Answer:
1, 2.2, 5.5, 10.2.
Step-by-step explanation: these are simplified to the nearest tenth
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)
21: The factors of 21 are 1,3,7,21
Jack's mom is purchasing thirteen tickets at a price of $11 each. This
equals a total of $143 in total spent. If Jack's mom has a credit card
limit of $500, then after purchasing $143 with the card, her available
amount to purchase additional things is $357. This impact on her
available credit is due to credit cards working on an available balance
system. When Jack's mom first received her credit card, a set balance or
total amount she could purchase with the card was set. In this example,
her total amount she could purchase with the card was $500. After her
purchase of the tickets for $143 was completed, she subtracted that
amount from her total available of $500 and that is why her available
amount to purchase is now $357.
