10x + 3
→ f(g(x)) means substitute x in f(x) by g(x)
∴ f(g(x)) = 2[g(x)] - 1
→ Equate the two right sides of f(g(x))
∴ 2[g(x)] - 1 = 10x + 3
→ Add 1 to both sides
∴ 2[g(x)] - 1 + 1 = 10x + 3 + 1
∴ 2[g(x)] = 10x + 4
→ Divide each term into both sides by 2
∵
=
+ 
∴ g(x) = 5x + 2
∴ The function of g(x) = 5x + 2
Answer:
D. 
Step-by-step explanation:
Pythagorean Theorem
Step-by-step explanation:
Subtracting equation (2) from equation (1)
Substituting d = - 3 in equation (1), we find:
Hence, first term is zero.
Answer:
r = 105
Step-by-step explanation:
Given quadratic equation:
x² − 9x − 6
Quadratic formula is given by:
(-b ± √b² - 4ac) ÷ 2a
For the equation: x² - 9x - 6
a = 1, b = -9 and c = -6
Substitute in the quadratic formula:
(-b ± √b² - 4ac) ÷ 2a
(-(-9) ± √(-9)² - 4(1*-6)) ÷ 2*1
= 9 ± √105 / 2
The solution of x² − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2
Therefore, the value of r is 105