Answer:
f(x)=-2x+9 g(x)=-4x^2+5x-3Now, f o g (x) = f{g(x)} = f(4x^2+5x-3) = 2(4x^2+5x-3) + 9 = 8x^2+10x-6 + 9
Step-by-step explanation:
(x+1)^2 +(y-1)^2 =9
x+ the x coordinate squared + y +the y coordinate squared = the radius squared
Step-by-step explanation:
35. 1000 m / 1 km = 10³
Move the decimal point 3 places to the right.
36. 100 cm / 1 m = 10²
Move the decimal point 2 places to the right.
37. 1 mm / 1000 μm = 10⁻³
Move the decimal point 3 places to the left.
38. 1 km / 1000 m × 1 m / 100 cm = 10⁻⁵
Move the decimal point 5 places to the left.
39. 1 Mm / 10⁶ m × 1 m / 10⁶ μm = 10⁻¹²
Move the decimal point 12 places to the left.
40. 100 cm / m × 1000 m / km = 10⁵
Move the decimal point 5 places to the right.
Answer:
b) the coefficient of x of jamie's polynomial is 5 .
c) The two polynomials are :
x³ + 4x² + 5x + 4
x³ - 2x² + 5x + 4
Step-by-step explanation:
consider these two Monic polynomials of degree 3:
P : x³ + ax² + bx² + c
Q : x³ + a₁x² + bx² + c
P × Q = x⁶+ (a+a₁)x⁵ + (aa₁+2b)x⁴ + (ab+a₁b+2c)x³ + (ac+a₁c+b²)x² +2bcx + c²
Now we compare the coefficients of P × Q and x⁶ + 2x⁵ +2x⁴ + 18x³ + 33x² + 40x + 16
b)
c² = 16 ⇒ c = 4 (c is positive)
2bc = 40 ⇒ 8b = 40 ⇒ b = 5 then the coefficient of x of jamie's polynomial is 5 .
c)
In order to find a and a₁ we need to solve this system:
a+a₁ = 2 a+a₁ = 2
⇔
aa₁+2b = 2 aa₁ = -8
Solve the system and you’ll get :
a = 4 and a₁ = -2 or a = -2 and a₁ = 4
Let’s choose a = 4 and a₁ = -2 then
the two polynomials are respectively:
P : x³ + ax² + bx² + c = x³ + 4x² + 5x + 4
Q : x³ + a₁x² + bx² + c = x³ - 2x² + 5x + 4
