Fide the area of 7.7m×2.m

Answer - D.

you basically find the equation of the line first and eliminate the wrong answers...

Strategy: before u do any of this, label your coordinates as (X1,Y1) and (X2,Y2) and u can choose any of ur points to be as x1 or x2 or y1 or y1...
basically, I'll choose (6,7) as (x1,y1) and (2,-1) as (x2,y2). SO,

First you have to find the gradient (m) of the line.
you do this by using the formula m = Y2-Y1 / X2-X1 (where '/' is division sign) ....
Put the numbers in their respective places and your gradient will be 2x. we put the x after our number to represent it as a gradient as the straight line formula is y = mx+c and you've found the m.
NOW.
use the formula Y-Y1=m(x-x1) to find the equation of the line.Again u can use any Y1 and X1 here but remember your m is 2

replace the digits and solve...Hopefully you'll get sth like this if you use the points (6,7):
Y-7 = 2(x-6) ....
y=2x-12+7...
Y=2x-5! <<<< this is your straight line equation!
Now all u gotta do is rearrange all your options into y = mx+c.
D. is incorrect as it gives us y=2x+5 and not y = 2x-5 unlike the others

Hope you get it!

7 0

3 years ago

The polynomial of degree 5, P ( x ) has leading coefficient a=1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of

ser-zykov [4K]

Answer:

$p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}$ , for $r_{1} = 0$

Step-by-step explanation:

The general form of quintic-order polynomial is:

$p_{5}(t) = a\cdot x^{5} + b\cdot x^{4} + c\cdot x^{3} + d\cdot x^{2} + e \cdot x + f$

According to the statement of the problem, the polynomial has the following roots:

$p_{5} (t) = (x - r_{1})\cdot (x-3)^{2}\cdot x^{2} \cdot (x+1)$

Then, some algebraic handling is done to expand the polynomial:

$p_{5} (t) = (x - r_{1}) \cdot (x^{3}-6\cdot x^{2}+9\cdot x) \cdot (x+1)\\p_{5} (t) = (x - r_{1}) \cdot (x^{4}-5\cdot x^{3} + 3 \cdot x^{2} + 9 \cdot x)$

$p_{5} (t) = x^{5} - (5+r_{1})\cdot x^{4} + (3 + 5\cdot r_{1})\cdot x^{3} +(9-3\cdot r_{1})\cdot x^{2} - 9 \cdot r_{1}\cdot x$

If $r_{1} = 0$ , then:

$p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}$

5 0

3 years ago

Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised $43.50 by selling 12 rolls of solid pa

enyata [817]

Answer:

Solid paper costs 1.75 each

Printed paper costs 2.50 each

Step-by-step explanation:

Given:

Ben = $43.50 (12 rolls solid paper and 9 rolls of printed paper)

Joel = $51.50 (8 rolls solid paper and 15 rolls of printed paper)

Let x = solid paper

Let y = printed paper

12x + 9y = 43.50

8x + 15y = 51.50

Find x:

8x + 15y = 51.50

8x = 51.50 - 15y

x = (51.50 - 15y)/8

Substitute x:

12x + 9y = 43.50

12(51.50 - 15y)/8 + 9y = 43.50

(618 - 180y)/8 + 9y = 43.50

8 (618 - 180y)/8 + 8*9y = 43.50 * 8

618 - 180y + 72y = 348

-108y = 348 - 618

-108y = -270

-108y/-108 = -270/-108

y = 2.50

x = (51.50 - 15y)/8

x = (51.50 - 15(2.5) /8

x = (51.50 - 37.50)/8

x = 14/8

x = 1.75

To check: x = 1.75 ; y = 2.5

12x + 9y = 43.50

12(1.75) + 9(2.5) = 43.50

21 + 22.50 = 43.50

43.50 = 43.50

8x + 15y = 51.50

8(1.75) + 15(2.5) = 51.50

14 + 37.50 = 51.50

51.50 = 51.50

6 0

3 years ago