Solve by square roots

1/3x^2-10=-37

0

Step-by-step explanation:

1/3x^2-10=-37

We move all terms to the left:

1/3x^2-10-(-37)=0

Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R

We add all the numbers together, and all the variables

1/3x^2+27=0

We multiply all the terms by the denominator

27*3x^2+1=0

Wy multiply elements

81x^2+1=0

a = 81; b = 0; c = +1;

Δ = b2-4ac

Δ = 02-4·81·1

Δ = -324

Delta is less than zero, so there is no solution for the equation

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet