Answer:
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
=a(x+4)(x-4i)(x+4i)
=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]
=a(x+4)(x²-16i²)
=a(x+4)(x²+16) [∵i² = -1]
=a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)

=0.83
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Answer:
-40
Step-by-step explanation:
-4 * 2 = -8
-8*-1= 8
12+8 = 20
20*(-2) =-40
Answer:
x = 11
Step-by-step explanation:
A segment parallel to a side of a triangle cuts off proportional segments on the sides.
48/6 = (3x + 7)/5
8 = (3x + 7)/5
3x + 7 = 40
3x = 33
x = 11
6.5 goes in the first box and 5.5 goes in the second box.
Explanation for first box: 13+2 is 15 and half of 15 is 7.5 so you need to take 13 and subtract 7.5. Once you do that, you end up with 6.5
Explanation for second box: (The negative 7 doesn't matter because you want the absolute value) 18+7 is 25 and half of 25 is 12.5. 18-12.5 is 5.5 so the answer would be 5.5