2+4+5+6+8+2+5+6= 38/8 = 4.75
2+4+5+6+8+2+5+6+7 = 45/9 = 5
5 - 4.75= 0.25
C. The mean increased by 0.25
Answer:
m∠J = 45° , m∠I = 45° and m∠M = 90°
And the ΔJIM is an isosceles right angled triangle.
Step-by-step explanation:
(a). In ΔJIM,
∠J = 2x + 15,
∠I = 5x - 30, and
∠M = 6x
Now, using angle sum property of a triangle that sum of all the angles in a triangle is 180°
⇒ ∠J + ∠I + ∠M = 180°
⇒ 2x + 15 + 5x - 30 + 6x = 180°
⇒ 13x -15 = 180°
⇒ 13x = 195
⇒ x = 15
Therefore, m∠J = 45° , ∠I = 45° and m ∠M = 90°
(b). Now, ΔJIM is a right angled triangle right angled at M.
Also, ∠J = ∠I = 45°
So, JM = IM ( because in a triangle sides opposite to equal angles are equal)
So, ΔJIM is an isosceles triangle because its two sides are equal.
Hence, ΔJIM is a right angled isosceles triangle right angled at M.
Answer:
2 and 5
Step-by-step explanation:
1. No solutions
2. Many solutions
3. No solutions
4. One solution
5. Many solutions
You need 864.52 sq. in. of blue tile.
We need to find the area of the large circle (including blue and yellow) and the area of the yellow circle.
We have the circumference of the blue circle, 113.097.
C = πd
113.097 = 3.14d
Divide both sides by 3.14:
113.097/3.14 = 3.14d/3.14
36.018 = d
The diameter is twice as much as the radius, so r = 36.018/2 = 18.009.
The area of a circle is given by the formula
A = πr²
A = 3.14(18.009)² = 1018.38 sq. in.
The area of the small yellow circle is given by
A = 3.14(7²) = 3.14(49) = 153.86
Subtracting these two, we have
1018.38 - 153.86 = 864.52 sq. in.
