Answer + Explanation + Theory
When a number is divided by a number it results in a quotient and a remainder
E.g. 9 / 4 = 2 remainder 1
9 is the dividend
4 is the divisor
2 is the quotient
1 is the remainder
Same way when a polynomial is divided by a linear expression
E.g.
Ax^2 + bx + c / (x-b) = (x+a) + r
Which can be rearranged to
ax^2 + bx + c = (x+a)(x-b) + r
When x = - a or b, only the remainder is left since either (x+a)(x-b) is 0.
If x = - a or b is substituted into the polynomial and the value is 0 then there is no remainder,
This would suggest (x+a) or (x-b) are factors of the polynomial.
Now apply this logic to these questions
1. Let’s assume (x-4) is a factor, this would mean that when x=4 is substituted into the polynomial the answer would be 0.
This is the case, therefore the remainder is 0.
2. Having seen the logic above (applied using the remainder and factor theorem) the linear expression is a factor of the polynomial.
First turn this into an equation
7x+8x+44.4=180
Now collect like terms
15x+44.4=180
Next take away 44.4 from 180
15x=135.6
Finally divide 135.6 by 15
x=9.04
To calculate the shaded angle substitute 9.04 for x
8x=8×9.04
8x=72.32
The shaded angle is 72.32°
Answer:
10.25
Step-by-step explanation:
13*13-8*8=105
=10.25
It would cost $770.56 per person. Hope this helps!
