Find any 5 rational numbers between; a) -1 and 2 b) −3 8 −5 14

Mathematics

1 answer:

kap26 [50]3 years ago

4 0

Answer:

Step-by-step explanation:

Hello,

You can list the following ones which are correct for a), b) and c)

$\boxed{\sf \bf \ \ 1, \dfrac{1}{2}, \dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5} \ \ }$

Thanks

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hree vertices of a rectangle are given. Find the coordinates of the fourth vertex. (–2, 4), (4, 0), (2, –3)

zhannawk [14.2K]

V1=(-2,4)=(x1,y1)→x1=-2, y1=4
V2=(4,0)=(x2,y2)→x2=4, y2=0
V3=(2,-3)=(x3,y3)→x3=2, y3=-3
V4=(x4,y4)→x4=?, y4=?

V1-V2
dx=x2-x1=4-(-2)=4+2→dx=6
dy=y2-y1=0-4→dy=-4

V4-V3
dx=x3-x4→6=2-x4
Solving for x4:
6=2-x4→6-2=2-x4-2→4=-x4→(-1)(4=-x4)→-4=x4→x4=-4

dy=y3-y4→-4=-3-y4
Solving for y4:
-4=-3-y4→-4+3=-3-y4+3→-1=-y4→(-1)(-1=-y4)→1=y4→y4=1

V4=(x4, y4)→V4=(-4, 1)

Answer: The coordinates of the fourth vertex are (-4,1)

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3 years ago

Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.

katrin [286]

You can find the remainder right away by simply plugging in $x=3$ . The polynomial remainder theorem guarantees that the value of $p(3)$ is the remainder upon dividing $p(x)$ by $x-3$ , but I digress...

Synthetic division yields

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.    |           6   -15     9
- - - - - - - - - - - - - - - - -
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which translates to

$\dfrac{2x^3-11x^2+18x-15}{x-3}=2x^2-5x+3-\dfrac6{x-3}$

(and note that $p(3)=2(3)^3-11(3)^2+18(3)-15=-6$ , as expected)

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