Given:
Area of the circle : 36 ft²
Area of the square : 3 6ft²
Circle:
A = π r²
36 ft² = 3.14 * r²
36 ft² / 3.14 = r²
11.46 = r²
√11.46 = r
3.39 = r diameter = 2 * r = 2 * 3.39 = 6.78 ft
Square:
A = a²
36 ft² = a²
√36 ft² = a
6 ft = a
6.78 ft - 6 ft = 0.78 ft ⇒ the table is sticking out from the glass
Diagonal of a square:
d = √ 6² + 6²
d = √ 36 + 36
d = √ 72
d = 8.49 ft
8.49 ft - 6.78 ft = 1.71 ft ⇒ the glass is sticking out from the table
To find value of y in times o x we have to transfrom this equation.
LEts do this
x-0.25y=1.5 /-x subtract x both sides
-0.25y=1.5-x /*4 multiply by 4 both sides
-0.25y*4=4(1.5-x)
-1y=6-4x /*-1 multiply both sides by -1
y=4x-6
Subtract 30, then factor the equation.
... x² = 30
... x² - 30 = 0
... (x -√30)(x +√30) = 0
By the zero product rule, the solutions are values of x that make a factor be zero.
... x - √30 = 0 . . . . the first factor is zero
... x = √30
... x + √30 = 0 . . . . the second factor is zero
... x = -√30
The solutions are . . .
... x = ±√30 . . . . . matches your 3rd choice
Check the picture below.
notice, the parent function is really f(x) = |x|, and the other are simply just vertical translations of it.
That’s the work if you want. X= -3
