Answer:
The answer to your question is (f°g)(x) = -5856x⁶ - 25529x⁴ -52710x² - 36220
Step-by-step explanation:
Data
f(x) = -12x³ + 19x² - 5
g(x) = 7x² + 15
find (f°g)(x)
Process
1.- Substitute g(x) in all the x of f(x)
(f°g)(x) = -12(7x² + 15)³ + 19(7x² + 15)² - 5
-Expand
(f°g)(x) = -12[4913x⁶ + 2205x⁴ + 4725x² + 3375] + 19(49x⁴ + 210x² + 225) - 5
-Simplify
(f°g)(x) = -58956x⁶ - 26460x⁴ - 56700x² - 40500 + 931x⁴ + 3990x² + 4275 -
5
-Result
(f°g)(x) = -5856x⁶ - 25529x⁴ -52710x² - 36220
Answer:
B. The value of C is 1
Step-by-step explanation:
Given:
- y = 2x + C is a tangent to parabola y² = 8x
To find:
A line being a tangent to curve means both equations are equal but there has to be only one interception between both graphs.
Therefore, substitute y = 2x+C in y² = 8x:
Expand the expression (2x+C)² using perfect square:
Simplify the equation:
The discriminant says:
- If b²-4ac > 0 then there are two real roots
- If b²-4ac = 0 then there is only one real root
- If b²-4ac < 0 then the are no real roots
For this, we choose b²-4ac = 0 since tangents only have one intersection.
Solve the equation for C:
Therefore, the value of C is 1
Answer:
x = -1
Step-by-step explanation:
3x - 10x + 5 = 5x + 17 (collect like terms)
-7x + 5 = 5x + 17 (subtract 5x on both sides)
-12x + 5 = 17 ( subtract 5 on each side)
-12x = 12 ( divide by -12 on each side)
x = -1
Answer:
6 1/18 table or technically 7 since 3 tables are for the girls and 3 for the boys then one extra table for the last boy.
Step-by-step explanation:
but if you had to choose one then it would be 7
Answer:
c a(n+10)
Step-by-step explanation:
[(-1)^(n+1)] × (5^n)
an > 0
a(n+5) = (-1)⁵ × 5^(n+5) < 0
a(n+10) = (-1)¹⁰ × 5^(n+10) > 0
a(n+15) = (-1)¹⁵ × 5^(n+15) < 0
Since a^n is positive, n is even
Odd powers of -1 are negative