Which integer is less than -3

Mathematics

2 answers:

LenKa [72]3 years ago

5 0

Integers less than -3 is -4 -5.... so on

slava [35]3 years ago

4 0

The integer less then -3 is -4 ,-5, ... and so on

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S t are positive integers

Sindrei [870]

Given:

The expanded form of $(x+s)(x-t)$ is $x^2+Kx-40$ .

Where, s, t, K are positive integers.

To find:

The smallest possible value of K.

Solution:

The expanded form of $(x+s)(x-t)$ is $x^2+Kx-40$ . It means,

$(x+s)(x-t)=x^2+Kx-40$

$x^2-tx+sx-st=x^2+Kx-40$

$x^2+(s-t)x-st=x^2+Kx-40$

On comping both sides, we get

$K=s-t$ ...(i)

K is a positive integer if s>t.

And

$st=40$

The factor pairs of 40 are (1,40), (2,20), (4,10), (5,8), (8,5), (10,4), (20,2) and (40,1).

Since s>t, therefore the possible values for (s,t) are (8,5), (10,4), (20,2) and (40,1).

Using (i), find the value of K for each factor pair.

$K=8-5=3$

$K=10-4=6$

$K=20-2=18$

$K=40-1=39$

Therefore, the smallest possible value of K is 3.

3 0

3 years ago

Write an equation of a line perpendicular to y = x + 4 in slope-intercept form that passes through the point (-2, 6)

Scrat [10]

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\ if\ m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\---------------------\\k:y=x+4;\ l:y=m_2x+b_2\\\\m_1=1\to m_2=-\dfrac{1}{1}=-1\\\\k\ \perp\ l\to l:y=-x+b_2\\\\The\ line\ "l"\ passes\ throught\ the\ point\ (-2;\ 6).\\Subtitute\ x=-2\ and\ y=6\ to\ the\ equation\ of\ the\ line\ "l":\\\\6=-(-2)+b_2\\6=2+b_2\ \ \ |subtract\ 2\ from\ both\ sides\\b_2=4\\\\Answer:\boxed{y=-x+4}$