Answer:
Below in bold.
Step-by-step explanation:
4x + y = 9
Let's put x = 0 then:
4(0) + y = 9
0 + y = 9
y = 9
So one. ordered pair that is a solution is (0, 9)
Answer:
1% of 4000 + 4% of B = 2% of (4000 + B)
40 + 0.04*B = 0.02( 4000 + B)
40 + 0.04* B = 80 + 0.02*B
40 + 0.04*B - 80 - 0.02B = 0
0.02*B - 40 = 0
0.02*B = 40
2B = 4000
B = 2000
Step-by-step explanation:
(X+3)(x)(x-4)
Hope that helps :)
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
