Perimeter = (20 + 2x) mm.
Step-by-step explanation:
The octopus pupil has length 20 mm and the expression for its area is given by (20x - 200) square mm.
If the width of the octopus pupil is w, then 20w = 20x - 200
⇒ w = (x - 10) mm.
Therefore, the expression for its perimeter is 2(Length + Width) = 2 ( 20 + x - 10) = 2( 10 + x) = (20 + 2x) mm. (Answer)
5/10 in 3 equivalent forms is: 1/2 2/4 4/8
Answer:
-24/13, yes
Step-by-step explanation:
<span>Slope-intercept form is Y = MX + B. This is in standard form, AX + BY = C. You have to move the X to the other side of the equation and simplify it. </span>
<span>10x - 2y = 10 </span>
<span>- 10x - 10x Subtract 10x from both sides </span>
<span>- 2y = - 10x + 10 Now everything is in the right place, but it still needs to be simplified. </span>
<span>Divide each term by -2, in order to isolate the variable Y. </span>
<span>- 2y/ - 2 = - 10x/ - 2 + 10/ - 2 </span>
<span>The answer is: y = 5x - 5</span>
Using polynomial long division, we get
3x^3+6x^2+11x
_____________
(x+2) | 3x^4-x^2+cx-2
-(3x^4+6x^3)
____________
6x^3-x^2+cx-2
- (6x^3+12x^2)
_____________
11x^2+cx-2
-(11x^2+22x)
__________
(22+c)x-2.
If you're wondering how I did the long division, what I essentially did was get the first value (at the start, it was 3x^4) and divided it by the first value of the divisor (which in x+2 was x) to get 3x^3 in our example. I then subtracted the polynomial by the whole divisor multiplied by, for example, 3x^3 and repeated the process.
For this to be a perfect factor, (x+2)*something must be equal to (22+c)x-2. Focusing on how to cancel out the 2, we have to add 2 to it. To add 2 to it, we have to multiply (x+2) by 1. However, there's a catch, which is that we subtract whatever we multiply (x+2) by, so we have to multiply it by -1 instead. We still need to cross out (22+c)x. Multiplying (x+2) by -1, we get
(-x-2) but by subtracting the whole thing from something means that we have to add -(-x-2)=x+2 to something to get 0. x+2-x-2=0, xo (22+c)x-2 must equal -x-2, meaning that (22+c)=-1 and c=-23
