Answer:
The correct graph is Graph A).
<span>D. 20 + 2âš10 units
To solve this, you simply need to calculate the length of each side of the triangle with the vertexes of A(3,4), B(-5,-2), and C(5,-2). The length of each side is simply calculated using the pythagoras theorem. Note that it doesn't matter what order you do the subtraction. The absolute value will be the same and if it happens to be negative, not a problem since it will become positive once you square the values.
So the length of side AB is
sqrt((3-(-5))^2 + (4-(-2))^2) = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10.
The length of side BC is
sqrt((-5 - 5)^2 + (-2 - (-2))^2) = sqrt(-10^2 + 0^2) = sqrt(100+0) = sqrt(100) = 10.
And finally, the length of side AC is
sqrt((3-5)^2 + (4-(-2))^2) = sqrt(-2^2 + 6^2) = sqrt(4+36) = sqrt(40)
= 2 * sqrt(10)
Finally, add all the lengths together.
10 + 10 + 2âš10 = 20 + 2âš10</span>
Answer:
SAS Postulate.
Step-by-step explanation:
Two triangles are congruent if anyone of the following postulates is true:
SAS - Two corresponding sides and the included angles are congruent to each other.
SSS - All the three corresponding sides are congruent.
ASA - Two corresponding angles and the included sides are congruent to each other.
AAS - Two corresponding consecutive angles and sides adjacent to either of the angles are congruent.
HL - If the corresponding hypotenuses and one corresponding legs are congruent to each other.
Here, in the figure, two corresponding sides and the included angle between them are congruent to each other.
So, the two triangles are congruent by SAS postulate.
Answer:
x = - 2.5
Step-by-step explanation:
Given that the sketch represents
y = x² + bx + c
The graph crosses the y- axis at (0 , - 14), thus c = - 14
y = x² + bx - 14
Given the graph crosses the x- axis at (2, 0), then
0 = 2² + 2b - 14
0 = 4 + 2b - 14 = 2b - 10 ( add 10 to both sides )
10 = 2b ( divide both sides by 2 )
b = 5
y = x² + 5x - 14 ← represents the graph
let y = 0 , then
x² + 5x - 14 = 0 ← in standard form
(x + 7)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
The x- intercepts are x = - 7 and x = 2
The vertex lies on the axis of symmetry which is midway between the x- intercepts, thus
the x- coordinate of the turning point is
=
= - 2.5
Walter is right cause 30x5 equals 150