Answer:Incorrect.
For example, two equations with same y intercept.
y = 2x + 3
y = 5x + 3
This system has only one solution.
Another example,
y = x + 7
y = x + 7
This system has infinitely many solutions.
So she is not correct because of the first example.
Step-by-step explanation:
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
Sample space= 1, 2, 3, 4, 5, 6
Outcomes= 2, 4, 6
Probability= Number of outcomes/ total number of outcomes
= 3/6 times 2( as 2 dices are rolled)
=6/12
=1/2
Therefore, the probability of getting 2 even number is 1/2
S1: 7x - 4x - 2 = 6 OK
S2: 3x - 2 = 6 OK
S3: 3x - 2 + 2 = 6 WRONG, correct is 3x - 2 + 2 = 6 + 2
Answer: c. Step 3, because a number has been added only to one side of the equation.
