Answer:
the equation of the axis of symmetry is 
Step-by-step explanation:
Recall that the equation of the axis of symmetry for a parabola with vertical branches like this one, is an equation of a vertical line that passes through the very vertex of the parabola and divides it into its two symmetric branches. Such vertical line would have therefore an expression of the form: 
, being that constant the very x-coordinate of the vertex.
So we use for that the fact that the x position of the vertex of a parabola of the general form: 
, is given by:
which in our case becomes:
Then, the equation of the axis of symmetry for this parabola is:
Answer:
Step-by-step explanation:
27 ) 2x² - x - 1 = 0
2x² - 2x + x - 1 = 0
2x ( x - 1) + (x - 1) = 0
(x - 1)(2x + 1) = 0
x - 1 = 0 ; 2x + 1 = 0
x = 1 ; 2x = -1
x = -1/2
x = 1 ; -1/2
Option b
28) Area of a rectangle = 24 cm²
length * width = 24
(3x +2 )(2x -1) = 24
3x(2x -1) + 2(2x - 1) = 24
3x *2x - 3x *1 + 2*2x - 2*1 = 24
6x² -3x + 4x - 2= 24
6x² + x - 2 -24 = 0
6x² + x - 26 = 0
6x² -12x + 13x - 26 = 0
6x(x - 2) + 13(x - 2) = 0
(x -2)(6x +13) = 0
x = 2 {Ignore 6x + 13 as it gives negative value}
length = 3x + 2 = 3*2 + 2 = 6 + 2 = 8 cm
Width = 2x - 1 = 2*2 - 1 = 4 - 1 = 3 cm
29) Area of square = 900 cm²
Side² = 900
(5x)² = 900
25x² = 900
x² = 900/25
x² = 36
x = √36 = √6*6
x = 6 cm
30) base = b cm
height = b + 2
Area of triangle = 24 cm²
b(b + 2) = 24*2
b² + 2b = 48
b² + 2b - 48 = 0
b² - 6b + 8b - 48 = 0
b(b - 6) + 8(b - 6) = 0
(b - 6) (b + 8) = 0
b - 6 = 0 {Ignore b +8 = 0 as it gives negative value}
b = 6 cm
height = 6+ 2 = 8 cm
Step-by-step explanation:
As ANC are collinear,
AB+BC=AC
so,
18+BC = 41
BC = 41-18
BC = 23 is the answer.
Square and Rhombus are the following quadrilaterals have diagonals that are always perpendicular to each other.
C. Square
D. Rhombus
<u>Step-by-step explanation:</u>
This implies the diagonals of a square and rhombus are perpendicular. The diagonals of a square and rhombus are a similar length. In elementary geometry, the property of being opposite is the connection between two lines which meet at a right angle. The property stretches out to other related geometric items.
Principally Perpendicular lines will be lines that cross at a right (90 degrees) edge. so when it goes under shape rhombus and square have the equivalent of a considerable number of sides parallelly.
